Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
The relationship between goal programming and fuzzy programming
Fuzzy Sets and Systems
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
A hybrid fuzzy-goal programming approach to multiple objective decision making problems
Fuzzy Sets and Systems
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Multi-objective optimization of structures topology by genetic algorithms
Advances in Engineering Software - Special issue on evolutionary optimization of engineering problems
A level set method for structural shape and topology optimization using radial basis functions
Computers and Structures
A hybrid topology optimization methodology combining simulated annealing and SIMP
Computers and Structures
Interval multi-objective optimisation of structures using adaptive Kriging approximations
Computers and Structures
Robust topology optimisation of bi-modulus structures
Computer-Aided Design
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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.