Elastodynamic thin plate bending analysis by boundary element method with Laplace transform

The boundary element method(BEM) is developed for the dynamic analysis of thin elastic plate bending problems with arbitrary boundary conditions. The formulation employs Laplace-transform technique, where the boundary integral equations are obtained on the Laplace transformed domain with the fundamental solutions derived from Kelvin's functions. The accuracy of the numerical results mainly depends on those of numerical estimation of the singular integral derived from the static term of the fundamental solutions. In the present paper, an BEM formulation based on a single boundary integral equation of the deflection, which employes a source point on both the boundary and outer region, is discussed in detail. A non-singular boundary integral equation is introduced on the transformed domain, which is obtained by superposition of the analyzed field and the referenced field with a uniform gradient of deflection. Numerical results obtained by the proposed method are compared with the analytical solutions and the other numerical solutions by means of several numerical examples. These examples also serve to illustrate the use of the proposed method.