RPT finiite-element formulation for linear dynamic analysis of orthotropic plates

This paper presents a nite-element formulation for dynamic analysis of orthotropic plates using two-variable Rened Plate Theory (RPT). Hamiltonʹs principle is employed to obtain the governing equations, and the semi-discrete approach is utilized for solving the equations. After constructing spatial weak form equations, a 4-node rectangular plate element with six Degrees Of Freedom (DOFs) per node is introduced for discretization of the domain. An unconditionally stable implicit Newmark scheme is used for temporal discretization. A MATLAB code with the capability of modelling both static and dynamic plate problems with various boundary conditions is generated. Several numerical problems are solved, and the obtained displacements and stresses are compared with the existing results in the literature. The results demonstrate the accuracy, simplicity, and eciency of the present method in dynamic analysis of plate problems.