横截面参数化网格变形算法及耐撞性优化应用

薄壁梁结构是汽车等运载工具的主要承载构件，提高该类结构的耐撞性对乘员安全具有重要意义。然而，形状优化设计要求多组有限元模型与仿真分析，因此需要特定的建模技术或人工交互。本文提出了一种基于横截面形状的参数化网格变形方法，以实现已有有限元模型的有效重用。以给定有限元模型为输入，采用基于各向异性径向基函数网格变形方法，并结合骨架内嵌空间，可快速生成适用于仿真分析的有限元模型变体。以S形梁轴向冲击耐撞性设计为例，采用所提方法改变构件塑性铰区域的横截面形状，可快速（低于4 s）获取100组局部变形有限元模型，并采用代理模型技术和多目标遗传算法优化结构耐撞性。数值结果显示，构件耐撞性获显著提高，验证了所提参数化变形方法的有效性，展示了与一般形状优化框架的可集成性。

A mesh deformation method parameterized by cross-sections and its application to crashworthiness optimization

Thin-walled beams are major load-bearing components for vehicles like automobiles,and it is of importance to improve the structural crashworthiness for passenger safety.However,shape optimization needs multiple finite element (FE) models for simulations,requiring specific modeling techniques or human intervention.This study reports a mesh deformation method parameterized by cross-sectional profiles of the FE models.The proposed method takes as input a legacy FE model,adopts a mesh deformation method based on anisotropic radial basis functions in the skeleton-embedding space,and thus can efficiently obtain FE model variants for simulations.In the optimal crashworthiness design of an S-shaped frame,the method was used to deform the plastic hinge regions of the model.It took less than 4 seconds to generate 100 locally deformed FE models for surrogate modeling.A Kriging model and a multi-objective genetic algorithm were employed to search for the optimal shape.Numerical results demonstrated considerable improvements in the crashworthiness of the S-shaped frame,proving the effectiveness of the method and showing its integrability with general shape optimization frameworks.