A topology optimization schema employing a condensation method for nonlinear frame structures with supplemental mass subjected to time‐varying excitation is presented. In the context of the design of structural frames, in certain applications, the supplemental mass can be order(s) of magnitude larger than the mass of the system itself. Thus, condensing the system of governing equations to only those associated with the supplemental mass, reduces the complexity and computational cost of the dynamic analysis and thus the optimization process. In addition to considering material nonlinearity, distributed plasticity, and multiaxial interactions, the hysteretic beam finite element (FE) model employed in this study has constant elastic stiffness and hysteretic matrices facilitating a Guyan‐type condensation of the nonlinear dynamic equations. Furthermore, the nonlinear dynamic equations and element evolution equations of hysteretic FE modeling are concisely presented as a system of first‐order nonlinear ordinary differential equations (ODEs) that can be solved using general ODE solvers. The schema is demonstrated on various design problems considering different arrangements of supplemental mass, where the objective is to minimize the volume of the structure subject to maximum displacement constraint using a single p‐norm.

中文翻译：

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补充质量的非线性结构框架采用凝聚法的拓扑优化

提出了一种采用缩合方法的非线性框架结构的拓扑优化方案，该非线性框架结构具有随时间变化激励的补充质量。在结构框架的设计中，在某些应用中，补充质量的数量级可以比系统本身的质量大几个数量级。因此，将控制方程式的系统浓缩为仅与补充质量相关联的方程式，可以减少动态分析的复杂性和计算成本，从而减少优化过程。除了考虑材料的非线性，分布的可塑性和多轴相互作用外，本研究中使用的滞回梁有限元（FE）模型还具有恒定的弹性刚度和滞回矩阵，有助于非线性动力学方程的Guyan型凝聚。此外，作为一阶非线性常微分方程（ODE）的系统，简明地提出了滞后FE建模的非线性动力学方程和元素演化方程，可以使用常规ODE求解器进行求解。该方案针对考虑了不同附加质量布置的各种设计问题进行了演示，其目的是使用单个p范数最小化受最大位移约束的结构的体积。