具有频率约束的结构拓扑优化新方法

提出一种基于拓扑组概念的实际方法，去寻求桁架的优化布局，桁架除了基频约束外，还外有应力，位移，欧拉失稳约束，考虑多种载荷情况，并假设每个原有节点的质量不变，优化的费用函数不仅包含构件费用，还包含节点费用。从原始结构着手，通过使用二进制组合算法来产生一系列具有不同节点分布的子结构，即拓扑组，优化之前需检查拓扑组的意义，如果一个拓扑组是无意义的，则被舍去，反之进入求解一个横截面积优化问题，为了避免结果奇异，在优化过程中，给被删去的构件一个微小的截面积，使一个给定的拓扑组的结构维数保持不变，使用一维抛物线插值法解决非线性约束问题，构成算法的一部分。桁架算例验证了解提出的方法的有效性。

A New Method for Truss Topology Optimization with Frequency Constraint

Abstract: This is a progress report of a project supported by NNSFC(National Natural Science Foundation of China). We present a new practical method for finding optimal topologies of trusses that are subjected to stress , displacement and Euler buckling constraints as well as fundamental frequency constraint. We take into consideration multiple loading conditions and assume the mass of each existing node to be constant. The cost function includes node cost as well as cost of truss members. Starting with a ground structure, we use binary number combinatorial algorithm to generate a number of topologies, which are a sequence of substructures with different node distributions. We examine the meaningfulness of each topology before optimizing it. We ignore the topologies that are meaningless. We optimize cross-sectional areas of truss members of meaningful topologies. In order to avoid a singular solution, we keep the dimension of the truss for a given topology unchanged by giving the truss member to be removed a tiny cross-sectional area. We use a one dimensional parabolic interpolation method to solve a non-linearly constrained problem. We give a numerical example which appears to demonstrate the efficiency of our proposed method.