复杂工况下土-结构体系的混合约束模态法

基于动态子结构法的原理,提出了线性-非线性混合约束模态综合法,对复杂工况下的二维地基土-箱型基础-上部剪力墙结构相互作用的非线性动力问题进行分析研究。复杂工况包含了一致黏弹性边界问题和基础与周边土体的高度非线性接触问题。依据土-结构相互作用体系存在局部非线性的特性,将体系划分为若干个线性和非线性子结构。在动力时程分析中对所有非线性子结构利用自编二次开发程序逐步提取等效特性矩阵,再与经势能判据截断准则减缩过的其他线性子结构组合后进行模态综合处理,推导出含有接触关系的子结构方程与含有一致黏弹性边界的子结构方程,最后形成复杂工况下含有各个子结构的模态综合方程。分析结果表明,混合约束模态综合法与ANSYS直接计算法求得的位移、速度、加速度、水平剪力、弯矩、层间位移角动态响应时程曲线吻合良好,证明线性-非线性混合约束模态综合法是求解复杂工况下的土-结构动力相互作用问题的有效可行方法。

Mixed constraint modal method for analysis of soil-structure system under complex conditions

Based on the principle of the dynamic substructure method, the mixed linear-nonlinear constraint modal method was proposed and applied to analysis of the two-dimensional nonlinear dynamic problem caused by the interactions between the foundation soil, box-type foundation, and upside shear wall structure under complex conditions. The complex conditions included the uniform viscoelastic boundary problem and the highly nonlinear contact problem between the foundation and surrounding soil. According to the local nonlinear feature of the soil-structure interactive system, the system was divided into several linear and nonlinear substructures. During the dynamic time history analysis, the self-compiled program based on second development was used to extract the equivalent characteristic matrices gradually for all the nonlinear substructures, which were combined with the linear substructures reduced by potential energy criterion-based truncation criterion. Then, synthesized modal processing was performed, and substructure equations considering the contact problem and involving the uniform viscoelastic boundary were deduced. Thus, a synthesized modal equation for each substructure was formed under the complex conditions. Results show that the dynamic response time history curves of the displacement, velocity, acceleration, horizontal shear force, bending moment, and interlayer displacement angle obtained by the mixed constraint modal method agree with those obtained by the ANSYS method, demonstrating that the mixed linear-nonlinear constraint modal method is an effective and feasible method of solving the soil-structure dynamic interaction problem under the complex conditions.