| The ideal homogeneous media don’t exist, but it’s full of various forms of inhomogeneousmedia in nature. With the development of science and technology, mechanics for theinhomogeneous media is increasingly concentrated on by the experts and scholars. The wavemotion problems in inhomogeneous media belong to the field of basic science research. Thereis great theoretical significance and wide application prospect in the future.Based on the idea of inhomogeneous finite element, the dynamic inhomogeneous finiteelement method is developed in this paper for transient analysis of wave motion problem inthe inhomogeneous media by using variation method, within the context of elastodynamics.The main work of this paper is listed as follows.1. The parameter distribution of the inhomogeneous media is described mathematically.Then, the dynamic inhomogeneous finite element for analysis of inhomogeneous media isderived from the variation method, and the general formula of the element stiffness matrix,element damping matrix and element mass matrix is given.2. In order to improve the speed of calculating element matrices in real engineering, theidea of isoparametric interpolation for the material parameter distribution is introduced in thispaper. Meanwhile, the necessary condition of this idea is given.3. By some examples, it is found that the form of the element matrices in this paper issymmetric matrix, and the dynamic inhomogeneous finite element method is more suitablefor the large engineering simulation than the conventional methods as the error is lower on thediscretization of material parameter distribution.4. The flowchart of dynamic finite element analysis MATLAB program is given. And,two simple numerical examples are simulated and analyzed. Then, it show that the method inthis paper is able to be degenerate into conventional finite element method. By comparingwave field characteristics, the advantage of dynamic finite element method can be found. |
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