| 1. |
- Amouzgar, Kaveh, 1980-, et al.
(författare)
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Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias
- 2017
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 55:4, s. 1453-1469
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Tidskriftsartikel (refereegranskat)abstract
- In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.
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| 2. |
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| 3. |
- Bendsoe, MP, et al.
(författare)
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Joakim Petersson 1968-2002 - Obituary
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:3
-
Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 4. |
- Bokhari, Ahmad Hasnain, 1986-, et al.
(författare)
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Topology optimization of an acoustic diode?
- 2021
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 63:6, s. 2739-2749
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Tidskriftsartikel (refereegranskat)abstract
- By using topology optimization, we consider the problem of designing a passive acoustic device that allows for one-way flow of sound waves; such a device is often colloquially referred to as an acoustic diode. The Helmholtz equation is used to model the time harmonic linear wave propagation together with a Dirichlet-to-Neumann (DtN) type boundary condition, and the finite element method is used for discretization. The objective of this study is to maximize the wave propagation in one direction (from left to right) and minimize the wave propagation in the reverse direction (from right to left) for planar incoming waves. The method of moving asymptotes (MMA) solves the optimization problem, and a continuation approach is used for the penalizing intermediate design variables. The results for the optimized waveguide show that more than 99.8% of the power of planar incoming waves get transmitted from left to right while less than 0.3% gets transmitted in the reverse direction for planar incoming waves in the specified frequency range. Since a true diode is a non-reciprocal device and here we used a linear acoustic wave model, which is basically reciprocal, we discuss details about how it appears to be possible to obtain a one-way waveguiding effect using this linear model.
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| 5. |
- Bokhari, Ahmad Hasnain, 1986-, et al.
(författare)
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Topology optimization of microwave frequency dividing multiplexers
- 2023
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 66:5
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Tidskriftsartikel (refereegranskat)abstract
- We use material-distribution-based topology optimization to design a three-port frequency dividing multiplexer at microwave frequencies. That is, by placing a good electric conductor inside the design domain, we aim to design a passive device that splits the incoming signal’s frequencies into two frequency bands and transmits them to their respective output ports. The Helmholtz equation models the time-harmonic wave propagation problem. We solve the governing equation using the finite element method. The adjoint variable method provides the required gradients, and we solve the topology optimization problem using Svanberg’s MMA algorithm. In this study, we present a technique for modeling the distribution of a good electric conductor within the design domain. In addition, we derive a power balance expression, which aids in formulating a series of three objective functions. In each successive objective function, we add more information and evaluate its impact on the results. The results show that by selecting a suitable objective function, we achieve more than 93.7% transmission for both the frequency bands. Moreover, the numerical experiments suggest that the optimization problem is self penalized and is sensitive to the initial design.
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| 6. |
- Cameron, Christopher, et al.
(författare)
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A method for optimization against cure-induced distortion in composite parts
- 2023
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media Deutschland GmbH. - 1615-147X .- 1615-1488. ; 66:3
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes a novel method developed for the optimization of composite components against distortion caused by cure-induced residual stresses. A novel ply stack alteration algorithm is described, which is coupled to a parametrized CAD/FE model used for optimization. Elastic strain energy in 1D spring elements, used to constrain the structure during analysis, serves as an objective function incorporating aspects of global/local part stiffness in predicted distortion. Design variables such as the number and stacking sequence of plies, and geometric parameters of the part are used. The optimization problem is solved using commercial software combined with Python scripts. The method is exemplified with a case study of a stiffened panel subjected to buckling loads. Results are presented, and the effectiveness of the method to reduce the effects of cure-induced distortion is discussed. © 2023, The Author(s).
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| 7. |
- Carlsson, Peter, et al.
(författare)
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A distributed computing system used for concurrent optimization methods on a violin top
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:5/6, s. 453-458
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Tidskriftsartikel (refereegranskat)abstract
- Concurrent optimization is performed with two optimization methods on a violin top. The optimization methods used are SA (Simulated Annealing) and MMA (Method of Moving Asymptotes). All calculations in this study are made in a distributed environment for arbitrary processing. The distributed environment is constructed using extended File Servers running on remote computers and clients on a local computer, which can transfer, start, terminate, and finally remove arbitrary Java RMI Servers from the remote computers. The required processing is performed with the RMI Servers.
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| 8. |
- Chalouhi, Elisa Khouri, et al.
(författare)
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Environmental and economical optimization of reinforced concrete overhang bridge slabs
- 2023
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Nature. - 1615-147X .- 1615-1488. ; 66:3
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Tidskriftsartikel (refereegranskat)abstract
- The dimensioning of overhang slabs in bridge decks is usually based on simplified, thus conservative methods. The resulting over-dimensioned overhang bridge slabs can also affect the design of the girders. In this paper, an optimization procedure for the design of this structural element is presented. The aim is to minimize investment cost and global warming potential in the material production stage simultaneously while fulfilling all safety requirements. The design variables used in this study are the thicknesses of the overhang slab and the height of the edge beam. However, a complete detailed design of reinforcement is performed as well. Both a single-objective and a multi-objective formulation of the nonlinear problem are presented and handled with two well-known optimization algorithms: pattern search and genetic algorithm. The procedure is applied to a case study, which is a bridge in Sweden designed in 2013. One single solution minimizing both objective functions is found and leads to savings in investment cost and CO2-equivalent emissions of 4.2% and 9.3%, respectively. The optimization procedure is then applied to slab free lengths between 1 and 3 m. The outcome is a graph showing the optimal slab thicknesses for each slab length to be used by designers in the early design stage.
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| 9. |
- Correa, Maicon Ribeiro, et al.
(författare)
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A transient thermoelastic mathematical model for topology optimization of support structures in additive manufacturing
- 2024
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Ingår i: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 67:3
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Tidskriftsartikel (refereegranskat)abstract
- This study presents a Topology Optimization (TO) methodology for determining the optimal distribution of support structures in the powder bed fusion Additive Manufacturing (AM) fabrication technology. The support structures enhance thermal dissipation, reducing distortion on overhang surfaces during the build process and improving printability. A novel transient thermoelastic layer-by-layer model simulates the AM process, evaluating temperature and displacement in partially built structures with supports. We propose two new objective functions related to part distortion, perform their adjoint sensitivity analysis, and present a comprehensive set of numerical experiments with different geometries and levels of overhang complexity. The numerical results show non-standard optimal support structures obtained using the proposed TO-AM methodology for different model parameters, including support volume, thermal anisotropy, time discretization method, and building times for each layer.
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| 10. |
- Dai, Xiaoxia, et al.
(författare)
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Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method
- 2018
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 57:6, s. 2193-2203
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a piecewise constant level set method for the topology optimization of steady Navier- Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.
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| 11. |
- Dalklint, Anna, et al.
(författare)
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Eigenfrequency constrained topology optimization of finite strain hyperelastic structures
- 2020
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 61:6, s. 2577-2594
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Tidskriftsartikel (refereegranskat)abstract
- This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.
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| 12. |
- Dalklint, Anna, et al.
(författare)
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Structural stability and artificial buckling modes in topology optimization
- 2021
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 64:4, s. 1751-1763
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Tidskriftsartikel (refereegranskat)abstract
- This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.
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| 13. |
- Dasari, Siva Krishna, 1988-, et al.
(författare)
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Predictive Modelling to Support Sensitivity Analysis for Robust Design in Aerospace Engineering
- 2020
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 61:5, s. 2177-2192
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Tidskriftsartikel (refereegranskat)abstract
- The design of aircraft engines involves computationally expensive engineering simulations. One way to solve this problem is the use of response surface models to approximate the high-fidelity time-consuming simulations while reducing computational time. For a robust design, sensitivity analysis based on these models allows for the efficient study of uncertain variables’ effect on system performance. The aim of this study is to support sensitivity analysis for a robust design in aerospace engineering. For this, an approach is presented in which random forests (RF) and multivariate adaptive regression splines (MARS) are explored to handle linear and non-linear response types for response surface modelling. Quantitative experiments are conducted to evaluate the predictive performance of these methods with Turbine Rear Structure (a component of aircraft) case study datasets for response surface modelling. Furthermore, to test these models’ applicability to perform sensitivity analysis, experiments are conducted using mathematical test problems (linear and non-linear functions) and their results are presented. From the experimental investigations, it appears that RF fits better on non-linear functions compared with MARS, whereas MARS fits well on linear functions.
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| 14. |
- Dersjö, Tomas, et al.
(författare)
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Efficient design of experiments for structural optimization using significance screening
- 2012
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 45:2, s. 185-196
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Tidskriftsartikel (refereegranskat)abstract
- When performing structural optimization of large scale engineering problems, the choice of experiment design is important. However, classical experiment designs are developed to deal with undesired but inevitable scatter and are thus not ideal for sampling of deterministic computational responses. In this paper, a novel screening and design of computer experiments algorithm is presented. It is based on the concept of orthogonal design variable significances and is applicable for problems where design variables do not simultaneously have a significant influence on any of the constraints. The algorithm presented uses significance orthogonality to combine several one-factor-at-a-time experiments in one several-factors-at-a-time experiment. The procedure results in a reduced experiment design matrix. In the reduced experiment design, each variable is varied exactly once but several variables may be varied simultaneously, if their significances with respect to the constraints are orthogonal. Moreover, a measure of influence, as well as an influence significance threshold, is defined. In applications, the value of the threshold is left up to the engineer. To assist in this choice, a relation between model simplification, expressed in terms of the significance threshold, and computational cost is established in a screening. The relation between efficiency and loss of accuracy for the proposed approach is discussed and demonstrated. For two solid mechanics type problems studied herein, the necessary number of simulations could be reduced by 25% and 64%, respectively, with negligible losses in accuracy.
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| 15. |
- Etman, L.F.P., et al.
(författare)
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Coordination specification in distributed optimal design of multilevel systems using the χ language
- 2005
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 29:3, s. 198-212
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Tidskriftsartikel (refereegranskat)abstract
- Coordination plays a key role in solving decomposed optimal design problems. Several coordination strategies have been proposed in the multidisciplinary optimization (MDO) literature. They are usually presented as a sequence of statements. However, a precise description of the concurrency in the coordination is needed for large multilevel or non-hierarchic coordination architectures. This article proposes the use of communicating sequential processes (CSP) concepts from concurrency theory for specifying and implementing coordination strategies in distributed multilevel optimization rigorously. CSP enables the description of the coordination as a number of parallel processes that operate independently and communicate synchronously. For this purpose, we introduce elements of the language χ, a CSP-based language that contains advanced data modeling constructs. The associated software toolkit allows execution of the specified coordination. Coordination specification using χ is demonstrated for analytical target cascading (ATC), a methodology for design optimization of hierarchically decomposed multilevel systems. It is shown that the ATC coordination can be compactly specified for various coordination schemes. This illustrates the advantage of using a high-level concurrent language, such as χ, for specifying the coordination of distributed optimal design problems. Moreover, the χ software toolkit is useful in implementing alternative schemes rapidly, thus enabling the comparison of different MDO methods.
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| 16. |
- Evgrafov, Anton, 1978
(författare)
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On globally stable singular truss topologies
- 2005
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 29:3, s. 170-177
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Tidskriftsartikel (refereegranskat)abstract
- We consider truss topology optimization problems including a global stability constraint, which guarantees a sufficient elastic stability of the optimal structures. The resulting problem is a nonconvex semi-definite program, for which nonconvex interior point methods are known to show the best performance. We demonstrate that in the framework of topology optimization, the global stability constraint may behave similarly to stress constraints, that is, that some globally optimal solutions are singular and cannot be approximated from the interior of the design domain. This behaviour, which may be called a global stability singularity phenomenon, prevents convergence of interior point methods towards globally optimal solutions. We propose a simple perturbation strategy, which restores the regularity of the design domain. Further, to each perturbed problem interior point methods can be applied.
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| 17. |
- Fan, Zhirui, et al.
(författare)
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Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method
- 2020
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 61:3, s. 983-998
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Tidskriftsartikel (refereegranskat)abstract
- Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the microstructure of the lattice material. To enable gradient optimization, sensitivities were outlined in detail. A density filter with a volume-preserving Heaviside projection was used to eliminate the risk of a checkerboard pattern and reduce the number of gray elements. A polynomial penalization scheme was employed to eliminate localized spurious eigenmodes in the low-density region. Finally, several numerical examples were performed to validate the proposed method. These numerical examples resulted in novel microstructural configurations with remarkably improved vibration resistance.
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| 18. |
- Fan, Zhirui, et al.
(författare)
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Nonlinear stiffness optimization with prescribed deformed geometry and loads
- 2022
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 65:2
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Tidskriftsartikel (refereegranskat)abstract
- Optimization based on traditional forward motion analysis to ensure a prescribed load distribution on a deformed geometry is challenging, since the load distribution is highly coupled to the deformed geometry, boundary conditions, and the optimized material layout. In contrast to traditional forward motion analysis, the deformed configuration is prescribed in the inverse motion analysis, and the undeformed configuration is the outcome of the analysis. Consequently, the inverse motion analysis is able to define an exact deformed geometry. In the present study, we make use of this key advantage to design structures with both an exact deformed geometry and a prescribed load distribution. The objective in the optimization is to minimize a general function of the nodal displacement vector. To formulate a well-posed optimization problem, the design is regularized using the partial differential equation filter and the sensitivity analysis is based on the adjoint method. The computational model is developed for neo-Hookean hyper-elasticity and the balance equations are discretized using the finite element method. The resulting nonlinear equations are solved using a conventional Newton–Raphson scheme. In the numerical examples, a cantilever beam with an embedded perfect circular shape is first considered. Next, a 2D gasket-like structure is designed, and finally, we consider a 3D structure with contact-like boundary conditions. In these examples, the prescribed deformed geometry is subject to a distributed external force. The examples show that the deformed geometry and load distribution can be exactly prescribed through stiffness optimization based on the inverse motion analysis.
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| 19. |
- Fellini, R., et al.
(författare)
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A sensitivity-based commonality strategy for family products of mild variation, with application to automotive body structures
- 2004
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 27:1-2, s. 89-96
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Tidskriftsartikel (refereegranskat)abstract
- Identification of the product platform is a key step in designing a family of products. This article presents a methodology for selecting the product platform by using information obtained from the individual optimization of the product variants. Under the assumption that the product variety requires only mild design changes, a performance deviation vector is derived by taking into consideration individual optimal designs and sensitivities of functional requirements. Commonality decisions are based on values of the performance deviation vector, and the product family is designed optimally with respect to the chosen platform. The proposed methodology is applied to the design of a family of automotive body structures. Variants are defined by changing the functional requirements they need to satisfy and/or the geometry of the associated finite element models.
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| 20. |
- Forsberg, Jimmy, et al.
(författare)
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On polynomial response surfaces and Kriging for use in structural optimization of crashworthiness
- 2005
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 29:3, s. 232-243
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Tidskriftsartikel (refereegranskat)abstract
- The accuracy of different approximating response surfaces is investigated. In the classical response surface methodology (CRSM) the true response function is usually replaced with a low-order polynomial. In Kriging the true response function is replaced with a low-order polynomial and an error correcting function. In this paper the error part of the approximating response surface is obtained from “simple point Kriging” theory. The combined polynomial and error correcting function will be addressed as a Kriging surface approximation.To be able to use Kriging the spatial correlation or covariance must be known. In this paper the error is assumed to have a normal distribution and the covariance to depend only on one parameter. The maximum-likelihood method is used to find the latter parameter. A weighted least-square procedure is used to determine the trend before simple point Kriging is used for the error function. In CRSM the surface approximation is determined through an ordinary least-square fit. In both cases the D-optimality criterion has been used to distribute the design points.From this investigation we have found that a low-ordered polynomial assumption should be made with the Kriging approach. We have also concluded that Kriging better than CRSM resolves abrupt changes in the response, e.g. due to buckling, contact or plastic deformation.
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| 21. |
- Forsberg, Jimmy, et al.
(författare)
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Topology optimization in crashworthiness design
- 2007
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 33:1, s. 1-12
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Tidskriftsartikel (refereegranskat)abstract
- Topology optimization has developed rapidly, primarily with application on linear elastic structures subjected to static loadcases. In its basic form, an approximated optimization problem is formulated using analytical or semi-analytical methods to perform the sensitivity analysis. When an explicit finite element method is used to solve contact–impact problems, the sensitivities cannot easily be found. Hence, the engineer is forced to use numerical derivatives or other approaches. Since each finite element simulation of an impact problem may take days of computing time, the sensitivity-based methods are not a useful approach. Therefore, two alternative formulations for topology optimization are investigated in this work. The fundamental approach is to remove elements or, alternatively, change the element thicknesses based on the internal energy density distribution in the model. There is no automatic shift between the two methods within the existing algorithm. Within this formulation, it is possible to treat nonlinear effects, e.g., contact–impact and plasticity. Since no sensitivities are used, the updated design might be a step in the wrong direction for some finite elements. The load paths within the model will change if elements are removed or the element thicknesses are altered. Therefore, care should be taken with this procedure so that small steps are used, i.e., the change of the model should not be too large between two successive iterations and, therefore, the design parameters should not be altered too much. It is shown in this paper that the proposed method for topology optimization of a nonlinear problem gives similar result as a standard topology optimization procedures for the linear elastic case. Furthermore, the proposed procedures allow for topology optimization of nonlinear problems. The major restriction of the method is that responses in the optimization formulation must be coupled to the thickness updating procedure, e.g., constraint on a nodal displacement, acceleration level that is allowed.
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| 22. |
- Fredricson, Harald
(författare)
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Topology optimization of frame structures : joint penalty and material selection
- 2005
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 30:3, s. 193-200
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design.
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| 23. |
- Fredricson, Harald, et al.
(författare)
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Topology optimization of frame structures with flexible joints
- 2003
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:3, s. 199-214
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Tidskriftsartikel (refereegranskat)abstract
- A method for structural topology optimization of frame structures with flexible joints is presented. A typical frame structure is a set of beams and joints assembled to carry an applied load. The problem considered in this paper is to find the stiffest frame for a given mass. By introducing design variables for beams and joints, a mass distribution for optimal structural stiffness can be found. Each beam can have several design variables connected to its cross section. One of these is an area-type design variable which is used to represent the global size of the beam. The other design variables are of length ratio type, controlling the cross section of the beam. Joints are flexible elements connecting the beams in the structure. Each joint has stiffness properties and a mass. A framework for modelling these stiffnesses is presented and design variables for joints are introduced. We prove a theorem which can be interpreted as the fact that the removal of structural elements, e.g. joints or beams, can be modelled by a small strictly positive material amount assigned to the element. This is needed for the computations of sensitivities used in the applied gradient based iterative method. Both two and three dimensional problems, as well as multiple load cases and multiple mass constraints, are treated.
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| 24. |
- Glorieux, Emile, 1989-, et al.
(författare)
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End-effector design optimisation and multi-robot motion planning for handling compliant parts
- 2018
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 57:3, s. 1377-1390
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Tidskriftsartikel (refereegranskat)abstract
- The deformation of compliant parts during material handling is a critical issue that can significantly affect the productivity and the parts' dimensional quality. There are multiple relevant aspects to consider when designing end-effectors to handle compliant parts, e.g. motion planning, holding force, part deformations, collisions, etc. This paper focuses on multi-robot material handling systems where the end-effector designs influence the coordination of the robots to prevent that these collide in the shared workspace. A multi-disciplinary methodology for end-effector design optimisation and multi-robot motion planning for material handling of compliant parts is proposed. The novelty is the co-adaptive optimisation of the end-effectors' structure with the robot motion planning to obtain the highest productivity and to avoid excessive part deformations. Based on FEA, the dynamic deformations of the parts are modelled in order to consider these during the collision avoidance between the handled parts and obstacles. The proposed methodology is evaluated for a case study that considers the multi-robot material handling of sheet metal parts in a multi-stage tandem press line. The results show that a substantial improvement in productivity can be achieved (up to 1.9%). These also demonstrate the need and contribution of the proposed methodology.
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| 25. |
- Gustafsson, Erik, et al.
(författare)
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Shape Optimization of Castings by using Successive Response Surface Methodology
- 2008
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 35:1, s. 11-28
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, an optimization routine for a thermomechanical problem is presented. The optimization routine is based on the successive response surface methodology where the panning and zooming technique presented by Stander and Craig has been implemented and improved. The optimization routine has been applied to an optimization problem of a three-dimensional beam that undergoes a solidification process. The material in the beam is assumed to be low-alloyed gray iron. The thermomechanical solidification analysis is uncoupled where, first, a thermal analysis is performed to determine the thermal history. This thermal history is then used to calculate the residual stresses in the beam. The residual stresses are solved by using classical J 2-plasticity with temperature-dependent material properties. The residual stresses from solidification are then carried on to the structural analysis where a mechanical load is applied. These are all linked together via scripts, and the commercial FE software Abaqus is used as the FE solver. The obtained maximum von Mises stress and mass information for every set of parameters are then exported to Matlab where general quadratic response surfaces are fitted by a least square method. Taken together, these response surfaces define a minimum of weight problem, which is solved by using sequential linear programming. To minimize the number of evaluations needed, the parameters are chosen to be D-optimally selected. The numerical results show that the residual stresses from solidification might influence the optimal shape significantly. The residual stress results have been compared with those obtained from casting simulation softwares, and the results are similar. The optimization has been compared with a commercial optimization software and shows very promising results.
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| 26. |
- Hassan, Emadeldeen, et al.
(författare)
-
Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size control
- 2018
-
Ingår i: Structural and multidisciplinary optimization (Print). - New York : Springer. - 1615-147X .- 1615-1488. ; 57:4, s. 1765-1777
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a density-based topology optimization approach to design compact wideband coaxial-to-waveguide transitions. The underlying optimization problem shows a strong self penalization towards binary solutions, which entails mesh-dependent designs that generally exhibit poor performance. To address the self penalization issue, we develop a filtering approach that consists of two phases. The first phase aims to relax the self penalization by using a sequence of linear filters. The second phase relies on nonlinear filters and aims to obtain binary solutions and to impose minimum-size control on the final design. We present results for optimizing compact transitions between a 50-Ohm coaxial cable and a standard WR90 waveguide operating in the X-band (8-12 GHz).
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| 27. |
- Hederberg, Hampus, et al.
(författare)
-
Topology optimization for fail-safe designs using moving morphable components as a representation of damage
- 2021
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 64, s. 2307-2321
-
Tidskriftsartikel (refereegranskat)abstract
- Designs obtained with topology optimization (TO) are usually not safe against damage. In this paper, density-based TO is combined with a moving morphable component (MMC) representation of structural damage in an optimization problem for fail-safe designs. Damage is inflicted on the structure by an MMC which removes material, and the goal of the design problem is to minimize the compliance for the worst possible damage. The worst damage is sought by optimizing the position of the MMC to maximize the compliance for a given design. This non-convex problem is treated using a gradient-based solver by initializing the MMC at multiple locations and taking the maximum of the compliances obtained. The use of MMCs to model damage gives a finite element-mesh-independent method, and by allowing the components to move rather than remain at fixed locations, more robust structures are obtained. Numerical examples show that the proposed method can produce fail-safe designs with reasonable computational cost.
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| 28. |
- Hilding, D
(författare)
-
A heuristic smoothing procedure for avoiding local optima in optimization of structures subject to unilateral constraints
- 2000
-
Ingår i: Structural and multidisciplinary optimization (Print). - 1615-147X .- 1615-1488. ; 20:1, s. 29-36
-
Tidskriftsartikel (refereegranskat)abstract
- Structural optimization problems are often solved by gradient-based optimization algorithms, e.g. sequential quadratic programming or the method of moving asymptotes. If the structure is subject to unilateral constraints, then the gradient may be nonexistent for some designs. It follows that difficulties may arise when such structures are to be optimized using gradient-based optimization algorithms. Unilateral constraints arise, for instance, if the structure may come in frictionless contact with an obstacle. This paper presents a heuristic smoothing procedure (HSP) that lessens the risk that gradient-based optimization algorithms get stuck in (nonglobal) local optima of structural optimization problems including unilateral constraints. In the HSP, a sequence of optimization problems must be salved. All these optimization problems have well-defined gradients and are therefore well-suited for gradient-based optimization algorithms. It is proves that the solutions of this sequence of optimization problems converge to the solution of the original structural optimization problem. The HSP is illustrated in a few numerical examples. The computational results show that the HSP can be an effective method for avoiding local optima.
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| 29. |
- Hofwing, Magnus, 1982-, et al.
(författare)
-
D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 42:1, s. 73-88
-
Tidskriftsartikel (refereegranskat)abstract
- In this work a hybrid method of a genetic algorithm and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.
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| 30. |
- Holmberg, Erik, et al.
(författare)
-
Fatigue constrained topology optimization
- 2014
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer-Verlag New York. - 1615-147X .- 1615-1488. ; 50:2, s. 207-219
-
Tidskriftsartikel (refereegranskat)abstract
- We present a contribution to a relatively unexplored application of topology optimization: structural topology optimization with fatigue constraints. A probability based high-cycle fatigue analysis is combined with principal stress calculations in order to find the topology with minimal mass that can withstand prescribed loading conditions for a specific life time. This allows us to generate optimal conceptual designs of structural components where fatigue life is the dimensioning factor.We describe the fatigue analysis and present ideas that makes it possible to separate the fatigue analysis from the topology optimization. The number of constraints is kept low as they are applied to stress clusters, which are created such that they give adequate representations of the local stresses. Optimized designs constrained by fatigue and static stresses are shown and a comparison is also made between stress constraints based on the von Mises criterion and the highest tensile principal stresses.
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| 31. |
- Holmberg, Erik, et al.
(författare)
-
Game theory approach to robust topology optimization with uncertain loading
- 2017
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 55:4, s. 1383-1397
-
Tidskriftsartikel (refereegranskat)abstract
- The paper concerns robustness with respect to uncertain loading in topology optimization problems with essentially arbitrary objective functions and constraints. Using a game theoretic framework we formulate problems, or games, defining Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.
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| 32. |
- Holmberg, Erik, et al.
(författare)
-
Stress constrained topology optimization
- 2013
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 48:1, s. 33-47
-
Tidskriftsartikel (refereegranskat)abstract
- This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.
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| 33. |
- Holmberg, Erik, et al.
(författare)
-
Worst-case topology optimization of self-weight loaded structures using semi-definite programming
- 2015
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 52:5, s. 915-928
-
Tidskriftsartikel (refereegranskat)abstract
- The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented.
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| 34. |
- Holmström, Andreas, 1978, et al.
(författare)
-
Optimization strategy in the development process with application to cast components
- 2008
-
Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-1488 .- 1615-147X. ; 35:1, s. 69-77
-
Tidskriftsartikel (refereegranskat)abstract
- At the development of commercial vehicles, it is necessary to develop cost-optimized components with respect to their entire lifetime. This requires a product development process that utilizes the possibility to simulate the product performance using modeling of different degrees of sophistication at any predefined level-of-detail (LOD). For example, the mechanical properties of a cast component depend strongly on the casting process, the simulation of which requires complex modeling at a high LOD. In this article, we propose an optimization strategy that is based on the LOD concept to develop cost-effective components. A sizing optimization of a cast model component is carried out with respect to both the mechanical and thermal response to exemplify the process. In particular, a (novel) global measure of the temperature in energy norm is introduced as an indicator of the "production fitness" to ensure high quality of the material properties. This measure is the thermal counterpart of the well-accepted mechanical strain energy. © 2007 Springer-Verlag Berlin Heidelberg.
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| 35. |
- Hu, Zhangli, et al.
(författare)
-
Second-order reliability methods : a review and comparative study
- 2021
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Nature. - 1615-147X .- 1615-1488. ; 64:6, s. 3233-3263
-
Forskningsöversikt (refereegranskat)abstract
- Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.
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| 36. |
- Hägg, Linus, 1988-, et al.
(författare)
-
Nonlinear filters in topology optimization : existence of solutions and efficient implementation for minimum compliance problems
- 2017
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 55:3, s. 1017-1028
-
Tidskriftsartikel (refereegranskat)abstract
- Material distribution topology optimization problems are generally ill-posed if no restriction or regularization method is used. To deal with these issues, filtering procedures are routinely applied. In a recent paper, we presented a framework that encompasses the vast majority of currently available density filters. In this paper, we show that these nonlinear filters ensure existence of solutions to a continuous version of the minimum compliance problem. In addition, we provide a detailed description on how to efficiently compute sensitivities for the case when multiple of these nonlinear filters are applied in sequence. Finally, we present large-scale numerical experiments illustrating some characteristics of these cascaded nonlinear filters.
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| 37. |
- Hägg, Linus, 1988-, et al.
(författare)
-
On minimum length scale control in density based topology optimization
- 2018
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 58:3, s. 1015-1032
-
Tidskriftsartikel (refereegranskat)abstract
- The archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.
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| 38. |
- Ivarsson, Niklas, et al.
(författare)
-
Topology optimization for designing periodic microstructures based on finite strain viscoplasticity
- 2020
-
Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 61:6, s. 2501-2521
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.
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| 39. |
- Jansson, Tomas, et al.
(författare)
-
Minimizing the risk of failure in a sheet metal forming process : optimization using space mapping with one-step and incremental solvers
- 2006
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 31:4, s. 320-332
-
Tidskriftsartikel (refereegranskat)abstract
- In the present paper, an optimization technique has been used to minimize the risk of failure in a sheet metal forming process. Two different types of finite element solvers, one using total plasticity and the other using incremental plasticity, have been used. A comparison between response surface methodology and space mapping (SM) with the one-step solver as surrogate model has been done. The conclusion of this study is that the use of the total plasticity theory drastically reduces the required computing time. Furthermore, the solution from the SM optimization algorithm is close to the solution obtained by the incremental plasticity solver.
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| 40. |
- Jansson, Tomas, et al.
(författare)
-
Using surrogate models and response surfaces in structural optimization : with application to crashworthiness design and sheet metal forming
- 2003
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:2, s. 129-140
-
Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.
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| 41. |
- Kasolis, Fotios, et al.
(författare)
-
Fixed-mesh curvature-parameterized shape optimization of an acoustic horn
- 2012
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 46:5, s. 727-738
-
Tidskriftsartikel (refereegranskat)abstract
- We suggest a boundary shape optimization approach in which the optimization is carried out on the coefficients in a boundary parameterization based on a local, discrete curvature. A fixed mesh is used to numerically solve the governing equations, in which the geometry is represented through inhomogeneous coefficients, similarly as done in the material distribution approach to topology optimization. The method is applied to the optimization of an acoustic horn in two space dimensions. Numerical experiments show that this method can calculate the horn's transmission properties as accurately as a traditional, body-fitted approach. Moreover, the use of a fixed mesh allows the optimization to create shapes that would be difficult to handle with a traditional approach that uses deformations of a body-fitted mesh. The parameterization inherently promotes smooth designs without unduly restriction of the design flexibility. The optimized, smooth horns consistently show favorable transmission properties.
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| 42. |
- Kaufmann, Markus, 1980-, et al.
(författare)
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Integrated cost/weight optimization of aircraft structures
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - Berlin Heidelberg : Springer. - 1615-147X .- 1615-1488. ; 41:2, s. 325-334
-
Tidskriftsartikel (refereegranskat)abstract
- A methodology for a combined cost/weight optimization of aircraft components is proposed. The objective function is formed by a simplified form of direct operating cost, i.e. by a weighted sum of the manufacturing costs and the component weight. Hence, the structural engineer can perform the evaluation of a design solution based on economical values rather than pure cost or weight targets.The parameter that governs the balance between manufacturing cost and weight is called weight penalty and incorporates the effect of fuel burn, environmental impact or contractual penalties due to overweight. Unlike previous work, the analytical cost model and structural models are replaced by commercially available software packages that allow a more realistic model of the manufacturing costs; further, arbitrary constraints for the structural analysis can be implemented. By means of parametric studies it is shown that the design solution strongly depends on the magnitude of the weight penalty.
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| 43. |
- Klarbring, Anders, 1957-, et al.
(författare)
-
A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements
- 2012
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 45:1, s. 147-149
-
Tidskriftsartikel (refereegranskat)abstract
- The present theoretical note shows how a naturalobjective function in stiffness optimization, including bothprescribed forces and non-zero prescribed displacements,is the equilibrium potential energy. It also shows how theresulting problem has a saddle point character that may beutilized when calculating sensitivities.
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| 44. |
- Klarbring, Anders
(författare)
-
Design optimization based on state problem functionals
- 2015
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Verlag (Germany). - 1615-147X .- 1615-1488. ; 52:2, s. 417-425
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a general mathematical structure for design optimization problems, where state problem functionals are used as design objectives.It extends to design optimization the general model of physical theories pioneered by Tonti (1972, 1976) and Oden and Reddy (1974, 1983). It turns out that the classical structural optimization problem of compliance minimization is a member of the treated general class of problems. Other particular examples, discussed in the paper, are related to Darcy-Stokes flow and pipe flow models. A main novel feature of the paper is the unification of seemingly different design problems, but the general mathematical structure also explains some previously not fully understood phenomena. For instance, the self-penalization property of Stokes flow design optimization receives an explanation in terms of minimization of a concave function over a convex set.
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| 45. |
- Klarbring, Anders, et al.
(författare)
-
Dynamical systems and topology optimization
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science Business Media. - 1615-147X .- 1615-1488. ; 42:2, s. 179-192
-
Tidskriftsartikel (refereegranskat)abstract
- This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.
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| 46. |
- Klarbring, Anders, et al.
(författare)
-
Dynamical systems, SIMP, bone remodeling and time dependent loads
- 2012
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Verlag (Germany). - 1615-147X .- 1615-1488. ; 45:3, s. 359-366
-
Tidskriftsartikel (refereegranskat)abstract
- The dynamical systems approach to sizing and SIMP topology optimization, introduced in a previous paper, is extended to the case of time-varying loads. A general dynamical system, satisfying a Lyaponov-type descent condition, is derived and specialized to a goal function combining stiffness and mass. For a cyclic time-dependent load it is indicated how, in the limit of short cycles compared to the overall time scale, this can be handled by multiple load cases. Numerical examples, both for a convex and a non-convex case, illustrates the theory.
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| 47. |
- Klarbring, Anders, et al.
(författare)
-
Minimizing crack energy release rate by topology optimization
- 2018
-
Ingår i: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 58:4, s. 1695-1703
-
Tidskriftsartikel (refereegranskat)abstract
- Fatigue cracked primary aircraft structural parts that cannot be replaced need to be repaired by other means. A structurally efficient repair method is to use adhesively bonded patches as reinforcements. This paper considers optimal design of such patches by minimizing the crack extension energy release rate. A new topology optimization method using this objective is developed as an extension of the standard SIMP compliance optimization method. The method is applied to a cracked test specimen that resembles what could be found in a real fuselage and the results show that an optimized adhesively bonded repair patch effectively reduces the crack energy release rate.
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| 48. |
- Klarbring, Anders, et al.
(författare)
-
Optimal design of fibre reinforced membrane structures
- 2017
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 56:4, s. 781-789
-
Tidskriftsartikel (refereegranskat)abstract
- A design problem of finding an optimally stiff membrane structure by selecting one–dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic orthotropic model by appropriate assumptions. The design problem is given in the form of two minimization statements. After finite element discretization, the separate treatment of each of the two statements follows from classical results and methods of structural optimization: the stiffest orientation of reinforcing fibers coincides with principal stresses and the separate selection of density of fibers is a convex problem that can be solved by optimality criteria iterations. Numerical solutions are shown for two particular configurations. The first for a statically determined structure and the second for a statically undetermined one. The latter shows related but non-unique solutions.
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| 49. |
- Klarbring, Anders, 1957-, et al.
(författare)
-
Topology optimization of hyperelastic bodies including non-zero prescribed displacements
- 2013
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 47:1, s. 37-48
-
Tidskriftsartikel (refereegranskat)abstract
- Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff–St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings.
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| 50. |
- Kokkolaras, Michael, et al.
(författare)
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Extension of the target cascading formulation to the design of product families
- 2002
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 24:4, s. 293-301
-
Tidskriftsartikel (refereegranskat)abstract
- The target cascading methodology for optimal product development is extended to product families with predefined platforms. The single-product formulation is modified to accommodate the presence of shared systems, subsystems, and/or components and locally introduced targets. Hierarchical optimization problems associated with each product variant are combined to formulate the product family multicriteria design problem, and common subproblems are identified based on the shared elements (i.e. the platform). The solution of the overall design problem is coordinated so that the shared elements are consistent with the performance and behaviour of the product variants. A simple automotive design example is used to demonstrate the proposed methodology.
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