基于独立连续变量和复合指数函数的位移约束平面连续体结构拓扑优化

为了进一步研究连续体结构拓扑优化模型的合理性和可行性,基于独立、连续、映射( independent continuous mapping,ICM)方法,在满足结构位移约束的条件下,通过引入复合指数形式过滤函数对位移约束下质量最小化( minimum weight with a displacement constraint,MWDC)模型进行了改进,建立了基于独立连续变量和复合指数函数的位移约束平面连续体结构拓扑优化模型,并进行了优化求解。同时,利用M语言,基于Matlab软件平台,开发了相应的拓扑优化计算程序,并针对4种典型平面连续体结构进行了数值验证,分别比较分析了体积约束下的柔顺度最小化( minimum compliance with a volume constraint,MCVC)模型、MWDC模型以及改进的MWDC模型所得到的最优拓扑结构。数值结果表明：采用复合指数形式过滤函数改进的MWDC优化模型迭代次数更少,优化求解计算效率更高。

Planar Continuum Structure Topology Optimization With Displacement Constraint Based on Independent Continuous Variables and Composite Exponential Function

To study the rationality and feasibility of the continuum structure topology optimization model, an improved minimum weight with a displacement constraint ( MWDC ) model by using exponential function was studied, which was based on the independent continuous mapping ( ICM) method. A new topology optimization model for the problem of planar continuum structure with independent continuous variables and displacement constraints was established and solved. At the same time, a calculator program was developed and compiled based on the MATLAB in accordance with the new method. In addition, four typical numerical examples were adopted to verify the presented method. The topological results by taking advantage of MCVC model, MWDC model and improved MWDC model were compared with the view of structural mass and iterative numbers. Numerical results show that there is obvious advantage to solve the problem of planar continuum structure topology optimization with the improved MWDC optimization model in terms of calculation efficiency.