CAE Software-Based Implementation Technique And Program System Of Topology Optimization

Topology optimization as a hot topic of structural optimization is well known for its great flexibility over shape optimization and size optimization. For various physical problems with various objectives, mathematical models could be distinct and should be solved following different procedures. It is of great importance to develop an integrated software system that could be used to solve a wide range of optimization problems. For this reason, this dissertation presents the design of such a software system, after introducing some theoretical issues. We implement topology optimization via homogenization and SIMP. The results of structural analysis are obtained by Strand7, one popular CAE package. Further treatments are added to eliminate numerical instabilities such as checkerboard and mesh dependence. The dissertation is organized as follows:(1) The interface between CAE package and optimization implementationThe rapid development of CAE has allowed us to take advantage of commercial packages to perform structural analysis in solving optimization problems. After analyzing and comparing various interfaces between topology optimization and existing packages, we studied the implementation of topology optimization with Strand7 as the FEM analyzer. By utilizing Strand7 API, optimization package is integrated with Strand7, and a software system is successfully developed.(2) The implementation of algorithms and treatments for numerical problemsIn this system, it is employed mathematical programming methods such as feasible direction method, sequential linear programming and sequential quadratic programming, and OC (optimization criteria) method based on SIMP approach. Numerical instabilities including checkerboard and mesh dependence can be eliminated effectively with a filtering algorithm.(3) The solution of optimization with different objective functionsTo extend the applications of our software system, topology optimization is implemented with the objectives of structural strain energy, mutual strain energy and temperature. Problems with Multi load case are also discussed. The proposed software system is validated by a number of numerical examples.This research was supported by the Major Program (10332010) of the National Nature Science Foundation of China, the Major Research Plan (973 Plan) (2006CB601205), theInnovation Team (10421292) Foundation of China and the Excellent Young Teacher's Program of MOE of China (2004).