| 1. |
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| 2. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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A Survey of Basic Mathematical Results for Frictional Contact Problems
- 2001
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Ingår i: From Convexity to Nonconvexity. - Dordrecht/Boston/London : Kluwer. - 0792371445 - 9780792371441 ; , s. -392
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.
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| 3. |
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| 4. |
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| 5. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
-
On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating
- 2005
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Ingår i: Proceedings of the Royal Society of Edinburgh. Section A Mathematics. - : The Royal Society. - 0308-2105 .- 1473-7124. ; 461:2057, s. 1261-1282
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.
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| 6. |
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| 7. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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Thermoelastic Contact with Frictional Heating
- 2006
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Ingår i: Nonsmooth Mechanics and Analysis,2003. - New York : Springer Science+business Media, inc.. ; , s. 61-
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Konferensbidrag (refereegranskat)
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| 8. |
- Barber, J.R., et al.
(författare)
-
Shakedown in frictional contact problems
- 2007
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Ingår i: 2007 Proceedings of the ASME/STLE International Joint Tribology Conference. - 0791838110 - 0791848108 ; , s. 517-519
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- If a linear elastic system with frictional interfaces is subjected to periodic loading, any slip which occurs generally reduces the tendency to slip during subsequent cycles and in some circumstances the system ‘shakes down’ to a state without slip. It has often been conjectured that a frictional Melan’s theorem should apply to this problem — i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. Here we discuss recent proofs that this is indeed the case for ‘complete’ contact problems if there is no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. By contrast, when coupling is present, the theorem applies only for a few special two-dimensional discrete cases. Counter-examples can be generated for all other cases. These results apply both in the discrete and the continuum formulation.
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| 9. |
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| 10. |
- Christensen, Peter, et al.
(författare)
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An introduction to structural optimization
- 2009. - 1
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Mechanical and structural engineers have always strived to make as efficient use of material as possible, e.g. by making structures as light as possible yet able to carry the loads subjected to them. In the past, the search for more efficient structures was a trial-and-error process. However, in the last two decades computational tools based on optimization theory have been developed that make it possible to find optimal structures more or less automatically. Due to the high cost savings and performance gains that may be achieved, such tools are finding increasing industrial use.This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.The mathematical prerequisites are kept to a bare minimum, making the book suitable for undergraduate, or beginning graduate, students of mechanical or structural engineering. Practicing engineers working with structural optimization software would also benefit from reading this book."--Publisher's website.
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| 11. |
- Daghighi, Abtin, et al.
(författare)
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F.E.M. Stress-Investigation of Scolios Apex
- 2018
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Ingår i: Open Biomedical Engineering Journal. - : Bentham Open. - 1874-1207. ; 12, s. 51-71
-
Tidskriftsartikel (refereegranskat)abstract
- In scoliosis, kypholordos and wedge properties of the vertebrae should be involved in determining how stress is distributed in the vertebral column. The impact is logically expected to be maximal at the apex.
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| 12. |
- Hilding, Daniel, et al.
(författare)
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Optimization of structures in frictional contact
- 2012
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 205-208:S1, s. 83-90
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes a new approach to optimization of linear elastic structures in frictional contact. It uses a novel method to determine an, in a specified sense, likely equilibrium state of the structure, using only the static equilibrium conditions. That is, no complex dynamic/quasi-static analyses have to be performed. The approach has the advantage that it is not necessary to know the complete load history, which is most often unknown for practical problems. To illustrate the theory, numerical results are given for the optimal design problem of sizing a truss to attain a more uniform normal contact force distribution.
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| 13. |
- Ireman, Peter, et al.
(författare)
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Gradient theory of damage coupled to frictional contact and wear, and its numerical treatment
- 2009
-
Ingår i: CMES - Computer Modeling in Engineering & Sciences. - : Tech Science Press. - 1526-1492 .- 1526-1506. ; 52:2, s. 125-158
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Tidskriftsartikel (refereegranskat)abstract
- In this paper finite element approaches for fretting fatigue are proposed on the basis of a non-local model of continuum damage coupled to friction and wear. The model is formulated in the frame-work of a standard material. In a previous paper this was done in the spirit of Maugin, where an extra entropy flux is introduced in the second law in order to include the gradient of the internal variable in a proper manner. In this paper we follow instead the ideas of Frémond and others, where this extra entropy flux is no longer needed, but instead new non-classical balance laws associated to damage, friction and wear, respectively, are derived from the principle of virtual power. The standard material is then defined as usual by state laws based on free energies and complementary laws based on dissipation potentials. In particular, we pick free energies and dissipation potentials that correspond to a non-local continuum damage model coupled to friction and wear. In addition, the boundary conditions at the contact interface creates a coupling between damage and wear. This is a key feature of our model, which makes it very useful in studies of fretting fatigue. By starting from a variational formulation of the governing equations, two different finite element algorithms are implemented. Both algorithms are based on a Newton method for semi-smooth equations. In the first algorithm the Newton method is applied to the entire system of equations, while in the second algorithm the system of equations is split into two different parts such that an elastic wear problem is solved for fixed damage followed by the solution of the damage evolution problem for the updated displacements and contact forces in an iterative process. The latter algorithm can be viewed as a Gauss-Seidel scheme. The numerical performance of the algorithms is investigated for three twodimensional examples of increasing complexity. Based on the numerical solutions, the behavior of the model is also discussed. For instance, it is shown numerically how the initiation of damage depends on the contact geometry, the coefficient of friction and the evolution of wear.
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| 14. |
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| 15. |
- Klarbring, Anders, 1957-, et al.
(författare)
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A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements
- 2012
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 45:1, s. 147-149
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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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| 16. |
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| 17. |
- Klarbring, Anders, 1957-, et al.
(författare)
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Asymptotic Modelling of Adhesive Joints
- 1999
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Ingår i: Mechanics of materials. - 0167-6636 .- 1872-7743. ; 28, s. 137-145
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Tidskriftsartikel (populärvet., debatt m.m.)
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| 18. |
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| 19. |
- Klarbring, Anders, 1957-, et al.
(författare)
-
Lazy zone bone remodeling theory and its relation to topology optimization
- 2012
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Ingår i: Annals of Solid and Structural Mechanics. - : Springer Berlin/Heidelberg. - 1867-6936 .- 1867-6944. ; 4:1-2, s. 25-32
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Tidskriftsartikel (refereegranskat)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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| 20. |
- Klarbring, Anders, 1957-, et al.
(författare)
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Minimization of Maximum Unilateral Force
- 1999
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 177:3-4, s. 215-234
-
Tidskriftsartikel (populärvet., debatt m.m.)
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| 21. |
- Klarbring, Anders, 1957-
(författare)
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Models of Mechanics
- 2006
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Ingår i: Meccanica. - Dordrecht : Springer. - 0025-6455 .- 1572-9648.
-
Bok (refereegranskat)abstract
- This textbook on models and modeling in mechanics introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation.
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| 22. |
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| 23. |
- Klarbring, Anders, 1957-, et al.
(författare)
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Residual Stress Fields in Soft Tissues
- 2004
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Ingår i: 21st International Congress of Theoretical and Applied Mechanics,2004. ; , s. 20-20
-
Konferensbidrag (refereegranskat)
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| 24. |
- Klarbring, Anders, 1957-, et al.
(författare)
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The Discrete Steady Sliding Problem
- 1999
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - 0044-2267 .- 1521-4001. ; 79:2, s. 75-90
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Tidskriftsartikel (populärvet., debatt m.m.)
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| 25. |
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| 26. |
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| 27. |
- Klarbring, Anders, 1957-, et al.
(författare)
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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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| 28. |
- Lundgren, Jonas, 1993-
(författare)
-
Internal Cooling Design Using Multiphysics Topology Optimization
- 2024
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis investigates topology optimization (TO) as a tool for designing optimal internal cooling configurations in components subjected to external hot gas streams. The work is motivated by the challenge of simultaneously considering objectives from multiple physics domains, and the rapid development of additive manufacturing (AM) in the industry, which makes it possible to realize highly complex TO designs. Against this background, a multi-physics TO approach is employed, involving the following physics domains: • Fluid mechanics: describes the flow of the coolant • Heat transfer: describes the coolant and component temperatures • Solid mechanics: describes the structural behaviour of the component Density-based TO is used to parametrize the design, such that the interpolation between solid and fluid material properties is governed by a spatially varying design variable. Temperature measures are considered as objectives in the non-convex optimization problems, and coolant mass flow and structural stiffness measures are considered as constraints. The design process is iterative: for a given design, the flow velocities are computed and used to calculate the temperature distribution, which in turn influences the domain’s structural response. These three equilibrium state problems are solved sequentially, followed by solving corresponding adjoint problems in reversed order, to acquire first-order sensitivity information used by the gradient-based optimization solver. Numerical simulations are carried out for geometries of varying degrees of complexity, resembling gas turbine guide vanes. The simulations cover a range of fidelity levels: from simpler 2D setups to more complex 3D setups with fine resolution, intended for execution on high-performance computing (HPC) clusters. Low-fidelity flow models are utilized in the TO process, while more advanced flow models are employed for design comparisons, and flow and heat response comparisons for given TO designs. The thesis consists of two parts: the first provides the theoretical framework, and the second includes appended papers. In Paper I, only the heat problem is included when modelling convection on internal boundaries identified using the design gradient. Fluid and solid mechanics are introduced in Paper II, where a conjugate heat transfer problem is augmented with a structural model coupled through thermal strains, with numerical examples in 3D. In Paper III, the simultaneous consideration of flow and heat objectives is formulated as a mathematical game between two players trying to minimize the average temperature in the domain and the coolant mass flow through the domain, respectively, with examples in 2D and 3D. The flow problems are the computational bottlenecks, and therefore, Paper IV demonstrates a 3D implementation investigating two different numerical techniques for solving the flow problem, with a voxelization approach for efficient meshing of complex geometries. Paper V presents an efficient, massively parallel HPC implementation for three-field flow-heat-structural models, and addresses further implementation details. This thesis highlights challenging aspects of large-scale multiphysics TO considering fluid mechanics, heat transfer, and solid mechanics.
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| 29. |
- Lundvall, Olle, et al.
(författare)
-
A flexible multi-body approach for frictional contact in spur gears
- 2004
-
Ingår i: Journal of Sound and Vibration. - : Elsevier. - 0022-460X .- 1095-8568. ; 278:3, s. 479-499
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper, a large rotational approach for dynamic contact problems with friction is proposed. The approach is used for modelling a spur gear pair with shafts and bearings. The model is obtained by superposing small displacement elasticity on rigid-body motions, and postulating tribological laws on the gear flanks. The finite element method is used to model the elastic properties of the gear pair. Shafts and bearings are represented by linear springs. The tribological laws of the contact interface are Signorini's contact law and Coulomb's law of friction. An important feature of the approach is that the difficulties of impacting mass nodes are avoided. The governing equations of the model are numerically treated by use of the augmented Lagrangian approach. In such manner the geometry of the gear flanks are well represented in the numerical simulations. It is possible to study accurately the consequences of different types of profile modifications as well as flank errors. In this work, the dynamic transmission error is studied. For instance, it turns out that the effect from profile modification is less significant for the transmission error when frictional effects are included.
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| 30. |
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| 31. |
- Martins, J.A.C, et al.
(författare)
-
Preface
- 1999
-
Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 177, s. 163-165
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Tidskriftsartikel (populärvet., debatt m.m.)
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| 32. |
- Olsson, Tobias, 1977-, et al.
(författare)
-
Boundary Value Problems of an Initially Stressed Body
- 2004
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The initial strain in a body can be described by a two-point tensor that maps tangent vectors between a local stress free configuration (manifolds) and the initially strained configuration. The initial strain tensor can be used to form a metric tensor and this metric can be used to induce a third manifold. The boundary value problem of an elastic body is in this paper formulated on these three manifolds: the induced manifold, the initially strained configuration and the local stress free configuration. Moreover, we consider a hyperelastic body with incompressible properties and we show that in that case, the divergence of the first Piola- Kirchhoff stress tensor defined on the initially strained configuration and on the induced manifold coincide. There-fore, we conclude that for an incompressible material, the boundary value problems stated on the initially strained configuration and on the induced manifold are the same.
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| 33. |
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| 34. |
- Strömberg, Niclas, 1968-, et al.
(författare)
-
Topology optimization of structures in unilateral contact
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 41:1, s. 57-64
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper a general framework for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilaterally constrained by rigid supports is considered. The supports are modeled by Signorini's contact conditions which in turn are treated by the augmented Lagrangian approach as well as by a smooth approximation. The latter approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equation and the two different contact formulations, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problems are solved by SLP. This is done by using a nested approach where the state equations are linearized and sensitivities are calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund's filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D as well as in 3D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.
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| 35. |
- Stålhand, Jonas, 1972-, et al.
(författare)
-
Aorta in vivo parameter identification using an axial force constraint
- 2005
-
Ingår i: Biomechanics and Modeling in Mechanobiology. - : Springer Science and Business Media LLC. - 1617-7959 .- 1617-7940. ; 3:4, s. 191-199
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Tidskriftsartikel (refereegranskat)abstract
- It was shown in a previous study by Stålhand et al. (2004) that both material and residual strain parameters for an artery can be identified noninvasively from an in vivo clinical pressure–diameter measurement. The only constraints placed on the model parameters in this previous study was a set of simple box constraints. More advanced constraints can also be utilized, however. These constraints restrict the model parameters implicitly by demanding the state of the artery to behave in a specified way. It has been observed in vitro that the axial force is nearly invariant to the pressure at the physiological operation point. In this paper, we study the possibility to include this behaviour as a constraint in the parameter optimization. The method is tested on an in vivo obtained pressure–diameter cycle for a 24-year-old human. Presented results show that the constrained parameter identification procedure proposed here can be used to obtain good results, and we believe that it may be applied to account for other observed behaviours as well.
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| 36. |
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| 37. |
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| 38. |
- Stålhand, Jonas, 1972-, et al.
(författare)
-
Towards in vivo aorta material identification and stress estimation
- 2004
-
Ingår i: Biomechanics and Modeling in Mechanobiology. - : Springer Science and Business Media LLC. - 1617-7959 .- 1617-7940. ; 2:3, s. 169-186
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses the problem of constructing a mechanical model for the abdominal aorta and calibrating its parameters to in vivo measurable data. The aorta is modeled as a pseudoelastic, thick-walled, orthotropic, residually stressed cylindrical tube, subjected to an internal pressure. The model parameters are determined by stating a minimization problem for the model pressure and computing the optimal solution by a minimization algorithm. The data used in this study is in vivo pressure–diameter data for the abdominal aorta of a 24-year-old man. The results show that the axial, circumferential and radial stresses have magnitudes in the span 0 to 180 kPa. Furthermore, the results show that it is possible to determine model parameters directly from in vivo measurable data. In particular, the parameters describing the residual stress distribution can be obtained without interventional procedures.
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| 39. |
- Suresh, Shyam, 1990-, et al.
(författare)
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An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization
- 2018
-
Ingår i: Proceedings of the 6th International Conference on Engineering Optimization – EngOpt 2018. - Cham, Switzerland : Springer. ; , s. 844-854
-
Konferensbidrag (refereegranskat)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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| 40. |
- Suresh, Shyam, 1990-
(författare)
-
Developments of Topology Optimization Methods for Additive Manufacturing involving High-cycle Fatigue
- 2023
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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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| 41. |
- Suresh, Shyam, 1990-
(författare)
-
Topology Optimization for Additive Manufacturing Involving High-Cycle Fatigue
- 2020
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)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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| 42. |
- Thore, Carl-Johan, 1981-, et al.
(författare)
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Game formulations for structural optimization under uncertainty
- 2020
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 121:1, s. 165-185
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Tidskriftsartikel (refereegranskat)abstract
- We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players -- a "designer" and "nature". The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element-discretized continua under worst-case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so-called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.
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| 43. |
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| 44. |
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| 45. |
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| 46. |
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| 47. |
- Torstenfelt, Bo, 1952-, et al.
(författare)
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Structural optimization of modular product families with application to car space frame structures
- 2006
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 32:2, s. 133-140
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Tidskriftsartikel (refereegranskat)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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| 48. |
- Wiker, Niclas, 1976-, et al.
(författare)
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The Darcy-Stokes Topology Optimization Problem
- 2006
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Ingår i: IUTAM Symposium on Topological Design Optimization of Structures, Mashines and Materials: Status and Perspectives,2005. - Dordrecht : Springer. ; , s. 551-
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Konferensbidrag (refereegranskat)abstract
- This paper treats the optimal layout of mixtures of regions of Stokes viscosity dominated flow and regions of Darcy porous flow. The problem of minimizing the potential of the state problem, representing essentially dissipation, is formulated, and can be shown to have a solution under appropriate filtering of the design. It can also be shown that the unfiltered design has a zero--one property. An area-to-point flow problem is solved for various filter radii.
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