Fuzzy tolerance multilevel approach for structural topology optimization

This paper presents a novel methodology, fuzzy tolerance multilevel programming approach, for applying fuzzy set theory and sequence multilevel method to multi-objective topology optimization problems of continuum structures undergoing multiple loading cases. Ridge-type nonlinear membership function...

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Veröffentlicht in:Computers & structures Jg. 84; H. 3; S. 127 - 140
Hauptverfasser: Luo, Zhen, Chen, Li-Ping, Yang, Jingzhou, Zhang, Yun-Qing, Abdel-Malek, Karim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Elsevier Ltd 2006
Elsevier Science
Schlagworte:
Computational techniques
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Fuzzy set theory
Mathematical methods in physics
Multi-objective
Numerical instabilities
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Tolerance multilevel programming approach
Topology optimization
Topology optimization
Fuzzy set theory
Numerical instabilities
Multi-objective
Tolerance multilevel programming approach
Geometrical shape
Multiobjective programming
Linear programming
Fuzzy programming
Topology
Fuzzy set
Modeling
Optimization
Weight
Fuzzy logic
Uncertain system
Sequential method
Non linear effect
Numerical stability
Structural analysis
ISSN:0045-7949, 1879-2243
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Zusammenfassung:This paper presents a novel methodology, fuzzy tolerance multilevel programming approach, for applying fuzzy set theory and sequence multilevel method to multi-objective topology optimization problems of continuum structures undergoing multiple loading cases. Ridge-type nonlinear membership functions in fuzzy set theory are applied to embody fuzzy and uncertain characteristics essentially involved by the objective and constraint functions. Sequence multilevel method is used to characterize the different priorities of loading cases at different levels making contribution to the final optimum solution, which is practically beneficial to reduce the subjective influence transferred by using weighted approaches. The solid isotropic material with penalization (SIMP) is adopted as the density-stiffness interpolation scheme to relax the original optimization problem and indicate the dependence of material properties with element pseudo-densities. Sequential linear programming (SLP) is used as the optimizer to solve the multi-objective optimization problem formulated using fuzzy tolerance multilevel programming scheme. Numerical instabilities, such as checkerboards and mesh dependencies are summarized and a duplicate sensitivity filtering method, in favor of contributing to the mesh-dependent optimum designs, is subsequently proposed to regularize the singularity of the optimization problem. The validation of the methodologies presented in this work has been demonstrated by detailed examples of numerical applications.
Bibliographie:ObjectType-Article-2
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2005.10.001