A topology optimization formulation is developed to find the stiffest structure with desirable material distribution subjected to seismic loads. Finite element models of the structures are generated and the optimality criteria method is modified using a simple penalty approach and introducing fictitious strain energy to simultaneously consider both material volume and displacement constraints. Different types of shear walls with/without opening are investigated. Additionally, the effects of shear wall-frame interaction for single and coupled shear walls are studied. Gravity and seismic loads are applied to the shear walls so that the definitions provide a practical approach for locating the critical parts of these structures. The results suggest new viewpoints for architectural and structural engineering for placement of openings.

中文翻译：

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地震作用下剪力墙结构的拓扑优化

开发了拓扑优化公式，以找到承受地震载荷的具有理想材料分布的最硬结构。生成结构的有限元模型，并使用简单的惩罚方法并引入虚拟应变能以同时考虑材料体积和位移约束，从而修改了最佳准则方法。研究了带/不带开口的不同类型的剪力墙。此外，研究了剪力墙-框架相互作用对单个剪力墙和耦合剪力墙的影响。重力和地震荷载被施加到剪力墙，因此定义为定位这些结构的关键部分提供了一种实用的方法。结果为开口的建筑和结构工程提出了新的观点。