土-结构非线性相互作用混合约束模态实施方法

第一作者姜忻良男，博士，教授，博士生导师，1951年生

邮箱：jiangxinliang@126.com

土-结构非线性相互作用混合约束模态实施方法

姜忻良，张海顺

(天津大学建筑工程学院滨海土木工程结构与安全教育部重点实验室，天津300072)

摘要：分析、探讨线性-非线性混合约束模态综合法用于土-结构相互作用的动力分析实施方法。据结构存在局部非线性特性，提出对整体结构划分为若干个线性、非线性子结构，对线性子结构只需一步提取特性矩阵并进行方程降阶，而对非线性子结构则逐步提取降阶后的等效特性矩阵。通过组装各子结构达到对整体结构特性矩阵的降阶处理。对非线性子结构凭借在小段时间Δt内利用分段等效线性化手段，通过ANSYS二次开发工具UPFs编辑写成可执行程序文件，并与MATLAB联立计算，实现特性矩阵提取。结果表明，该方法求得结构的各阶频率和动态响应时程曲线与ANSYS直接计算吻合良好。可逐步提取等效弹塑性特性矩阵，为采用变化的特性矩阵对结构进入塑性阶段深层次分析研究提供有效方法。

关键词：土-结构相互作用；约束模态综合法；势能判据截断准则；局部非线性；弹塑性刚度矩阵

收稿日期：2013-11-08修改稿收到日期：2014-03-31

中图分类号:TU317.1文献标志码：A

基金项目：国家“863”计划资助项目(2013AA040103)；河南省高等学校精密制造技术与工程重点学科开放实验室开放基金资助(PMTE201308A)

Mixed constraint modal method for nonlinear soil-structure interaction

JIANGXin-liang，ZHANGHai-shun(School of Civil Engineering, Tianjin University/Key Laboratory of Coastal Civil Engineering Structure and Safety, Ministry of Education, Tianjin 300072, China)

Abstract:Here, the implementation technique of the linear-nonlinear mixed constraint modal synthesis method was analyzed for soil-structure dynamic interaction. According to the local nonlinear feature, the whole structure was divided into several linear and nonlinear sub-structures. Those linear sub-structures just required only one step to extract the characteristic matrices and reduce equation order, while for nonlinear sub-structures, they needed step by step to extract the reduced order equivalent characteristic matrices. By assembling the above sub-structures, the order of the whole structural characteristic matrix was reduced. For the nonlinear sub-structures, using the piecewise equivalent linearization method within a small time interval Δt, an executable program file to extract the characteristic matrices was edited by means of ANSYS secondary development tools UPFs and the simultaneous computation was done with MATLAB. Results show that the modal frequencies and dynamic response time history curves obtained with the above method agree well with those obtained with ANSYS direct calculation; using this method can extract the equivalent elastic-plastic feature matrices step by step, and it provides an effective tool for further studying the plastic phase dynamic analysis of structures with time-varying characteristic matrices.

Key words:soil-structure interaction; constrained modal synthesis method; potential energy mode cut-off criterion; local nonlinear; elastic-plastic stiffness matrix

解决地基土-结构动力相互作用(SSI)问题时，有限元法为离散化强有力工具，但因其自由度太多致直接求解十分困难。……