基频约束的框架结构拓扑优化

Topology Optimization for Frame Structures With Base Frequency Constraint

目前考虑频率约束的拓扑优化主要集中在连续体结构,以框架结构为研究对象的较少,为了得到满足频率约束的最优框架拓扑结构,需要对满足频率约束的框架结构拓扑优化进行研究.基于独立连续映射(independent,continuous and mapping,ICM)方法,将0-1型离散拓扑变量转化为[0,1]区间上的连续变量,建立了以重量最小为目标、基频为约束的框架结构拓扑优化模型.在对框架结构频率约束进行性态研究的基础上,引入2组不同的幂函数作为过滤函数,将频率约束近似显式化.将目标和约束均表示为拓扑变量的一阶泰勒展开式,建立线性规划模型,采用运动极限控制拓扑变量步长,避免迭代震荡,保证优化精度.数值算例表明:基于ICM方法的线性规划模型可高效解决基频约束下的框架结构拓扑优化问题.

The topology optimization with frequency constraints is mainly focused on the continuum structures currently,however,the researches on topology optimization for frame structures with frequency constraints are relatively less. To obtain the optimal frame structures with frequency constraint,it is necessary to conduct research on the topology optimization for frame structures with frequency constraint.Based on ICM（ independent,continuous and mapping） method,the zero-one type discrete topology variables are transformed into the continuous topology variables between zero and one. A continuous topology optimization model is established to minimize the weight with frequency constraint. Based on the behavior research of frequency constraints for frame structures, two different power functions were introduced as the filter function to explicit the frequency constraints approximately. The object and constraints were both expressed as the first-order Taylor expansions of topology variables to establish the linear programming model. The movable limits were adopted to control the step size of topology variables in order to avoid the iterative oscillation and ensure the optimization accuracy. The numerical examples show that the linear programming model based on ICM method can efficiently solve the topology optimization problem with base frequency constraint for frame structures.