An approach for the topology optimization of structures composed of nonlinear beam elements under time-varying excitation is presented. Central to this approach is a hysteretic beam finite element model that accounts for distributed plasticity and axial-moment interaction through appropriate hysteretic interpolation functions and yield/capacity function, respectively. Nonlinearity is represented via the hysteretic variables for curvature and axial deformations that evolve according to first order nonlinear ordinary differential equations (ODEs), referred to as evolution equations, and the yield function. Hence, the governing dynamic equilibrium equations and hysteretic evolution equations can thus be concisely presented as a system of first-order nonlinear ODEs that can be solved using general ODE solvers without the need for linearization. The approach is applied for the design of frame structures with an objective to minimize the total volume in the domain, such that the maximum displacement at specified node(s) satisfies a specified constraint (i.e., drift limit) for the given excitation. The maximum displacement is approximated using the p-norm and thus permits the completion of the analytical sensitivities required for gradient-based updating. Several numerical examples are presented to demonstrate the approach for the design of structural frames subjected to pulse, harmonic, and seismic base excitation. Topologies obtained using the suggested, nonlinear approach are compared to solutions obtained from topology optimization problems assuming linear-elastic material behavior. These comparisons show that although similarities between the designs exist, in general the nonlinear designs differ in composition and, importantly, outperform the linear designs when assessed by nonlinear dynamic analysis.

提出了一种时变激励下非线性梁单元结构的拓扑优化方法。这种方法的核心是滞后梁有限元模型，该模型分别通过适当的滞后插值函数和屈服/承载力函数来考虑分布的可塑性和轴向矩相互作用。非线性通过曲率和轴向变形的滞后变量表示，这些变量根据一阶非线性常微分方程（ODE）（称为演化方程）和屈服函数演化。因此，可以将控制动态平衡方程和滞后演化方程简明地表示为一阶非线性ODE的系统，该系统可以使用常规ODE求解器进行求解而无需线性化。该方法被应用于框架结构的设计，其目的是使域中的总体积最小化，以使得对于给定的激励，指定节点处的最大位移满足指定约束（即，漂移极限）。最大位移使用p范数近似，因此可以完成基于梯度的更新所需的分析灵敏度。给出了几个数值示例，以说明受脉冲，谐波和地震基础激励的结构框架设计方法。使用建议的非线性方法获得的拓扑与假设线性弹性材料行为的拓扑优化问题获得的解决方案进行了比较。这些比较表明，尽管设计之间存在相似之处，