Abstract
The SPR (Superconvergent Patch Recovery) method proposed by Zienkiewicz and Zhu (1992) is incorporated in the time integration process of the dynamic plane shell equation. The SPR method is employed to compute the second-order spatial differentiations such as Laplacian of displacement, and to evaluate the restoration force due to flexural rigidity. The defects of rank deficiency of an SPR matrix and hourglass mode instability are overcome by remedies proposed by Yue and Robbins Jr. (2007), and Flanagan and Belytschko (1981), respectively. The proposed numerical method is validated with comparison of the theoretical and numerical results of a free vibration of a circular disk.
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