求解材料非线性系统动力响应的新方法

Novel Approach for Solving Dynamic Response of Material Nonlinear System

本文有两方面的内容:(1)结合解析方法和数值方法优点,本文提出求解材料非线性系统动力分析的新方法,并推导了相关公式。新方法利用了分段Lagrange插值多项式和Duhamel积分来求解非线性系统动力响应。当动力荷载表示为分段多项式时,在本构关系的每一个直线段上,可以求出Duhamel积分的精确解。再考虑到刚度转换点上位移和速度的连续性,我们就可以在整个时域上给出非线性系统动力响应的精确解。由于有精确解作为基础,因而和逐步积分法相比,本文方法不但具有较高的计算精度,大大减少了计算工作量,而且彻底地避免了许多数值方法所常遇到的收敛性和稳定性问题。(2)本文提出在原有单层工业厂房结构的侧面加设斜拉杆的抗震加固改造方案,并将此计算方法应用于它的抗震加固计算中。

There are two contents in this paper:(1)Combining the merits of analytic method and numerical method,this paper proposed a novel approach for dynamic analysis of material non linear systems with the related form ulae derived.The proposed approach uses the piecewise Lagrange interpolating polynomial and the Duhamel integral for solution of dynamic response of nonl inear system.When a dynamic load is e xpressed as a piecewise polynomial,the Duhamel integral can be analytically solved in every branch of the constitutive relationship.Additionally,by employing the continuity of displacement and v elocity on the transitional point of the stiffness,an exact solution of n onlinear dynamic response can be given on the whole of the time domain.Because it is based on analytic solution,the prop osed method not only offers much higher ac curacy and requires less computatio nal effort than the traditional step-by-step integration solution technique,but also thoroughly avoids the problem s of convergence and stability encou ntered in many numerical procedures.(2)The seismic strengthening scheme of a single-story industrial building by adding lateral bracings was proposed,and the proposed computational approach was appl ied to the evaluation of the strength ened single-story industrial building.