多位移约束下渐进结构拓扑优化设计

Evolutionary structural topology optimization designs with multiple displacement constraints

渐进结构优化方法通用性好,程序实现简单,能获得一系列黑白分布的优化拓扑,但它难于求解多约束拓扑优化问题。为了将渐进结构优化方法拓展到求解多约束拓扑优化问题,针对多位移约束下结构体积最小的结构拓扑优化问题,采用有理分式材料模型,建立刚度与拓扑变量的关系;构建求解多约束拉格朗日乘子的近似优化问题模型和其光滑对偶算法;而后,给出单元灵敏度数计算公式和渐进结构优化算法;最后给出了两个验证算例,所得结果验证了该方法的正确性和有效性。

The Evolutionary Structural Optimization（ESO） method is easily utilized to be programmed, and is of wide engineering applications, and may be adopted to obtain the optimum structure with black and white distribution material property. However, it＇ s difficult to solve the problem of muhi-constrained topology optimization by using it. To extend this method to the case of multi- constrained topology optimization, for the problem of topology optimization with multiple displacement constraints, the relationship between the stiffness and the topology variables is built by using the Rational Approximation for Material Properties（ RAMP）, and a series of approximate models and a smooth dual algorithm are constructed to solve Lagrange multipliers. Then, the calculation formula of element sensitivities and a novel evolutionary structural optimization algorithm are given. Finally, two examples are presented to demonstrate the validity and effectiveness of the proposed method.