| 1. |
- 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
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 2. |
- 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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| 3. |
- 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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| 4. |
- Fredricson, Harald, et al.
(författare)
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Topology optimization of frame structures with flexible joints
- 2003
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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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| 5. |
- Hilding, D
(författare)
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A heuristic smoothing procedure for avoiding local optima in optimization of structures subject to unilateral constraints
- 2000
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Ingår i: Structural and multidisciplinary optimization (Print). - 1615-147X .- 1615-1488. ; 20:1, s. 29-36
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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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| 6. |
- Jansson, Tomas, et al.
(författare)
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Using surrogate models and response surfaces in structural optimization : with application to crashworthiness design and sheet metal forming
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:2, s. 129-140
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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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| 7. |
- Kokkolaras, Michael, et al.
(författare)
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Extension of the target cascading formulation to the design of product families
- 2002
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 24:4, s. 293-301
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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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| 8. |
- Marklund, Per-Olof, et al.
(författare)
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Optimization of a car body component subjected to side impact
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 21:5, s. 383-392
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Tidskriftsartikel (refereegranskat)abstract
- This paper explores structural optimization methods applied to a car side impact. The use of local and global approximation methods has been compared, resulting in a recommendation that global approximation methods should be used for this kind of transient loading problems. The numerical simulations have been carried out using the explicit finite element program LS-DYNA. The problem studied is the weight minimization of the B-pillar, situated between the front and the rear door of the car, without compromising the safety of the car occupants. All results are related to the original B-pillar in the SAAB 95 car. By using global approximations in the form of linear and quadratic response surfaces it is shown that the weight of the B-pillar can be reduced by 25% without the loss of safety.
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| 9. |
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| 10. |
- Patriksson, Michael, 1964, et al.
(författare)
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Stochastic bilevel programming in structural optimization
- 2001
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 21:5, s. 361-371
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Tidskriftsartikel (refereegranskat)
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| 11. |
- Redhe, Marcus, et al.
(författare)
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An investigation of structural optimization in crashworthiness design using a stochastic approach
- 2004
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 27:6, s. 446-459
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Tidskriftsartikel (refereegranskat)abstract
- In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.
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| 12. |
- Redhe, Marcus, et al.
(författare)
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Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique
- 2004
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 27:5, s. 411-420
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this work is to illustrate how a space mapping technique using surrogate models together with response surfaces can be used for structural optimization of crashworthiness problems. To determine the response surfaces, several functional evaluations must be performed and each evaluation can be computationally demanding. The space mapping technique uses surrogate models, i.e. less costly models, to determine these surfaces and their associated gradients. The full model is used to correct the gradients from the surrogate model for the next iteration. Thus, the space mapping technique makes it possible to reduce the total computing time needed to find the optimal solution. First, two analytical functions and one analytical structural optimization problem are presented to exemplify the idea of space mapping and to compare the efficiency of space mapping to traditional response surface optimization. Secondly, a sub-model of a complete vehicle finite element (FE) model is used to study different objective functions in vehicle crashworthiness optimization. Finally, the space mapping technique is applied to a structural optimization problem of a large industrial FE vehicle model, consisting of 350.000 shell elements and a computing time of 100 h. In this problem the intrusion in the passenger compartment area was reduced by 32% without compromising other crashworthiness parameters.
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| 13. |
- Redhe, Marcus, 1975-, et al.
(författare)
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Using the response surface methodology and the D-optimality criterion in crashworthiness related problems
- 2002
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 24:3, s. 185-194
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to determine the efficient number of experimental points when using the response surface methodology in crashworthiness problems.The D-optimality criterion is used as experimental design method. Two application models have been studied, one square tube and one front rail from Saab Automobile AB. Both models were fully parameterized in the preprocessor LS-INGRID but only two design variables were used. The optimization package LS-OPT was used to determine the design of experiments using the D-optimality criterion. Both models were subjected to an impact into a rigid wall and the simulations were carried out using LS-DYNA. A general recommendation is to to use 1.5 times the minimum number of experimental points. A more specialized recommendation is for linear surfaces 1.5, elliptic surfaces 2.2 and for quadratic surfaces 1.6 times the minimum number of experimental points.
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| 14. |
- Rietz, Andreas, et al.
(författare)
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Simultaneous shape and thickness optimization
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 23:1, s. 14-23
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Tidskriftsartikel (refereegranskat)abstract
- The topic of this paper is to minimize the flexibility of a sheet with respect to its thickness and shape of boundary. These characteristics will be considered in the same algorithm, which both prevent suboptimization and mean that the user does not have to supervise the use of linked optimization tools. The refined boundary description also makes it possible to include pressure loads in this setting.
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| 15. |
- Rietz, A
(författare)
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Sufficiency of a finite exponent in SIMP (power law) methods
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 21:2, s. 159-163
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Tidskriftsartikel (refereegranskat)abstract
- A common way to perform discrete optimization in shape or topology optimization is to use a method called the artificial power law or SIMP. The focus of this paper is to show that this method gives a, discrete solution under some conditions. Examples from topology optimization are included for illustrative purposes.
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| 16. |
- Stolpe, Mathias, et al.
(författare)
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A stress-constrained truss-topology and material-selection problem that can be solved by linear programming
- 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. 126-129
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of simultaneously selecting the material and determining the area of each bar in a truss structure in such a way that the cost of the structure is minimized subject to stress constraints under a single load condition. We show that such problems can be solved by linear programming to give the global optimum, and that two different materials are always sufficient in an optimal structure.
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| 17. |
- Svanberg, Krister
(författare)
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A note on stress-constrained truss topology optimization
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:1, s. 62-64
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this brief note is to demonstrate that general-purpose optimization methods and codes should not be discarded when dealing with stress-constrained truss topology optimization. By using a disaggregated formulation of the considered problem, such methods may find also "singular optima", without using perturbation techniques like the epsilon-relaxed approach.
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| 18. |
- Svanberg, Krister
(författare)
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An alternative interpolation scheme for minimum compliance topology optimization
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 22:2, s. 116-124
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Tidskriftsartikel (refereegranskat)abstract
- We consider the discretized zero-one continuum topology optimization problem of finding the optimal distribution of two linearly elastic materials such that compliance is minimized. The geometric complexity of the design is limited using a constraint on the perimeter of the design. A common approach to solve these problems is to relax the zero-one constraints and model the material properties by a power law which gives noninteger solutions very little stiffness in comparison to the amount of material used. We propose a material interpolation model based on a certain rational function, parameterized by a positive scalar q such that the compliance is a convex function when q is zero and a concave function for a finite and a priori known value on q. This increases the probability to obtain a zero-one solution of the relaxed problem.
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| 19. |
- Svanberg, Krister
(författare)
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On the trajectories of penalization methods for topology optimization
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 21:2, s. 128-139
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Tidskriftsartikel (refereegranskat)abstract
- We consider the discretized zero-one minimum compliance topology optimization problem of elastic continuum structures under multiple load conditions. The binary design variables indicate presence or absence of material in the finite elements. A common approach to solve these problems is to relax the binary constraints, i.e. allow the design variables to attain values between zero and one, and penalize intermediate values to obtain a "black and white" (zero-one) design. To avoid convergence to a local minimum, it has been suggested that a continuation method should be used, where the penalized problems are solved with increasing penalization. In this paper, the trajectories associated with optimal solutions to the penalized problems, for continuously increasing penalization, are studied on some carefully chosen examples. Two different penalization techniques are used. The global trajectory is defined as the path followed by the global optimal solutions to the penalized problems, and we present examples for which the global trajectory is discontinuous even though the original zero-one problem has a unique solution. Furthermore, we present examples where the penalization method combined with a continuation approach fails to produce a black and white design, no matter how large the penalization becomes.
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| 20. |
- Svanberg, Krister
(författare)
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On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization
- 2001
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 21:2, s. 140-151
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Tidskriftsartikel (refereegranskat)abstract
- We consider the nonconvex problem of minimizing the weight of a linearly elastic truss structure subject to stress constraints under multiple load conditions. The design variables are the cross-sectional areas of the elements, and the stress constraints are imposed only on elements with strictly positive areas. To avoid degenerate feasible domains, it has been suggested that the stress constraints of the original problem should be relaxed by a positive scalar epsilon, leading to the so-called epsilon -relaxed problem. In this paper, the trajectories associated with optimal solutions of the epsilon -relaxed problems, for continuously decreasing values of epsilon, are studied in detail on some carefully chosen examples. The global trajectory is defined as the path followed by the global optimal solution to the epsilon -relaxed problem, and we present two parameterized examples for which the global trajectory is discontinuous for arbitrarily small values of epsilon > 0. From that we conclude that, in practice, a sequence of solutions to the epsilon -relaxed problem for decreasing values on epsilon may not converge to the global optimal solution of the original problem, even if the starting point is on the global trajectory.
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| 21. |
- Tinnsten, Mats
(författare)
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Optimization of acoustic response : a numerical and experimental comparison
- 2000
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 19:2, s. 122-129
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Tidskriftsartikel (refereegranskat)abstract
- Acoustic optimization within structural dynamics involves automatic changes of structural design variables such as geometric dimensions, shell thickness, material parameters, fiber density and orientation angles, and others to obtain minimum noise or a specified sound quality in specified regions inside or outside the structure. The objective of the present paper is to compare numerical optimization results with experimental ones. The analysed structure is geometrically simple; a closed cylinder. The objective function is the sound intensity at specified points outside the structure. The variable used is the shell thickness. The structural dynamic behaviour is analysed with the finite element method and the acoustic analysis is performed with the boundary element method.
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| 22. |
- Tinnsten, Mats, et al.
(författare)
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Stochastic optimization of acoustic response : a numerical and experimental comparison
- 2002
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 23:6, s. 405-411
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Tidskriftsartikel (refereegranskat)abstract
- The objective of the work presented is to compare results from numerical optimization with experimental data and to highlight and discuss the differences between two fundamentally different optimization methods. The problem domain is minimization of acoustic emission and the structure used in the work is a closed cylinder with forced vibration of one end. The optimization method used in this paper is simulated annealing (SA), a stochasticmethod. The results are compared with those from a gradient-based method used on the same structure in an earlier paper (see Tinnsten 2000).
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| 23. |
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