Analysis of the dynamic response for Kirchhoff plates by the element-free Galerkin method

Abstract

Dynamic response analysis involves examining structural behavior under dynamic loading conditions. Transient dynamic analysis emerges as a method employed to assess the responses of deformable bodies. Due to the depth analysis of transient responses for thin plates, the associated error analysis work becomes particularly important. In this work, we conduct stability and convergence analysis of the element-free Galerkin (EFG) method for the dynamic response of Kirchhoff plate model. We start by discretizing the thin plate dynamics using the EFG method for the spatial domain and the central difference scheme for the temporal domain. Stability and convergence analysis for transient responses, including deflection and moment responses, are derived similarly to those in two-dimensional transient structural dynamic analysis. The key to the analysis is transforming the governing equations and clamped boundary conditions into a weak formulation with penalty terms using the penalty method. The main results demonstrate a significant correlation between the error estimate and both nodal spacing and time step size. Additionally, the continuity of the approximation functions and the selection of penalty factors significantly affect numerical accuracy. To validate the theoretical results, we conduct numerical experiments involving clamped square and L-shaped plates with uniform and nonuniform node distributions, as well as a perforated plate model. Furthermore, we investigate the impact of node influence domains and penalty factors on numerical accuracy, facilitating parameter selection for practical engineering applications.