Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Linear programming 1: introduction
Linear programming 1: introduction
Topology optimization of structures: A minimum weight approach with stress constraints
Advances in Engineering Software - Special issue on design optimization
Topology optimization of continuum structures with Drucker-Prager yield stress constraints
Computers and Structures
Topology optimization considering static failure theories for ductile and brittle materials
Computers and Structures
Structural and Multidisciplinary Optimization
Stress constrained topology optimization
Structural and Multidisciplinary Optimization
An optimization approach for constructing trivariate B-spline solids
Computer-Aided Design
Development of a novel phase-field method for local stress-based shape and topology optimization
Computers and Structures
Finite Elements in Analysis and Design
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
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Structural topology optimization problems have been traditionally stated and solved by means of maximum stiffness formulations. On the other hand, some effort has been devoted to stating and solving this kind of problems by means of minimum weight formulations with stress (and/or displacement) constraints. It seems clear that the latter approach is closer to the engineering point of view, but it also leads to more complicated optimization problems, since a large number of highly non-linear (local) constraints must be taken into account to limit the maximum stress (and/or displacement) at the element level. In this paper, we explore the feasibility of defining a so-called global constraint, which basic aim is to limit the maximum stress (and/or displacement) simultaneously within all the structure by means of one single inequality. Should this global constraint perform adequately, the complexity of the underlying mathematical programming problem would be drastically reduced. However, a certain weakening of the feasibility conditions is expected to occur when a large number of local constraints are lumped into one single inequality. With the aim of mitigating this undesirable collateral effect, we group the elements into blocks. Then, the local constraints corresponding to all the elements within each block can be combined to produce a single aggregated constraint per block. Finally, we compare the performance of these three approaches (local, global and block aggregated constraints) by solving several topology optimization problems.