An efficient numerical method for dynamic analysis of polygonal plate under moving loads

Abstract

Plate structures under moving loads are frequently encountered in practical engineering. Over the past decades, the moving-load models for plates are mainly developed for rectangular plates. In this study, an efficient numerical method is developed for triangular and quadrilateral plates, which are the two most representative polygonal plates and also the basic elements to form general polygon plates. To avoid the mismatch between the moving load and nodes that encountered in Finite Element Method (FEM), the entire domain of the plate is firstly mapped into a square domain using the isoparametric shape functions. The domain decomposition method is also introduced to handle the general polygon shaped plates, whereas the penalty function method is adopted to handle arbitrary boundary conditions. The first-order shear deformation theory (FSDT) is used to describe the elastic deflection of the plates, and then the deformation fields in the mapped domain are spatially discretized by using Chebyshev polynomials of the first kind (CPOFK). Afterwards, the governing equations of motion is derived using Lagrange’s equation, in which the inertia force, Coriolis force and centrifugal force due to the interactions between the moving load and supporting plates are taken into account simultaneously. The mode reduction method is employed to reduce the dimension of dynamic equations, and then the first-order generalized-α method is used to solve the dynamic response in time domain. Finally, the correctness and efficiency of the presented method are validated from convergence analysis and comparisons.