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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。
Finite element method has been widely used in various fields of engineering technology. The problem of using this method to solve the dynamics of a physics field that varies over time is still at a less mature stage. There are some successful ways to solve the elastic wave propagation problem. It belongs to the finite element method to solve such problems, such as configuration method, variational method using Gurtin variational principle, and the solution of finite element equations derived from various mechanics. In this paper, the method of Fourier transform is used to transform the dynamic finite element equation of the time domain into the frequency domain, and avoids the problem of eigenvalue. At the same time, it is discussed theoretically. Through the concrete calculation, the reliability of this method is verified, some applied research is done, and a design of inversion detection by finite element method in seismic exploration project is proposed.