基于等几何边界元法和粒子群优化算法的结构形状优化

STRUCTURAL SHAPE OPTIMIZATION BY ISOGEOMETRIC BOUNDARY ELEMENT METHOD

等几何边界元法是将计算机辅助几何设计(CAGD)中描述几何边界的非均匀有理B样条(NURBS)基函数作为边界元法中的形函数。该方法不仅能精确地描述几何边界,且几何设计、仿真分析和形状优化采用统一的数学描述即NURBS,从而避免了重复地划分网格和优化中的网格畸变问题,提高设计、仿真和优化效率。本文将等几何边界元法和粒子群优化算法相结合,讨论了二维线弹性结构的形状优化。相对基于梯度的优化算法,无梯度的粒子群优化算法可以避免繁杂的敏感性分析过程,使优化的实现过程更为简便。数值算例验证了基于粒子群优化算法的等几何边界元法在结构形状优化中的有效性和精度。

In Isogeometric boundary element method(IGA-BEM), Non-Uniform Rational B-Splines(NURBS) which are used for describing the geometric boundary in a computer-aided geometric design(CAGD) are employed as shape functions of Boundary Element Method. IGA-BEM not only can accurately describe the geometric boundary, but also unify the design model, analysis model and optimization model, so it can avoid the repeated meshing and mesh distortion problems in the optimization process and it also can improve the efficiency of the design, calculation and optimization. In this article IGA-BEM is combined with particle swarm optimization(PSO) to study the shape optimization of two-dimensional linear elastic structure. Compared with the gradient-based optimization algorithms, gradient-free PSO algorithm can avoid the complicated sensitivity analysis process and make the optimization process easier. The efficiency and accuracy of the combined isogeometric boundary element method-PSO are demonstrated through two shape optimization examples.