摘要
The shape optimization is studied by adopting the domain integrated method which is based on the calculus of variations during the shape design sensitivity analysis. A new method of improving the efficiency of the design velocity field analysis and the quality of the finite element method (FEM) mesh is put forward. The sensitivity analysis which is based on the calculus of variations is used in the shape optimization. The design velocity field is solved by Herrmann method. An example shows that both the quality of the FEM mesh and the efficiency of the computing of the design velocity field are improved by Herrmann method. So the effect and the efficiency of the shape optimization are guaranteed. If using sensitivity analysis which is based on the calculus of variations in the shape optimization, the sensitivity analysis can be a relatively independent module. The efficiency of computing the design velocity field and the quality of mesh will be improved by using Herrmann method.
探讨了基于变分法的敏度分析在形状优化设计中的应用 ,提出敏度分析过程中提高速度场求解效率和有限元网格质量的新方法 .在形状优化设计中采用基于变分法的敏度分析方法 ,设计速度场采用Hermann网格均匀化法进行求解 .算例表明优化过程中采用Herrmann网格均匀化法求解设计速度场 ,可以提高优化过程中网格的质量 ,速度场的求解效率也得到极大的提高从而优化的效果和效率都有明显提高 .在形状优化过程中 ,采用基于变分法的敏度分析 ,可以使敏度分析成为单独模块 ,在进行设计速度场求解时采用Herrmann法 ,使速度场求解的效率和优化过程的质量得到保证 .
