二维连续体的拓扑优化设计研究

Topology Optimum Design of 2D Continum Structures

目的为二维连续体的拓扑优化提供一种基于材料弹性模量的解析敏度求解方法．利用该方法开发一套二维连续体的拓扑优化设计程序．方法用以可变弹性模量作为设计变量的新方法对连续体进行拓扑优化设计，使拓扑优化在各向同性连续材料的前提下，用解析法求解敏度。结果用研制出的二维连续体优化设计程序ＴＯＯＰ２Ｄ对一受载平面板进行拓扑形状优化，达到在最大应力基本不变的条件下减轻结构重量的优化目标．结论算例检验证明，该方法可以对二维连续体进行结构形式和几何形状综合性的结构优化设计．

Aim\ To present a new method of analytic algorithm for solving sensitivity and develop a topology optimization program based on this method Methods In topology optimization program, the analytic algorithm for solving sensitivity method was based on selecting the modulus of elasticity as the design variable, which was realized on the condition of isotropy Results The program was used to optimize a loaded plane structure and a satisfying result was obtained Conclusion The developed program (TOOP2D) can be used to optimize any loaded plane structures The method can be used with the shape optimum design method to optimize the shape and topology of structure