The purpose of this paper is to present a simplified nonlinear equations-model that is intended to design shape memory alloy (SMA) dampers in three-dimensional structures of unsymmetrical-plan and in yielding shear-frames. The equations-model is based on a schematic idealization of the SMA damper's hysteretic behavior and the structure's transient tangent stiffness matrix, which corresponds to yielding shear-frames, and is commensurate with structural design methodologies. As of today, there are very few seismic design methodologies that use SMA dampers. In this paper, the analytical equations-model is implemented in a seismic retrofit search algorithm modified for SMA dampers. The algorithm sequentially places the SMA dampers at the story with the maximum interstory drift gain magnitude, calculated using the transfer function matrix between the ground acceleration components and the frames' interstory drifts. The transfer function matrix stems from a linear state-space formulation, but the tangent stiffness matrix is nonlinear. In order to cater to this issue, a new iterative approach suggests updating the tangent stiffness matrix in accordance with the transfer function matrix's peak interstory drift magnitudes – until the tangent stiffness matrix converges. A numerical example shows that the iterative process takes no more than two iterations.

本文的目的是提出一种简化的非线性方程模型，该模型旨在设计非对称平面三维结构和屈服剪切框架中的形状记忆合金（SMA）阻尼器。方程模型基于SMA阻尼器的滞回特性和结构的瞬态切线刚度矩阵的理想化原理，该矩阵对应于屈服剪切框架，并与结构设计方法相对应。到目前为止，很少有使用SMA阻尼器的抗震设计方法。在本文中，解析方程模型是在针对SMA阻尼器修改的地震改造搜索算法中实现的。该算法按顺序将SMA阻尼器放置在具有最大层间漂移增益幅度的楼层上，使用地面加速度分量和框架的层间漂移之间的传递函数矩阵来计算。传递函数矩阵源自线性状态空间公式，但切线刚度矩阵是非线性的。为了解决这个问题，一种新的迭代方法建议根据传递函数矩阵的峰值层间漂移量来更新切线刚度矩阵，直到切线刚度矩阵收敛为止。数值示例表明，迭代过程最多进行两次迭代。一种新的迭代方法建议根据传递函数矩阵的峰值层间漂移量来更新切线刚度矩阵，直到切线刚度矩阵收敛为止。数值示例表明，迭代过程最多进行两次迭代。一种新的迭代方法建议根据传递函数矩阵的峰值层间漂移量来更新切线刚度矩阵，直到切线刚度矩阵收敛为止。数值示例表明，迭代过程最多进行两次迭代。