In addition, such solutions are reachable only with simple geometrical configurations and boundary conditions. However, existing analytical methods are limited, as it is very challenging to find an exact solution to a class of dynamic problems. IntroductionĪnalysis of structural dynamics problems is a crucial step in many engineering applications. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions. Several numerical test problems are solved and compared against previously published numerical solutions. 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. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions.
In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. 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.
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