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The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.

FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis