论文部分内容阅读
提出了一种基于位移约束的类周期性连续体结构拓扑优化设计的方法。为了获得类周期性结构的最优拓扑,将优化的结构区域划分成若干个子区域;为了解决目标函数振荡问题,在每一迭代步形成并引入变位移约束限,以单元相对密度指数幂的倒数作为设计变量,建立了位移约束的显式近似式,并形成了以结构质量作为目标函数、以位移作为约束条件的类周期性结构拓扑优化近似模型;本文通过改进对偶求解方法,建立了拉格朗日乘子迭代求解公式;引入虚拟子域设计变量,建立了类周期性结构各子区域单元设计变量之间的联系,满足了指定的类周期性约束条件,并推导出了设计变量迭代公式;最后给出了梁结构拓扑设计和双坡梯形屋钢屋架设计的算例。结果表明:随着周期数的增加,子结构尺寸对最优拓扑的影响减弱;优化迭代过程中没有目标函数振荡现象。以上结果验证了本文方法的可行性和有效性。
A method of topological optimization design for quasi-periodic continuum structure based on displacement constraints is proposed. In order to obtain the optimal topology of the quasi-periodic structure, the optimized structure region is divided into several sub-regions. In order to solve the objective function oscillation problem, a constrained displacement transformation is formed and introduced at each iteration step, taking the inverse of the exponential power of unit relative density As design variables, an explicit approximation of displacement constraints was established and a topology approximation model of quasi-periodic structure with structure quality as objective function and displacement as constraint condition was established. In this paper, by improving the dual solution method, Longday multiplier iterative solution formula; the introduction of virtual subdomain design variables, the establishment of the periodic structure of the sub-regional unit design variables to meet the specified periodic constraints, and deduced the design variable iteration formula Finally, some examples of the topological design of beam structure and the design of double-slope trapezoidal steel truss truss are given. The results show that with the increase of the number of cycles, the influence of substructure size on the optimal topology is weakened and there is no objective function oscillation in the optimization iteration process. The above results verify the feasibility and effectiveness of the proposed method.