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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Vydáno v:	Computers & structures Ročník 84; číslo 3; s. 127 - 140
Hlavní autoři:	Luo, Zhen, Chen, Li-Ping, Yang, Jingzhou, Zhang, Yun-Qing, Abdel-Malek, Karim
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Elsevier Ltd 2006 Elsevier Science
Témata:	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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Abstract	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.
AbstractList	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.
Author	Abdel-Malek, Karim Luo, Zhen Yang, Jingzhou Zhang, Yun-Qing Chen, Li-Ping
Author_xml	– sequence: 1 givenname: Zhen surname: Luo fullname: Luo, Zhen organization: Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China – sequence: 2 givenname: Li-Ping surname: Chen fullname: Chen, Li-Ping organization: Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China – sequence: 3 givenname: Jingzhou surname: Yang fullname: Yang, Jingzhou email: jyang@engineering.uiowa.edu organization: Center for Computer-Aided Design, The University of Iowa, 111 Engineering Research Facility, Iowa City, IA 52246, USA – sequence: 4 givenname: Yun-Qing surname: Zhang fullname: Zhang, Yun-Qing organization: Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China – sequence: 5 givenname: Karim surname: Abdel-Malek fullname: Abdel-Malek, Karim organization: Center for Computer-Aided Design, The University of Iowa, 111 Engineering Research Facility, Iowa City, IA 52246, USA
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Keywords	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
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Snippet	This paper presents a novel methodology, fuzzy tolerance multilevel programming approach, for applying fuzzy set theory and sequence multilevel method to...
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SubjectTerms	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
Title	Fuzzy tolerance multilevel approach for structural topology optimization
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