A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates

Abstract

A new numerical technique combining the ®nite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate. Two-dimensional problems in the frequency domain are studied. The interior part of the plate containing cracks or inclusions is modeled by the conventional ®nite element method. The exterior parts of the plate are modeled by the strip element method that can deal problems of in®nite domain in a rigorous and ef®cient manner. Numerical examples are presented to validate the proposed technique and demonstrate the ef®-ciency of the proposed method. It is found that, by combining the ®nite element method and the strip element method, the shortcomings of both methods are avoided and their advantages are maintained. This technique is ef®cient for wave scattering in anisotropic laminates containing inclusions and/or cracks of arbitrary shape. IntroductionThe ®nite element method (FEM) has been widely used to solve mechanical engineering problems. The major advantage of the FEM is its applicability to a wide range of structures of complex geometry. The main disadvantage of the FEM is the need for large volume of memory because the discretization for the FEM produces a large number of node variables, which leads to a large matrix size. This disadvantage becomes even more critical for wave propagation problems, as very ®ne mesh is usually required to achieve a desired accuracy. To overcome this disadvantage, many techniques have been developed, such as bandwidth storage and sky-line storage techniques. In many explicit FEM packages, components in the stiffness and mass matrices are assembled only in the process of solving the equations. Therefore there is no need to store all the components of these matrices. However, this storage saving technique is dif®cult to apply for problems in the frequency domain. New numerical analysis, such as ®nite strip method (Cheung, 1976), boundary element method (Beskos, 1987), strip element method (SEM) suggested by Achenbach (1994, 1995), have also been proposed to reduce the size of the matrices. However none of these methods can replace FEM for their limitations or accuracy. There are dif®culties in applying the ®nite strip method for structures of complex geometry with complex boundary conditions. The BEM is dif®cult to apply for elastodynamic problems in anisotropic and inhomogeneous solids, because there are no simple Green's functions for such materials. The SEM can solve wave scattering problems very ef®ciently for plates with horizontal (Liu and Lam, 1994) or vertical cracks as well as rectangular inclusions . However, the SEM at this stage is dif®cult to apply for plates of irregular shapes or plates containing cracks and inclusions of irregular shape.It is ideal to combine the FEM with analytical methods or other numerical methods to minimize the FEM discretization to a relatively small but complex region. Researches on wave scattering in plates have been carried out using combined met...

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