TY - JOUR
T1 - Fuzzy tolerance multilevel approach for structural topology optimization
AU - Luo, Zhen
AU - Chen, Li Ping
AU - Yang, Jingzhou
AU - Zhang, Yun Qing
AU - Abdel-Malek, Karim
N1 - Funding Information:
The research work is supported by the National “863” High-Tech Development Project of China, under grant No. 2003AA001031, and the National “973” Key Fundamental Research Project of China, under grant No. 2003CB716207. The authors would like to show their appreciation to the anonymous reviewers for their insightful comments.
PY - 2006/1
Y1 - 2006/1
N2 - 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.
AB - 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.
KW - Fuzzy set theory
KW - Multi-objective
KW - Numerical instabilities
KW - Tolerance multilevel programming approach
KW - Topology optimization
UR - http://www.scopus.com/inward/record.url?scp=28544452264&partnerID=8YFLogxK
U2 - 10.1016/j.compstruc.2005.10.001
DO - 10.1016/j.compstruc.2005.10.001
M3 - Article
AN - SCOPUS:28544452264
SN - 0045-7949
VL - 84
SP - 127
EP - 140
JO - Computers and Structures
JF - Computers and Structures
IS - 3-4
ER -