A NEW MODIFICATION IN DECOUPLED SCALED BOUNDARY METHOD WITH DIAGONAL COEFFICIENT MATRICES FOR ANALYSIS OF 2D ELASTOSTATIC AND TRANSIENT ELASTODYNAMIC PROBLEMS

The scaled boundary based methods are commonly known as semi-analytical approaches, which have very good accuracy and efficiency for solving various kinds of problems. In this paper, a new trend for improvement of the decoupled scaled boundary-finite element method (DSBFEM) in order to solve the 2D elastostatic and elastodynamic problems is provided. In this technique, only the boundaries of the problem domain are discretized by specific sub-parametric elements. Mapping functions are employed as a class of higher-order Lagrange polynomials which are set at Gauss-Lobatto-Legendre control points,so, the special shape functions, Gauss-Lobatto-Legendre numerical integration, and the integral form of the weighted residual method lead to the diagonal coefficient matrices in the governing equations. The main differences between the study conducted and the prior researches regarding decoupled scaled boundary-finite element method is that here in, geometry production procedure of the interpolation function, integration of the different is selected, and using this approach, we could reduce the complexity of the DSBFEM. Validity and accuracy of the present method are demonstrated through two benchmark elastostatic problems and three benchmark elastodynamic problems that are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.