无网格局部Petrov-Galerkin法分析板弯曲的剪切自锁问题

Shear Locking Analysis of Plate Bending Problem by Using Meshless Local Petrov-Galerkin Method

用径向基函数构造无网格局部Petrov-Galerkin方法的形函数,插值函数具有Kronecker delta函数性质,因此可以很方便地施加本质边界条件.分析了板弯曲时剪切自锁现象产生的原因,利用无网格局部Petrov-Galerkin方法对两对边固支另对边简支中厚板的弯曲进行了分析和计算.发现无网格方法相对于有限元法等传统数值方法能更好地避免剪切锁死现象,并提出了避免剪切自锁现象发生的有效措施.

The shape function of the meshless local Petrov-Galerkin method is constructed by using the ra- dial basis functions and possesses Kronecker Delta function properties. Therefore, the essential boundary conditions can be easily imposed. Causation of shear locking occurring in plate bending is analyzed. Ben- ding problems for plate with two sides simply supported, the other two sides clamped boundary condi- tions, are analyzed by the meshless local Petrov-Galerkin method in this paper. It is found that the shear locking is easier to avoid in the meshless method than in the finite element method, and the measures of avoiding the shear locking are presented.