Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity.

*(English)*Zbl 1352.74467Summary: The present work addresses shape sensitivity analysis and optimization in two-dimensional elasticity with a regularized isogeometric boundary element method (IGABEM). Non-uniform rational B-splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations. With the advantage of tight integration of design and analysis, the application of IGABEM in shape optimization reduces the mesh generation/regeneration burden greatly. The work is distinct from the previous literatures in IGABEM shape optimization mainly in two aspects: (1) the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations, eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives, which were the main implementation difficulty in IGABEM, and (2) although based on the same Computer Aided Design (CAD) model, the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh, thus achieving a balance between less design variables for efficiency and refined mesh for accuracy. This technique was initially used in isogeometric finite element method and was incorporated into the present IGABEM implementation.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

65N38 | Boundary element methods for boundary value problems involving PDEs |

49M25 | Discrete approximations in optimal control |

65D07 | Numerical computation using splines |

74B05 | Classical linear elasticity |

##### Keywords:

shape optimization; isogeometric boundary element method; regularized boundary integral equations##### Software:

XFEM
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\textit{H. Lian} et al., Int. J. Numer. Methods Eng. 106, No. 12, 972--1017 (2016; Zbl 1352.74467)

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