基于最小转换能原理的一种逐步积分法  

A STEP-BY-STEP INTEGRATION METHOD BASED ON PRINCIPLE OF MINIMUM TRANSFORMED ENERGY

作　　者：刘铁林[1] 刘钧玉[2] 

机构地区：[1]沈阳建筑大学土木工程学院,辽宁沈阳110168 [2]大连理工大学土木水利学院,辽宁大连116024

出　　处：《工程力学》2005年第2期38-42,共5页Engineering Mechanics

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：基于Benthien_Gurtin 给出的拉普拉斯空间上相应的最小转换能原理,将拉普拉斯空间上的泛函恢复到原空间后给出一个只含单重卷积形式的泛函。对此泛函相继进行空间和时间域离散分别给出了新的泛函。采用含非时间步参数的三次Hermite 插值函数逼近节点位移,给出了一种用于动力响应分析的无条件稳定逐步积分算法。通过对算法的稳定性研究,选取了参数的合适值。精度分析和数值算例表明提出的方法是一种可以应用于工程实际并具有较高精度的方法。Based on Benthien_Gurtin’s principle of minimum transformed energy in linear elastodynamics in Laplace space, functional in the form of single convolution integral is obtained by restoring the functional in the Laplace space back into the original space. By successively spatial and temporal discretization, functionals after spatial and temporal discretization are obtained respectively. Cubic Hermite interpolation functions with a non-time-step parameter are adopted to approximate the nodal displacement in local time domain. A unconditionally stable step-by-step integration method is finally presented based on the variational operation. The parameter can control the stability of the algorithm better and its optimum value is selected according to the unconditionally stable analysis. Examples show that the algorithm possesses satisfactory accuracy and it is an effective method for the investigations of dynamic response problems in practical engineering.

关 键 词：工程力学 动力响应分析 逐步积分法 最小转换能原理 非时间步参数 

分 类 号：O347[理学—固体力学] O242[理学—力学]