有限元素法的一种频率域计算方法及其应用

A COMUTING TECHNIQUE IN FREQUENCY DOMAIN WITH FINITE ELEMENT METHOD AND ITS APPLICATIONS

长春地质学院

Changchun Geological College

有限元素法已经广泛地应用于工程技术各个领域中。用这种方法解决随时间变化的物理场的动态问题还处在不十分成熟的阶段。解决弹性波传播问题已有一些成功的方法。属于有限元素法解决这类问题的有配置法、引用Gurtin变分原理等的变分方法、以及解从各种力学原理导出的有限元方程的方法。本文用富里叶变换的方法把时间域动态有限元方程转换到频率域,并且避开了特征值的问题,同时从理论上进行了探讨。通过具体计算,验证了这种方法的可靠性,进行了一些应用上的研究,并提出在地震勘探工程中用有限元素法进行反演检测的一种设计。

The finite element method has been widely used in different fields of engineering. However, it is still in experimental stage to solve the dynamic problem of changing physical field with time by this method. Up to now, there are some successful methods for solving the problem of elastic wave propagation. Those methods involved in the finite element method are: (1) disposition method) (2) variational method cited from Gurtin's variational principle; and (3) the method after solving the finite element equation derived from various principles of mechanics. In this paper, the Fourier transform is used to convert the dynamic finite element equation from time-domain into frequency domain, thus evading the problem of eigenvalue; and a theroetical approach to it has been made.The reliability of this method has been verified through computations and some of its applications have been studied. A design for inverse detection in seismic prospecting engineering using the finite element method is also put forward in this paper.