基于Fourier级数展开的Laplace数值逆变换  

NUMERICAL INVERSION OF LAPLACE TRANSFORS IN VISCOELASTIC PROBLEMS BY FOURIER SERIES EXPANSION

作　　者：彭凡[1] 陈耀军[1] 刘一凡[1] 傅衣铭[1] 

机构地区：[1]湖南大学力学与航空航天学院,长沙410082

出　　处：《力学学报》2008年第2期215-221,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：湖南省自然科学基金(05JJ30008)

摘　　要：研究了基于Fourier级数展开的Laplace数值逆变换在黏弹性力学问题中的有效应用,这类方法的关键涉及计算参数的选择.构造了优化模型,对计算参数寻优,以黏弹性层合圆柱薄壳在轴压下的准静态变形以及受突加内压黏弹性圆筒在平面应变条件下的动应力响应为例阐述方法的应用.结果表明:通过优化模型能有效地确定计算参数;且当反演参数与计算时间的乘积在一定范围内时,Fourier级数展开法均能给出一致的结果,由此,可按与计算时间成反比的关系来确定反演算法中的参数.In this paper, the effective application of numerical inversion of Laplace transforms, based on Fourier series expansions developed by Dubner, Abate and Durbin, is studied for problems of viscoelastic mechanics. A crucial free parameter is involved in this sort of method and required to be reasonably valued for particular application in advance since its improper choice leads to obvious errors. An optimal model to determine the free parameter is constructed in the paper and its applicability is validated by the numerical inversion of two types of simple functions. As examples to illustrate the practical implementation of proposed method, the quasi-static and dynamic analysis, within the scope of axisymmetric problem, are performed for viscoelastic laminated circular cylindrical shells under uniformly axial pressure and viscoelastic cylinder subjected to inner pressure with abrupt loading respectively. Numerical experiments show that the optimal model yields valid free parameter, and the production of free parameter and calculation time t lies in a definite range. Also it is concluded that the free parameter can be set to be inversely proportional to t with the proportional coefficient chosen among an effective range or determined directly by the result from optimal model for specific calculation time, and the range of this proportional coefficient is considered to be irrelevant to parameter T.

关 键 词：黏弹性 Laplace数值反演 优化 计算参数 准静态响应 动态响应 

分 类 号：O302[理学—力学] O177.6