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Title of Journal: Struct Multidisc Optim

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Abbravation: Structural and Multidisciplinary Optimization

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Springer-Verlag

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DOI

10.1016/j.achaem.2015.07.163

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1615-1488

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On symmetry and nonuniqueness in exact topology o

Authors: George I N Rozvany
Publish Date: 2010/09/14
Volume: 43, Issue: 3, Pages: 297-317
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Abstract

The aim of this article is to initiate an exchange of ideas on symmetry and nonuniqueness in topology optimization These concepts are discussed in the context of 2D trusses and grillages but could be extended to other structures and design constraints including 3D problems and numerical solutions The treatment of the subject is pitched at the background of engineering researchers and principles of mechanics are given preference to those of pure mathematics The author hopes to provide some new insights into fundamental properties of exact optimal topologies Combining elements of the optimal layout theory of Prager and the author with those of linear programming it is concluded that for the considered problems the optimal topology is in general unique and symmetric if the loads domain boundaries and supports are symmetric However in some special cases the number of optimal solutions may be infinite and some of these may be nonsymmetric The deeper reasons for the above findings are explained in the light of the above layout theoryThe author is grateful to Martin Bendsoe Rafi Haftka Ming Zhou Tomasz Lewinski and Tomasz Sokol for discussing some relevant aspects of topology optimization Special thanks are due to the reviewers of this article for many useful suggestions including the proof of Conjectures 2 and 3 Financial support from OTKA Grant No K 81185 is thankfully acknowledgedSince the number of variables in this formulation is 2m for any basic solution we need 2m equality constraints eg Strang 1980 Chapter 8 some of which were originally inequalities Let the number of static equations be r and the number of zero member forces k

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Other Papers In This Journal:
  1. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics
  2. Multi-dimensional optimization of functionally graded material composition using polynomial expansion of the volume fraction
  3. Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems
  4. Single-level composite wing optimization based on flexural lamination parameters
  5. Topology optimization of composite structures with data-driven resin filling time manufacturing constraint
  6. A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods
  7. Minimum weight design of solid annular plates under an assigned limit ring load
  8. A sensitivity-based commonality strategy for family products of mild variation, with application to automotive body structures
  9. A new reliability analysis method based on the conjugate gradient direction
  10. Aircraft wing box optimization considering uncertainty in surrogate models
  11. Multidisciplinary dynamic optimization of horizontal axis wind turbine design
  12. Geometrical aspects of optimum truss like structures for three-force problem
  13. Advances in optimization of highrise building structures
  14. Topology optimization of fail-safe structures using a simplified local damage model
  15. Topology optimization of frame structures with flexible joints
  16. A concurrent subspace collaborative optimization architecture to structural synthetical optimization design
  17. Topology optimization of internal partitions in a flow-reversing chamber muffler for noise reduction
  18. Material interpolation schemes for unified topology and multi-material optimization
  19. Variational proof of optimality criteria for Michell structures with pre-existing members
  20. Drop test simulation and surrogate-based optimization of a dishwasher mechanical structure and its packaging module
  21. Resolving issues with member buckling in truss topology optimization using a mixed variable approach
  22. Adaptive infill sampling criterion for multi-fidelity optimization based on Gappy-POD
  23. A comparative study of uncertainty propagation methods for black-box-type problems
  24. Multiobjective optimization for crash safety design of vehicles using stepwise regression model
  25. A double-distribution statistical algorithm for composite laminate optimization
  26. Robust design optimization by polynomial dimensional decomposition
  27. A crossing sensitivity filter for structural topology optimization with chamfering, rounding, and checkerboard-free patterns
  28. Hybrid evolutionary algorithm and application to structural optimization
  29. Topology optimization of shell structures using adaptive inner-front (AIF) level set method
  30. Harmony search algorithm for minimum cost design of steel frames with semi-rigid connections and column bases
  31. Optimization of a contact surface
  32. A multi-objective, multidisciplinary design optimization methodology for the conceptual design of a spacecraft bi-propellant propulsion system
  33. Optimum design of a controlled cable stayed bridge subject to earthquakes
  34. Design optimization of a runflat structure based on multi-objective genetic algorithm
  35. On minimum compliance problems of thin elastic plates of varying thickness
  36. On the analytical derivation of the Pareto-optimal set with applications to structural design
  37. Hierarchical model calibration for designing piezoelectric energy harvester in the presence of variability in material properties and geometry
  38. Topology optimization of free vibrating continuum structures based on the element free Galerkin method
  39. Fracture resistance via topology optimization
  40. Analysis and optimal design of plates and shells under dynamic loads – II: optimization
  41. Approximation of the critical buckling factor for composite panels
  42. Adhesive surface design using topology optimization
  43. Optimal design of hydraulic support
  44. A modified ant colony algorithm for the stacking sequence optimisation of a rectangular laminate
  45. Topology optimization of inertia driven dosing units
  46. Shape sensitivity analysis using a fixed basis function finite element approach
  47. Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics
  48. Globally optimal benchmark solutions to some small-scale discretized continuum topology optimization problems
  49. Multi-constrained topology optimization via the topological sensitivity
  50. A multi-objective differential evolution approach based on ε-elimination uniform-diversity for mechanism design
  51. Metamodeling by symbolic regression and Pareto simulated annealing
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