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A meshless local Petrov-Galerkin (MLPG) approach for 3-dimensional elasto-dynamics. (English) Zbl 1181.74152
Summary: A Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-dynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transient structural analysis. The present numerical technique imposes a correction to the accelerations, to enforce the kinematic boundary conditions in the MLS approximation, while using an explicit time-integration algorithm. Numerical examples for solving the transient response of the elastic structures are included. The results demonstrate the efficiency and accuracy of the present method for solving the elasto-dynamic problems, and its superiority over the Galerkin finite element method.

74S30 Other numerical methods in solid mechanics (MSC2010)
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics