扩展的Hellinger-Reissner原理及特殊层合杂交应力元

建立了一种非匀质材料新的、扩展的Hellinger-Reissner原理，发展了当一个单元域划分为不同材料特性子域、其元内应力场沿子域表面不连续、且位移场在子域表面也急剧变化时，一个非匀质有限元刚度列式便利方法。这种列式亦可用于对每层横向剪应变均独立处置的厚层板。基于此变分原理建立了新的具有一个无外力圆柱表面的层合杂交应力元，单元各层独立假定的应力场通过以自然坐标表示的非协调位移为权函数使齐次平衡方程变分满足的理性方法及严格满足给定圆柱面上无外力条件得到，位移场在元间及层间连续条件则分别通过Lagrange乘子进行了松弛。数值算例表明：这类新型元可有效地分析具有多类圆柱形槽孔的厚、中厚及薄层板自由孔边应力分布。

Extended Hellinger-Reissner Principle and Special Hybrid Stress Multilayer Elements

A new extended Hellinger-Reissner variational principle for non-homogeneous material has been developed which provides a convenient procedure for deriving the stiffness matrix of a non-homogeneous element that can be subdivided into regions of different material properties. In such case some of stress components along the interface and the displacement across the interface may become discontinuous. This formulation can also be used for thick laminated plates in which transverse shear stress of each layer is independent. One kind of new assumed stress hybrid multilayer element with a traction-free cylindrical surface is derived by the use of the extended principle. The stresses of each layer are interpolated by the natural coordinates and are obtained by the use of internal displacement as weight function to impose the equilibrium conditions in a variational sense. The stresses also satisfy the traction-free conditions over the cylindrical surface exactly. The continuous conditions of the displacement between the layers and the elements are relaxed by using Lagrange multipliers respectively. Numerical results show that the present elements are much more efficiency than the ordinary assumed stress hybrid elements and the conventional assumed displacement elements for analyzing stress distribution around difference types of cylindrical notches in thin to thick laminated composites when very coarse meshes are used.