Construction of a Mindlin pseudospectral plate element and evaluating efficiency of the element

Abstract

In this paper, a Mindlin pseudospectral plate element is constructed to perform static, dynamic, and wave propagation analyses of plate-like structures. Chebyshev polynomials are used as basis functions and Chebyshev–Gauss–Lobatto points are used as grid points. Two integration schemes, i.e., Gauss–Legendre quadrature (GLEQ) and Chebyshev points quadrature (CPQ), are employed independently to form the elemental stiffness matrix of the present element. A lumped elemental mass matrix is generated by only using CPQ due to the discrete orthogonality of Chebyshev polynomials and overlapping of the quadrature points with the grid points. This results in a remarkable reduction of numerical operations in solving the equation of motion for being able to use explicit time integration schemes. Numerical calculations are carried out to investigate the influence of the above two numerical integration schemes in the elemental stiffness formation on the accuracy of static and dynamic response analyses. By comparing with the results of ABAQUS, this study shows that CPQ performs slightly better than GLEQ in various plates with different thicknesses, especially in thick plates. Finally, a one dimensional (1D) and a 2D wave propagation problems are used to demonstrate the efficiency of the present Mindlin pseudospectral plate element.