Nonlinear Dynamic Analysis of Three-Dimensional Elasto-Plastic Solids by the Meshless Local Petrov-Galerkin (MLPG) Method

The meshless local Petrov-Galerkin approach is proposed for the nonlinear dynamic analysis of three-dimensional (3D) elasto-plastic problems. Galerkin weak-form formulation is applied to derive the discrete governing equations. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a unit test function and local weak-form formulation in three dimensional continua for the general dynamic problems is derived. Three dimensional Moving Least-Square (MLS) approximation is considered as shape function to approximate the field variable of scattered nodes in the problem domain. Normality hypothesis of plasticity is adopted to define the stress-strain relation in elasto-plastic analysis and the unknown plastic multiplier is obtained by the consistency condition. Von Mises yield criterion in three dimensional space is used as a yield function to determine whether the material has yielded. The Newmark time integration method in an incremental form is used to solve the final system of nonlinear second order Ordinary Differential Equations (ODEs). Several numerical examples are given to demonstrate the accuracy and effectiveness of the present numerical approach.