The scaled boundary finite element method for plate bending problems

Abstract

This thesis presents an efficient and accurate semi-analytical solution procedure, based upon the scaled boundary finite element method (SBFEM), for modeling thin plates under transverse loadings and different types of boundary conditions. The key formulation is established within the framework of Kirchhoff’s plate bending theory. A standard weighted residual technique is then applied together with the discretization along the scaled boundary direction to derive the scaled boundary finite element equations. Standard implementations including the numerical integration, the determination of eigenvalues and eigenvectors, a procedure for solving a system of linear ordinary differential equations, and a linear solver are adopted to construct all involved unknown functions. An h-hierarchical adaptive procedure with the moment-recovery error estimator is also integrated into the present implementation to further enhance its computational performance and reduce meshing effort. A selected set of results is reported to demonstrate the accuracy and convergence of computed solutions and the computational performance of the developed technique.