【摘要】 基于Mindlin-Reissner板的Hellinger-Reissner变分原理,构造了一个高性能的免闭锁低阶板元。借助能量优化条件,构造了一个7参数的弯矩场,并假设单元内部的弯矩和剪力严格满足平衡方程。在一个简化插值算子的帮助下,得到一个高精度免闭锁的四边形杂交板元。数值结果表明,新板元对畸形网格具有很好的性能,而且在极薄板时是免闭锁的。更多还原

【Abstract】 It is the purpose of this paper to design a high-performance locking-free low-order plate element,based on the Hellinger-Reissner variational principle of Mindlin-Reissner plates.By means of the energy optimization condition,we present a 7-parameter bending moment field,and assume that the equilibrium equations associating bending moments with shear forces are satisfied strictly within the elements.With the aid of a reduced interpolation operator,we obtain an accurate locking-free quadrilateral hybrid element.The numerical experiments reveal that the proposed plate element possesses good properties despite distorted meshes,and is free of shear locking in the case of very thin plates.更多还原