Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm

In the design of functionally graded materials, bi-directional design offers greater design freedom than the typical single-direction approach. This paper studies the shape and size design of variable-thickness bi-directional functionally graded plates (2D-FGPs) with multi-objective optimization. A...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 366; S. 113017
Hauptverfasser: Wang, Chao, Koh, Jin Ming, Yu, Tiantang, Xie, Neng Gang, Cheong, Kang Hao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.07.2020
Elsevier BV
Schlagworte:
Algorithms
Basis functions
Bi-directional functionally graded plates
Design optimization
Functionally gradient materials
Generalized iso-geometrical analysis
GIGA
IMOPSO
Mapping
Material distribution
Mechanical properties
Multiple objective analysis
Mutation
Optimization algorithms
Pareto optimization
Particle swarm optimization
Plates
Resonant frequencies
Shape optimization
Shear deformation
Material distribution
IMOPSO
Bi-directional functionally graded plates
Particle swarm optimization
GIGA
Generalized iso-geometrical analysis
ISSN:0045-7825, 1879-2138
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Zusammenfassung:In the design of functionally graded materials, bi-directional design offers greater design freedom than the typical single-direction approach. This paper studies the shape and size design of variable-thickness bi-directional functionally graded plates (2D-FGPs) with multi-objective optimization. A method integrating generalized iso-geometrical analysis (GIGA) and an improved multi-objective particle swarm optimization algorithm (IMOPSO) is proposed, with numerous technical advantages. B-spline basis functions in two dimensions are used to robustly represent the volume fraction distribution, with volume fraction and shape profile at control points located along the plane set to be design variables. The mechanical behavior of the 2D-FGPs is treated with a third-order shear deformation theory and a non-uniform rational basis spline (NURBS)-based GIGA scheme. The IMOPSO algorithm incorporates chaotic sequence mapping, a diversity feedback mechanism, and a hybrid mutation mechanism to mitigate premature convergence and enhance evolution of the Pareto frontier. A number of test examples are provided, on square, circular, and gear FGPs with various loading configurations, optimizing for natural frequency and mass. •GIGA–IMOPSO method for simulating and optimizing variable-thickness 2D-FGPs.•Generalized geometric analysis (GIGA) based on third-order shear deformation theory.•Improved multi-objective particle swarm optimization algorithm (IMOPSO).•Test examples on square, circular, and gear FGP; different loading configurations.•Presented approach shown to outperform other methods.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2020.113017