Structural topology optimization with implicit design variable—optimality and algorithm
This paper presents a novel formulation for structural topology optimization in which both cost function and constraints are expressed in terms of an implicit design variable—the iso-line/surface threshold of a characteristic response function, such as a strain or mutual strain energy density functi...
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| Veröffentlicht in: | Finite elements in analysis and design Jg. 47; H. 8; S. 922 - 932 |
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| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
01.08.2011
Elsevier |
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| ISSN: | 0168-874X, 1872-6925 |
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| Abstract | This paper presents a novel formulation for structural topology optimization in which both cost function and constraints are expressed in terms of an implicit design variable—the iso-line/surface threshold of a characteristic response function, such as a strain or mutual strain energy density function. A new material representation model is developed to implicitly describe material usage in a given design domain in terms of one implicit design variable. Based on the Karush–Kuhn–Tucker (KKT) necessary conditions, optimality criteria for finding solutions are established and then employed to develop a simple algorithm for one-material minimum mean compliance and compliant mechanism problems. The algorithm consists of sequentially moving iso-surface threshold (MIST) of chosen characteristic response function. Numerical examples are then presented to validate the proposed algorithm MIST for the minimum mean compliance, compliant mechanism, and fully stressed design problems. |
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| AbstractList | This paper presents a novel formulation for structural topology optimization in which both cost function and constraints are expressed in terms of an implicit design variable - the iso-line/surface threshold of a characteristic response function, such as a strain or mutual strain energy density function. A new material representation model is developed to implicitly describe material usage in a given design domain in terms of one implicit design variable. Based on the Karush-Kuhn-Tucker (KKT) necessary conditions, optimality criteria for finding solutions are established and then employed to develop a simple algorithm for one-material minimum mean compliance and compliant mechanism problems. The algorithm consists of sequentially moving iso-surface threshold (MIST) of chosen characteristic response function. Numerical examples are then presented to validate the proposed algorithm MIST for the minimum mean compliance, compliant mechanism, and fully stressed design problems. |
| Author | Tong, Liyong Lin, Jiangzi |
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| Keywords | Structural topology optimization Algorithm Karush–Kuhn–Tucker conditions Optimality criteria Compliant mechanism Geometrical shape Karush-Kuhn-Tucker conditions Constraint Strain energy Energy function Energy density Topology Modeling Optimization Characteristic function Finite element method Design process Mechanism synthesis Karush Kuhn Tucker method Optimality condition Cost function Optimality criterion Density function Structural analysis |
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| SubjectTerms | Algorithm Algorithms Calculus of variations and optimal control Design engineering Exact sciences and technology Fundamental areas of phenomenology (including applications) Karush–Kuhn–Tucker conditions Mathematical analysis Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Optimality criteria Physics Response functions Sciences and techniques of general use Solid mechanics Static elasticity (thermoelasticity...) Strain Structural and continuum mechanics Structural topology optimization Thresholds Topology optimization |
| Title | Structural topology optimization with implicit design variable—optimality and algorithm |
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