一种基于位移型Gurtin变分原理的逐步积分法  

Step-by-step Integration Method Based on Gurtin Variational Principle of Displacement Model

作　　者：宋立娜[1] 李勇军[1] 

机构地区：[1]辽宁工学院土木建筑系,辽宁锦州121001

出　　处：《辽宁工学院学报》2006年第1期56-59,共4页Journal of Liaoning Institute of Technology(Natural Science Edition)

基　　金：辽宁省科技厅博士起动基金资助项目(20021070);辽宁省教育厅科学研究计划资助项目(202152047)

摘　　要：本文基于位移型Gurtin变分原理,利用经过空间离散后的只含单重卷积形式的泛函,在局部时间域上采用初位移、初速度和末位移、末加速度同时加入一种非时间步参数的插值函数形式对时间域进行离散,给出了一种计算结构动力响应的逐步积分法。对于基于位移型Gurtin变分原理建立的数值算法,采用双参数θ和α能够有效地控制算法的稳定性。文中通过对该计算格式的稳定性研究,确定了合适的非时间步参数α的值以及数值计算时所采用的θ值。精度分析和数值算例表明本文方法具有较高精度,是一种适合于研究结构动力响应问题的时程分析方法。Based on Gurtin variational principle of displacement model, a kind of unconditionally stable step-by-step integration method was presented. A single convolution integral functional was done after spatial discretization operation was adopted. For the temporal discretization, the interpolation function that consists of initial displacement, initial velocity, later instant displacement, and later instant acceleration with a non-time-step parameter α in them was used to approximate the modal, displacements within local time domain. The introduction of two parameters θ and a can effectively control the stability of the new algorithm obtained from Gurtin variational principle of displacement model. The optimum values of non-time-step parameter α and parameter θ are determined by the stability analysis of the new algorithm. Accuracy analysis and numerical examples show that the new algorithm possesses satisfying accuracy, and is an effective step-by-step integration method for the calculations of dynamic response in practical engineering.

关 键 词：位移型Gurtin变分原理 非时间步参数 逐步积分法 动力响应分析 

分 类 号：O347[理学—固体力学] O242[理学—力学]