Least-weight design of perforated elastic plates for given compliance: Nonzero Poisson's ratio
Computer Methods in Applied Mechanics and Engineering
Exploiting symmetry in boundary element methods
SIAM Journal on Numerical Analysis
Boundary value problems with symmetry and their approximation by finite elements
SIAM Journal on Applied Mathematics
Optimal Design of Thin Plates by a Dimension Reduction for Linear Constrained Problems
SIAM Journal on Control and Optimization
Michell cantilevers constructed within a half strip. Tabulation of selected benchmark results
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Non-uniqueness and symmetry of optimal topology of a shell for minimum compliance
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Optimal design of a class of symmetric plane frameworks of least weight
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Discussion on symmetry of optimum topology design
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Application of topology optimization to design an electric bicycle main frame
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Symmetry and asymmetry of solutions in discrete variable structural optimization
Structural and Multidisciplinary Optimization
Symmetry properties in structural optimization: some extensions
Structural and Multidisciplinary Optimization
Exploring new tensegrity structures via mixed integer programming
Structural and Multidisciplinary Optimization
On the optimal layout of structures subjected to probabilistic or multiply loading
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
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The aim of this article is to initiate an exchange of ideas on symmetry and non-uniqueness 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 non-symmetric. The deeper reasons for the above findings are explained in the light of the above layout theory.