薄板弯曲问题的P型杂交解析有限元方法

P-VERSION HYBRID ANALYTICAL FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS

本文采用两套变量构造有限元试函数空间,在单元内部要求试函数精确满足平衡微分方程,在单元边界上对位移和转角分别用Peano 升阶函数插值.然后利用广义变分原理建立了一种薄板弯曲问题的p 型杂交解析有限元方法.与常规有限元法相比,该方法不必进行过细的网格剖分,通过增加单元插值多项式的阶数p 来提高精度.此外,该方法还具有积分计算只需在单元边界上进行、单元刚度矩阵和载荷向量具有嵌入结构、协调程度可以自动控制等优点.

Two sets of trial functions with different variables are constructed for the admissible space of the finiteelement analysis.The trial functions satisfy the equilibrium differential equation inside elements,while thedeflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpo-lation functions.Then,a generalized variational principle is applied to set up the p-version hybrid analyti-cal finite element method for the plate bending problems.The accuracy of the finite element computationcan be improved by means of increasing the order of the interpolation polynomials with fixed mesh.In thefinite element formulation,to obtain the stiffness matrices and the load vectors the quadratures only needto be performed over the edges of the elements.These matrices and vectors possess embedding structure.The conformability between the elements can be controlled automatically.