Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics

Rozvany, G. I. N.

doi:10.1007/s001580050174

Cited by 468 publications

(219 citation statements)

References 65 publications

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“…the distribution or layout of material inside) of a design domain subjected to loads and boundary conditions, so as to extremize one or more objectives. Recent research in topology optimization has been in the development of finite element based numerical methods as they can deal with complex topologies involving different types of materials [15]. Among numerical methods, especially popular are the so-called ISE (Isotropic Solid or Empty) topologies, in which blocks of finite elements (called ground 00 00 00 00 00 00 00 00 00 00 11 11 11 11 11 11 11 11 11 11 elements) can either contain the given isotropic material (i.e.…”

Section: Results Ii: Design Features Through Superpositionmentioning

confidence: 99%

Temporal Innovization: Evolution of Design Principles Using Multi-objective Optimization

Bandaru

Deb

2015

Lecture Notes in Computer Science

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Abstract. Multi-objective optimization yields multiple solutions each of which is no better or worse than the others when the objectives are conflicting. These solutions lie on the Pareto-optimal front which is a lower-dimensional slice of the objective space. Together, the solutions may possess special properties that make them optimal over other feasible solutions. Innovization is the process of extracting such special properties (or design principles) from a trade-off dataset in the form of mathematical relationships between the variables and objective functions. In this paper, we deal with a closely related concept called temporal innovization. While innovization concerns the design principles obtained from the trade-off front, temporal innovization refers to the evolution of these design principles during the optimization process. Our study indicates that not only do different design principles evolve at different rates, but that they start evolving at different times. We illustrate temporal innovization using several examples.

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Section: Results Ii: Design Features Through Superpositionmentioning

confidence: 99%

Temporal Innovization: Evolution of Design Principles Using Multi-objective Optimization

Bandaru

Deb

2015

Lecture Notes in Computer Science

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“…Most general problems involve material distribution in a design space with given loads and boundary conditions. The design space can be analysed using the finite element method (Rozvany, 2001) or structure-specific methods with the optimisation process carried out by several techniques such as topological-derivatives, level-sets or genetic algorithm.…”

Section: Structural Optimisation Gamentioning

confidence: 99%

A Retrospective Analysis of the Evolution of Pratt Trusses in Indiana

Fehér

Baranyai

2017

Period. Polytech. Arch.

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“…The optimization algorithm, i.e., the steepest descent, is based on the gradient at the current point in the design space, thus it sees no global information about the objective function and constraints, and all improvements of the structure is made based on local information at the current point in the design space. Therefore, it cannot perform a global search [28].…”

Section: Sensitivity Of the Perimeter Term And Volume Constraintmentioning

confidence: 99%

Stiffness optimization of geometrically nonlinear structures and the level set based solution

Xia

Shi

2016

Int. J. Simul. Multisci. Des. Optim.

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-Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.

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Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics

Cited by 468 publications

References 65 publications

Temporal Innovization: Evolution of Design Principles Using Multi-objective Optimization

Temporal Innovization: Evolution of Design Principles Using Multi-objective Optimization

A Retrospective Analysis of the Evolution of Pratt Trusses in Indiana

Stiffness optimization of geometrically nonlinear structures and the level set based solution

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