Application of Overlapping Finite Element for Free and Forced Vibration Analysis of 2D Linear Elastic Solids

Purpose: It is well known that the difficulties in constructing an appropriate mesh limit the performance of the traditional finite element method in practical applications. Recently, the overlapping finite element method (OFEM) has been presented to increase the efficiency of the low-order finite elements. However, more studies on the overlapping finite element in dynamic analyses are still pursued. In this paper, the OFEM is extended into the two-dimensional linear elastic solid dynamic analysis. Methods: The abilities of the OFEM in the free vibration of two-dimensional linear elastic solids are first examined. Then, the Bathe time integration method, which is a direct time integration scheme, is introduced to assess the performance of the employed element in the forced vibration analysis. Through several typical numerical examples, the accuracy of natural frequencies, convergence rate, and computational efficiency obtained from the overlapping element are evaluated. In addition, the numerical stability regarding the matrix conditioning and the sensitivity to the irregular mesh in OFEM is also studied. Results: The numerical tests demonstrate that, compared with the conventional finite elements, the overlapping elements can lead to much more precise solutions with high computation efficiency and are almost distortion insensitive. Conclusion: The OFEM is an effective method and can significantly reduce the meshing difficulties in dynamic problems, and thus can perform well in vibration analyses of complex structures.