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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Bibliographic Details
Published in:Finite elements in analysis and design Vol. 47; no. 8; pp. 922 - 932
Main Authors: Tong, Liyong, Lin, Jiangzi
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.08.2011
Elsevier
Subjects:
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
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
ISSN:0168-874X, 1872-6925
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2011.03.004