| 1. |
- Eriksson, Robert, et al.
(author)
-
OPTIMIZING THERMAL BARRIER COATING DESIGN USING STRUCTURAL OPTIMIZATION METHODS
- 2017
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In: PROCEEDINGS OF THE ASME TURBO EXPO: TURBINE TECHNICAL CONFERENCE AND EXPOSITION, 2017, VOL 6. - : AMER SOC MECHANICAL ENGINEERS. - 9780791850916
-
Conference paper (peer-reviewed)abstract
- Thermal barrier coatings (TBCs) are used in gas turbines to reduce creep, thermo-mechanical fatigue, and oxidation, or to allow for reduced air cooling. TBCs may fail due to fatigue. Structural optimization methods were applied to optimize the. TBC thickness in such a way as to increase the life of the TBC. The TBC thickness was varied for three cases: 1) minimizing TBC volume, 2) minimizing TBC maximum effective stress, and 3) minimizing compliance (minimizing the strain energy). The results from the optimization were used to estimate the relative change in TBC life via a strain energy based failure criterion and a Coffin-Manson-like expression. Minimization of volume had limited use due to limitations in the current implementation. Minimization of effective stress did not give any significant increase in life. The minimization of compliance increased the estimated TBC life at highly stressed regions.
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| 2. |
- Fredriksson, B, et al.
(author)
-
Numerical Solutions to Contact, Friction and Crack problems with Applications
- 1984
-
In: Engineering computations. - : Emerald. - 0264-4401 .- 1758-7077. ; 1:2, s. 133-143
-
Journal article (peer-reviewed)abstract
- The importance of contact and friction problems in different application areas is discussed. Methods and algorithms for numerical solutions using the finite element method are presented. Both elastic and elastic plastic materials are included as well as combination of contact and crack problems. The methods are applied to practical applications such as bolted joints, lugs and roller bearings.
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| 3. |
- Fredriksson, Billy, et al.
(author)
-
Pressure Distribution in Crowned Roller Contacts
- 1984
-
In: Engineering Analysis. - 0955-7997. ; 1:1, s. 32-39
-
Journal article (peer-reviewed)abstract
- The fatigue life of a roller bearing is heavily influenced by the crowning profile of the rollers. The pressure distribution for different types of crowning has been studied. For solving this three-dimensional contact problem a numerical procedure for analysis of general elasto-static contact problems has been used. The method is based on an incremental and iterative algorithm applied to a set of linear equations established with finite element technique. The contact surfaces are assumed to be perfectly smooth, dry and frictionless. The pressure distribution between the bodies has been compared with results obtained from other methods. The influence on the pressure distribution by the free boundary at the end of the finite cylinders has also been investigated. It is also shown that it is possible to use the same finite element model to study different types of crowning, thus making it efficient to perform paramater surveys. A method of obtaining required or ‘optimal’ pressure distribution is suggested.
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| 4. |
- Gustafsson, Erik, 1976-
(author)
-
Optimization of Castings by using Surrogate Models
- 2007
-
Licentiate thesis (other academic/artistic)abstract
- In this thesis structural optimization of castings and thermomechanical analysis of castings are studied.In paper I an optimization algorithm is created by using Matlab. The algorithm is linked to the commercial FE solver Abaqus by using Python script. The optimization algorithm uses the successive response surfaces methodology (SRSM) to create global response surfaces. It is shown that including residual stresses in structural optimization of castings yields an optimal shape that differs significantly from the one obtained when residual stresses are excluded.In paper II the optimization algorithm is expanded to using neural networks. It is tested on some typical bench mark problems and shows very promising results. Combining paper I and II the response surfaces can be either analytical functions, both linear and non-linear, or neural networks. The optimization is then performed by using sequential linear programming or by using a zero-order method called Complex. This is all gathered in a package called StuG-OPT.In paper III and IV focus is on the thermomechanical problem when residual stresses are calculated. In paper III a literature review is performed and some numerical simulations are performed to see where numerical simulations can be used in the industry today. In paper IV simulations are compared to real tests. Several stress lattices are casted and the residual stresses are measured. Simulations are performed by using Magmasoft and Abaqus. In Magmasoft a J2-plasticity model is used and in Abaqus two simulations are performed using either J2-plasticity or the ”Cast Iron Plasticity” available in Abaqus that takes into account the different behavior in tension and compression for grey cast iron.
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| 5. |
- Hilding, D., et al.
(author)
-
A computational methodology for shape optimization of structures in frictionless contact
- 2001
-
In: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 190:31, s. 4043-4060
-
Journal article (peer-reviewed)abstract
- This paper presents a computational methodology for shape optimization of structures in frictionless contact, which provides a basis for developing user-friendly and efficient shape optimization software. For evaluation it has been implemented as a subsystem of a general finite element software. The overall design and main principles of operation of this software are outlined. The parts connected to shape optimization are described in more detail. The key building blocks are: analytic sensitivity analysis, an adaptive finite element method, an accurate contact solver, and a sequential convex programing optimization algorithm. Results for three model application examples are presented, in which the contact pressure and the effective stress are optimized. cr 2001 Elsevier Science B.V. All rights reserved.
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| 6. |
- Holmberg, Erik, et al.
(author)
-
Fatigue constrained topology optimization
- 2014
-
In: Structural and multidisciplinary optimization (Print). - : Springer-Verlag New York. - 1615-147X .- 1615-1488. ; 50:2, s. 207-219
-
Journal article (peer-reviewed)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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| 7. |
- Holmberg, Erik, et al.
(author)
-
Global and clustered approaches for stress constrained topology optimization and deactivation of design variables
- 2013
-
Conference paper (other academic/artistic)abstract
- We present a global (one constraint) version of the clustered approach previously developed for stress constraints, and also applied to fatigue constraints, in topology optimization. The global approach gives designs without large stress concentrations or geometric shapes that would cause stress singularities. For example, we solve the well known L-beam problem and obtain a radius at the internal corner.The main reason for using a global stress constraint in topology optimization is to reduce the computational cost that a high number of constraints impose. In this paper we compare the computational cost and the results obtained using a global stress constraint versus using a number of clustered stress constraints.We also present a method for deactivating those design variables that are not expected to change in the current iteration. The deactivation of design variables provides a considerable decrease of the computational cost and it is made in such a way that approximately the same final design is obtained as if all design variables are active.
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| 8. |
- Holmberg, Erik
(author)
-
Stress and fatigue constrained topology optimization
- 2013
-
Licentiate thesis (other academic/artistic)abstract
- This thesis concerns structural optimization in conceptual design stages, for which constraints that are adapted to industrial requirements have been developed for topology optimization problems. The objective of the project has been to identify and solve problems that today prevent structural optimization from being used in a broader sense in the avionic industry; the main focus has been on stress and fatigue constraints in topology optimization.The thesis consists of two parts. The rst part gives an introduction to topology optimization and describes the developed methods for stress and fatigue constraints. In the second part, two papers are included, where the stress and fatigue constraints are evaluated, respectively.In the rst paper, a clustered approach is presented, where stress constraints are applied to stress clusters, rather than points on the structure. This allows for a trade-o between computational time and accuracy, as the number of clusters and thus constraints can be varied. Dierent approaches for how to sort stress evaluation points into clusters and how to update the clusters, such that the results are suciently accurate for conceptual designs, are developed and evaluated. The two-dimensional examples conrm the theoretical discussions and the designs that are obtained have managed to avoid large stress concentrations, even for problems with an initial stress singularity. Compared to the traditional stiness based designs, the stress constrained designs are considered to be closer to a nal design, which will decrease the total product development time.The second paper uses the methodology developed in the rst paper and applies it to high-cycle fatigue constraints. Using loads described by a variable load spectrum and material data from fatigue tests, the tensile principal stresses are constrained by a limit that is determined such that fatigue failure will not occur. In the examples, where the mass is minimized subjected to fatigue and static stress constraints, simple topologies are obtained and the structural parts are sized with respect to the critical fatigue stress and the yield limit. Stress concentrations are again avoided, for example by the creation of a radius around an internal corner. A comparison between static stress constraints based on the von Mises criterion and the highest tensile principal stresses is given and the examples clearly show the characteristics of the two formulations.
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| 9. |
- Holmberg, Erik, et al.
(author)
-
Stress constrained topology optimization
- 2013
-
In: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 48:1, s. 33-47
-
Journal article (peer-reviewed)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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| 10. |
- Holmberg, Erik, 1985-
(author)
-
Topology optimization considering stress, fatigue and load uncertainties
- 2016
-
Doctoral thesis (other academic/artistic)abstract
- This dissertation concerns structural topology optimization in conceptual design stages. The objective of the project has been to identify and solve problems that prevent structural topology optimization from being used in a broader sense in the avionic industry; therefore the main focus has been on stress and fatigue constraints and robustness with respect to load uncertainties.The thesis consists of two parts. The first part gives an introduction to topology optimization, describes the new contributions developed within this project and motivates why these are important. The second part includes five papers.The first paper deals with stress constraints and a clustered approach is presented where stress constraints are applied to stress clusters, instead of being defined for each point of the structure. Different approaches for how to create and update the clusters, such that sufficiently accurate representations of the local stresses are obtained at a reasonable computational cost, are developed and evaluated.High-cycle fatigue constraints are developed in the second paper, where loads described by a variable-amplitude load spectrum and material data from fatigue tests are used to determine a limit stress, for which below fatigue failure is not expected. A clustered approach is then used to constrain the tensile principal stresses below this limit.The third paper introduces load uncertainties and stiffness optimization considering the worst possible loading is then formulated as a semi-definite programming problem, which is solved very efficiently. The load is due to acceleration of point masses attached to the structure and the mass of the structure itself, and the uncertainty concerns the direction of the acceleration. The fourth paper introduces an extension to the formulated semi-definite programming problem such that both fixed and uncertain loads can be optimized for simultaneously.Game theory is used in the fifth paper to formulate a general framework, allowing essentially any differentiable objective and constraint functions, for topology optimization under load uncertainty. Two players, one controlling the structure and one the loads, are in conflict such that a solution to the game, a Nash equilibrium, is a design optimized for the worst possible load.
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| 11. |
- Hozić, Dženan, et al.
(author)
-
Density Filter Control of Thickness-to-Length Change of Composite Structures
- 2013
-
Conference paper (other academic/artistic)abstract
- The homogenized material optimization (HMO) problem is a novel structural optimization problem that we have developed for optimization of fiber reinforced composite structures. In the HMO problem we apply a smeared-out approach to model the material properties of fiber reinforced composite materials. The objective of the HMO problem is to maximize the stiffness of a composite structure by means of finding the optimal distribution of composite material, belonging to a fixed set of fiber orientations, across the design domain. In order to obtain manufacturable solutions, we have introduced a linear density filter as a restriction method to control the thickness variation across the design domain. To examine the effect of the density filter on the thickness variation and the objective function value of composite structures, obtained in the HMO problem, we have performed numerical tests for different load cases, mesh densities and range of the filter radius.It is observed that for the present problem the thickness variation was mesh-independent. Both the thickness variation and objective function value depend on the load case used in the HMO problem. For all load cases the thickness variations exhibits an approximately piece-wise linear behaviour for increased filter radius. Furthermore, it was observed that an increase of filter radius would result in an moderate increase in objective function value for the solutions obtained from the HMO problem. From these results we conclude that by using a density filter, the HMO problem can be used to obtain manufacturable designs for composite structures.
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| 12. |
- Hozić, Dženan, et al.
(author)
-
Stiness and Lay-up Optimization of Composite Structures based on a Homogenized Material Approach
- 2013
-
Other publication (other academic/artistic)abstract
- In the present work we propose a two phase composite structure optimization method based on a novel material homogenization approach. It consists of a stiffness and a lay-up optimization problem, respectively, with the aim of obtaining manufacturable composite structures with maximized stiffness properties. The method is applied to a cantilever plate, and numerical tests were performed for three load cases and for a number of parameters settings. The results show that the proposed method can obtain manufacturable composite structures with maximized stiffness properties. In the first phase of the method, the stiffness optimization problem provides an optimal distribution of the composite material, such that the stiffness properties of the structureare maximized. The second phase, the lay-up optimization problem, provides a manufacturable lay-up sequence of discrete plies which attempts to retain the stiffness properties of the structure from the first phase.
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| 13. |
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| 14. |
- Klarbring, Anders, et al.
(author)
-
Dynamical systems and topology optimization
- 2010
-
In: Structural and multidisciplinary optimization (Print). - : Springer Science Business Media. - 1615-147X .- 1615-1488. ; 42:2, s. 179-192
-
Journal article (peer-reviewed)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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| 15. |
- Klarbring, Anders, et al.
(author)
-
Dynamical systems, SIMP, bone remodeling and time dependent loads
- 2012
-
In: Structural and multidisciplinary optimization (Print). - : Springer Verlag (Germany). - 1615-147X .- 1615-1488. ; 45:3, s. 359-366
-
Journal article (peer-reviewed)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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| 16. |
- Klarbring, Anders, et al.
(author)
-
Growth, Optimzation and Configurational Forces
- 2008
-
In: In D. Ambrosi, K. Garikipati and E. Kuhl (Eds) Mini-Workshop: The Mathematics of Growth and Remodelling of Soft Biological Tissues. - Oberwohlfach : Mathematisches Forschungsinstitut. ; , s. 2239-2243
-
Conference paper (peer-reviewed)
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| 17. |
- Klarbring, Anders, 1957-, et al.
(author)
-
Lazy zone bone remodeling theory and its relation to topology optimization
- 2012
-
In: Annals of Solid and Structural Mechanics. - : Springer Berlin/Heidelberg. - 1867-6936 .- 1867-6944. ; 4:1-2, s. 25-32
-
Journal article (peer-reviewed)abstract
- The connection between apparent density-type bone remodeling theories and density formulations of topology optimization is well known from a large number of publications and its theoretical basis has recently been discussed by making use of a dynamical systems approach to optimization. The present paper takes this connection one step further by showing how the Coleman–Noll procedure of rational thermodynamics can be used to derive general dynamical systems, where a special case includes the lazy zone concept of bone remodeling theory. It is also shown how a numerical solution method for the dynamical system can be developed by using the sequential convex approximation idea. The method is employed to obtain a series of solutions that show the influence of modeling parameters representing elements of plasticity and viscosity in the growth process.
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| 18. |
- Klarbring, Anders, et al.
(author)
-
Minimizing crack energy release rate by topology optimization
- 2018
-
In: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 58:4, s. 1695-1703
-
Journal article (peer-reviewed)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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| 19. |
- Klarbring, Anders, et al.
(author)
-
Nutrient modulated structural design with application to growth and degradation
- 2015
-
In: Zeitschrift für angewandte Mathematik und Mechanik. - : WILEY-V C H VERLAG GMBH. - 0044-2267 .- 1521-4001. ; 95:11, s. 1323-1334
-
Journal article (peer-reviewed)abstract
- Phenomena such as biological growth and damage evolution can be thought of as time evolving processes, the directions of which are governed by descendent of certain goal functions. Mathematically this means using a dynamical systems approach to optimization. We extend such an approach by introducing a field quantity, representing nutrients or other non-mechanical stimuli, that modulate growth and damage evolution. The derivation of a generic model is systematic, starting from a Lyaponov-type descent condition and utilizing a Coleman-Noll strategy. A numerical algorithm for finding stationary points of the resulting dynamical system is suggested and applied to two model problems where the influence of different levels of nutrient sensitivity are observed. The paper demonstrates the use of a new modeling technique and shows its application in deriving a generic problem of growth and damage evolution. (C) 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim
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| 20. |
- Klarbring, Anders, et al.
(author)
-
ODE Approach to Topology Optimization
- 2009
-
In: 8th World Congress on Structural and Multidisciplinary Optimization, June 1-5, 2009, Lisbon, Portugal. - Lissabon, Portugal. ; , s. 1148-1148
-
Conference paper (peer-reviewed)
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| 21. |
- Klarbring, Anders, et al.
(author)
-
Optimal design of fibre reinforced membrane structures
- 2017
-
In: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 56:4, s. 781-789
-
Journal article (peer-reviewed)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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| 22. |
- Klarbring, Anders, et al.
(author)
-
Topology optimization of flow networks
- 2003
-
In: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:35-36, s. 3909-3932
-
Journal article (peer-reviewed)abstract
- The field of topology optimization is well developed for load carrying trusses, but so far not for other similar network problems. The present paper is a first study in the direction of topology optimization of flow networks. A linear network flow model based on Hagen-Poiseuille's equation is used. Cross-section areas of pipes are design variables and the objective of the optimization is to minimize a measure, which in special cases represents dissipation or pressure drop, subject to a constraint on the available (generalized) volume. A ground structure approach where cross-section areas may approach zero is used, whereby the optimal topology (and size) of the network is found.A substantial set of examples is presented: Small examples are used to illustrate difficulties related to non-convexity of the optimization problem, larger arterial tree-type networks, with bio-mechanics interpretations, illustrate basic properties of optimal networks, the effect of volume forces is exemplified.We derive optimality conditions which turns out to contain Murray's law, thereby, presenting a new derivation of this well known physiological law. Both our numerical algorithm and the derivation of optimality conditions are based on an e-perturbation where cross-section areas may become small but stay finite. An indication of the correctness of this approach is given by a theorem, the proof of which is presented in an appendix. © 2003 Elsevier B.V. All rights reserved.
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| 23. |
- Marciniec, A, et al.
(author)
-
Load Distribution in flexibly Supported Three-Row Roller Slew Bearings
- 1994
-
In: Tribology Transactions. - : Informa UK Limited. - 1040-2004 .- 1547-397X. ; 37:4, s. 757-762
-
Journal article (peer-reviewed)abstract
- In general, slew bearings are less firmly supported by their mounting structures than small bearings. Hence, the load distribution around the bearing may be vastly different than that predicted by classic bearing formulas. The finite element method has been employed to determine load distribution in a three-row roller slew bearing mounted between two flexible, ring shaped supporting structures composed of beam elements. A special bar element modeling the system of two opposite rollers in contact with its raceways has been elaborated. The influence of the nonlinear force displacement characteristics of each of the rollers, as well as the influence of gaps between the rollers and its raceways have been taken into account. The nonlinear contact problem has been solved utilizing the Newton-Raphson method with continually updated stiffness matrix due to both element nonlinearity and contact status. The effect of a number of design parameters on the load distribution has been investigated.
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| 24. |
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| 25. |
- Selskog, Pernilla, et al.
(author)
-
Kinematics of the Heart : Finite Element and 3D Time-Resolved Phase Contrast Magnetic resonance Imaging
- 2002
-
In: Proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields.
-
Conference paper (peer-reviewed)abstract
- The complex three-dimensional structure of the heart muscle (myocardium) has anisotropic, non-linear and time-dependent mechanical properties. During the cardiac cycle, the myocardium undergoes large elastic deformations as a consequence of the active muscle contraction along the muscle fibers and their relaxation, respectively. A four-dimensional (4D) description (three spatial dimensions + time) of the mechanical properties of the myocardium would be of interest in the assessment of myocardial function. Time-resolved 3D phase contrast MRI makes it possible to quantify all three velocity components, which is necessary to as accurately as possible describe the velocities in the heart. The velocity data may be used for investigation of the deformation of the heart and calculation of strain in the myocardial wall. We present a method for estimation of myocardial kinematics using finite elements and 3D time-resolved phase contrast MRI.
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| 26. |
- Suresh, Shyam, 1990-, et al.
(author)
-
An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization
- 2018
-
In: Proceedings of the 6th International Conference on Engineering Optimization – EngOpt 2018. - Cham, Switzerland : Springer. ; , s. 844-854
-
Conference paper (peer-reviewed)abstract
- We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.
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| 27. |
- Suresh, Shyam, 1990-
(author)
-
Developments of Topology Optimization Methods for Additive Manufacturing involving High-cycle Fatigue
- 2023
-
Doctoral thesis (other academic/artistic)abstract
- Additive manufacturing (AM) is a versatile manufacturing process which is gaining popularity in the automotive and aerospace industries. Through AM one can manufacture complex structures and combined with topology optimization (TO) a powerful design tool that provides great freedom in geometric form emerges. The goal of the research presented in this thesis is to develop new TO methods that consider specific properties related to AM for metals. In particular, anisotropy, non-homogeneity in the form of surface effects, and constraints on high-cycle fatigue (HCF) damage are treated. In the first paper of the thesis, an HCF constraint is introduced into a TO problem where the total structural mass is minimized. The HCF model is based on a continuous-time approach in contrast to more conventional cycle-counting approaches. It is based on the concept of a moving endurance surface, and a system of ordinary differential equations is used to predict the fatigue damage at every point in the design domain. The model is capable of handling arbitrary load histories, including most non-proportional loads. Gradient-based optimization is utilized, and the fatigue sensitivities are determined by the adjoint method. In the subsequent papers, several extensions are made to the original HCFconstrained TO problem: The HCF model is extended so that it is applicable not only to isotropic materials but also to transversely isotropic materials. The anisotropic properties are manifested in the constitutive elastic response and in the fatigue properties. Acceleration of fatigue and sensitivity analyses by extrapolation is introduced, making the treatment of an unlimited number of load cycles possible. Simultaneous optimization of build orientation and topology, considering stress- and HCF constraints, is performed. For better prediction of fatigue, especially for non-proportional loads, the original continuous-time HCF model is modified using a quadratic polynomial endurance function. In the final paper, a new TO method, taking surface layer effects into account, is introduced. This essentially models the impaired mechanical properties observed in as-built AM components compared to components having polished surfaces. Numerical test problems as well as application-like problems are solved in all papers to exemplify the applicability of the developed TO methodology.
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| 28. |
- Suresh, Shyam, et al.
(author)
-
Topology optimization accounting for surface layer effects
- 2020
-
In: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 62:6, s. 3009-3019
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Journal article (peer-reviewed)abstract
- Metal AM (additive manufacturing) components are generally inhomogeneous and have different microstructure in the bulk compared with (contour) regions near the surface. This, as well as rough as-built surfaces, affects mechanical properties. In this paper, we develop a topology optimization method that considers such inhomogeneities. The method is a direct extension of standard density-based methods using linear filtering for regularization, and a second filtering of the design variables is used to identify a surface layer, the thickness of which is given by the filter radius. Domain extension is used in order to properly identify such layers at the boundary of the design domain. The method is generally applicable but is demonstrated for stiffness optimization. Both two- and three-dimensional problems are treated. A general property of the method is that the topological complexity is reduced, i.e. the optimized designs get fewer and thicker structural members as the width of the surface layer is increased.
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| 29. |
- Suresh, Shyam, 1990-
(author)
-
Topology Optimization for Additive Manufacturing Involving High-Cycle Fatigue
- 2020
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Licentiate thesis (other academic/artistic)abstract
- Additive Manufacturing (AM) is gaining popularity in aerospace and automotive industries. This is a versatile manufacturing process, where highly complex structures are fabricated and together with topology optimization, a powerful design tool, it shares the property of providing a very large freedom in geometrical form. The main focus of this work is to introduce new developments of Topology Optimization (TO) for metal AM.The thesis consists of two parts. The first part introduces background and theory, where TO and adjoint sensitivity analysis are described. Furthermore, methodology used to identify surface layer and high-cycle fatigue are introduced. In the second part, three papers are appended, where the first paper presents the treatment of surface layer effects, while the second and third papers provide high-cycle fatigue constraint formulations.In Paper I, a TO method is introduced to account for surface layer effects, where different material properties are assigned to bulk and surface regions. In metal AM, the fabricated components in as-built surface conditions significantly affect mechanical properties, particularly fatigue properties. Furthermore, the components are generally in-homogeneous and have different microstructures in bulk regions compared to surface regions. We implement two density filters to account for surface effects, where the width of the surface layer is controlled by the second filter radius. 2-D and 3-D numerical examples are treated, where the structural stiffness is maximized for a limited mass.For Papers II and III, a high-cycle fatigue constraint is implemented in TO. A continuous-time approach is used to predict fatigue-damage. The model uses a moving endurance surface and the development of damage occurs only if the stress state lies outside the endurance surface. The model is applicable not only for isotropic materials (Paper II) but also for transversely isotropic material properties (Paper III). It is capable of handling arbitrary load histories, including non-proportional loads. The anisotropic model is applicable for additive manufacturing processes, where transverse isotropic properties are manifested not only in constitutive elastic response but also in fatigue properties. Two optimization problems are solved: In the first problem the structural mass is minimized subject to a fatigue constraint while the second problem deals with stiffness maximization subjected to a fatigue constraint and mass constraint. Several numerical examples are tested with arbitrary load histories.
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| 30. |
- Suresh, Shyam, et al.
(author)
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Topology optimization using a continuous-time high-cycle fatigue model
- 2020
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In: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 61:3, s. 1011-1025
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Journal article (peer-reviewed)abstract
- We propose a topology optimization method that includes high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach where the evolution of damage in each point of the design domain is governed by a system of ordinary differential equations, which employs the concept of a moving endurance surface being a function of the stress and back stress. Development of fatigue damage only occurs when the stress state lies outside the endurance surface. The fatigue damage is integrated for a general loading history that may include non-proportional loading. Thus, the model avoids the use of a cycle-counting algorithm. For the global high-cycle fatigue constraint, an aggregation function is implemented, which approximates the maximum damage. We employ gradient-based optimization, and the fatigue sensitivities are determined using adjoint sensitivity analysis. With the continuous-time fatigue model, the damage is load history dependent and thus the adjoint variables are obtained by solving a terminal value problem. The capabilities of the presented approach are tested on several numerical examples with both proportional and non-proportional loads. The optimization problems are to minimize mass subject to a high-cycle fatigue constraint and to maximize the structural stiffness subject to a high-cycle fatigue constraint and a limited mass.
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| 31. |
- Thellner, Mikael, et al.
(author)
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Topology optimization with design-dependant using simultaneous shape and topology variation
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Other publication (other academic/artistic)abstract
- We present a new method for topology optimization with design-dependent loads. In traditional topology optimization a fixed design domain on which the loads and constraints are specified is used. Such an approach can not handle loads which depend on the design. Here we introduce domain shape variation. using techniques from shape optimization, simultaneously with topology optimization. For topology optimization we use the SIMP interpolation function together with a filter as restriction method. The stiffness of the structure is maximized given a limited alllount of material. Three numerical examples are presented which illustrates the proposed method.
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| 32. |
- Thore, Carl-Johan, et al.
(author)
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Penalty regulation of overhang in topology optimization for additive manufacturing
- 2019
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In: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 60:1, s. 59-67
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Journal article (peer-reviewed)abstract
- Several filter approaches that introduce additive manufacturing-related overhang constraints in topology optimization exist. However, a drawback of these is that exact satisfaction of overhang constraints produces sharp inward corners resulting in stress singularities. The present paper therefore modifies such filter approaches by a penalty formulation, where the choice of penalty factor regulates how closely the overhang constraint is satisfied. By appropriately choosing certain weight factors in the penalty function, the cost of support structures is also reflected in the formulation in a simple and computationally inexpensive way. The method is demonstrated by parameter studies using the classical MBB beam, using both structured and unstructured meshes.
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| 39. |
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| 40. |
- Torstenfelt, Bo, 1952-, et al.
(author)
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Structural optimization of modular product families with application to car space frame structures
- 2006
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In: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 32:2, s. 133-140
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Journal article (peer-reviewed)abstract
- This paper extends classical structural optimization from single-product optimization to optimization of a whole family of products that have common modules. It integrates the family commonality problem with the finite element models of the structures. A general mathematical frame where optimization is seen as a balance between cost and performance is given. The most obvious cost function is mass, while performance is taken to be a weighted sum of compliances. As a case study, a car product family consisting of three products is presented. These three products are a base model, a seven-seat version, and a pickup version. The study shows how optimal results are effected by requiring modules to be shared between products. Loads emanating from prescribed acceleration fields that simulate crash situations are used. This is a proof-of-concept paper which is a first step toward including more general manufacturing costs than mass and performance measures other than compliance.
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| 41. |
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