Three Dimensional Elasto-dynamic Analysis of Thick Plates by the Meshless Local Petrov-Galerkin Method

In this paper, three dimensional (3D) elasto-dynamic analysis of thick plates based on Meshless Local Petrov- Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are distributed in the 3D analyzed domain and each node is surrounded by a cubic subdomain to which a local integral equation is applied. The meshless approximation based on the Three dimensional Moving Least-Square (MLS) is employed as shape function to approximate the field variable of scattered nodes in the problem domain. The Newmark family of methods is used to numerically time integration of system of coupled second order ODEs. Numerical examples for solving the transient response of the elastic thick plates are demonstrated. The numerical efficiency of the proposed meshless method is illustrated by the comparison of results obtained from previous literatures.

Keywords:

MLPG method , Elasto-dynamic analysis , MLS approximation , Thick plates