厚板低阶广义协调矩形元

A new generalized conforming rectangular element for thick plates

采用常内力状态下的广义协调条件，将剪切变量用结点挠度和转角表示，导出一个具有１２个自由度的厚板、薄板都通用的矩形弯曲单元。此单元的自由度少，精度高，能通过分片检验，不出现剪切闭锁现象，具有位移型单元简便实用的优点。

The method proposed by authors for the formulation of generalized conforming elements is modified in this paper. The generalized compatibility condition under constant stress is introduced and a new generalized conforming rectangular element for thick and thin plates with 12 degrees of freedom is developed. In the formulation, shear deformation is introduced without increasing the number of degrees of freedom. The present element is free from locking effect in the limit case of thin plate and can be applied to both thick and thin plate bending problems. By satisfying the generalized compatibility conditions under constant stress, the patch test can always be satisfied and convergence toward an exact solution is guaranteed. Numerical examples show that the present method gives results with high accuracy. Being a displacementbased method, this new method can be derived and implemented in a routine manner.