二维粘弹性结构动力响应的边界元法分析

Boundary Element Analysis of Transient Response for Two—dimensional Viscoelastic Structures

本文应用直接边界单元法结合Laplace变换和反变换技术,建立了粘弹性结构动态响应分析的一个较好的数值求解方法。在Laplace变换区域中,应用边界单元法求出相应的变换解,然后再应用改进的Dufbh方法进行Laplace反变换,求出实时区域内的解。根据磨光函数理论,引入了Lanczos因子,改进了Durbin数值反变换方法的计算精度和效率。计算证明,本方法具有计算精度高,数据准备简单,所需计算机的容量少等优点。

This paper developes a boundary element method for transient response of two—dimensional viscoelastic structures in terms of the Laplace transform and inversion technique. By applying the boundary element method. the transform solution can be obtained in Laplace domain. Then an improved Durbin's numerical inversion method is applied for inversion and the real time solution can be solved in time domain. Based upon the Smoothing function theory, a Lanczos factor is intriduced in Laplace inversion formulation, as results, the accuracy and efficiency of Durbin's numerical inversion method is improved a lot. The calculation results reveal that the method developed in the present work has some advantages in increasing the accuracy, simplying input data and decreasing computer cost.