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Structural shape optimization by IGABEM and particle swarm optimization algorithm. (English) Zbl 1403.74234
Summary: In this paper, a new approach is developed for structural shape optimization, which consists in coupling the particle swarm optimization (PSO) algorithm and the isogeometric boundary element method (IGA-BEM). The IGA-BEM is based on the combination of the isogeometric analysis (IGA) and the boundary element method (BEM), where Non-Uniform Rational B-Splines (NURBS) are employed as shape functions for geometry parameterization and approximation of the field variables. The method inherits the main advantage of the IGA-based shape optimization, i.e., the control points are used as design variables, thus the design model, analysis model and optimization model are uniformly described with the NURBS, providing easy communication between the three models and resulting in a smooth optimized boundary. However, the main feature of the proposed method is the use of PSO, which provides an attractive gradient-free alternative to complicated sensitivity analysis. The efficiency and accuracy of the proposed approach are demonstrated through four 2D shape optimization examples.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74P10 Optimization of other properties in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
49M25 Discrete approximations in optimal control
65D07 Numerical computation using splines
90C59 Approximation methods and heuristics in mathematical programming
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