轴对称杂交应力元的优化列式

文章把杂交元的单元优化设计原理应用于轴对称问题,从优化条件的轴对称形式出发,导出了这类杂交应力元的优化列式。其优化性能突出表现在离散模型对于计算背景（如网格的形式、单元的畸变和材料的不可压缩性等）的广泛适应性。文章还对优化杂交元的收敛、以及伪剪应力等问题开展了讨论,并与轴对称问题的其它有限元方法进行了计算比较。

OPTIMIZING FORMULATION OF AXISYMMETRIC HYBRID STRESS ELEMENTS

In developing assumed stress hybrid elements, a major obstacle is how to select the rational element stress patterns. It is very difficult to find the equilibrating stress trial functions for axisymmetric problems. The early works in this aspect were in an experience state. In recent years, a new way for formulation of hybrid elements was suggested by Pian et al and it has become a basis of determining element stress patterns. In the derivation, however, some perturbation treatments are usually needed and the corresponding axisymmetric hybrid elements are not universal to regular and irregular meshes. In the present paper the optimizing priciple of hybrid finite elements is applied to axisymmetric analysis so the problems mentioned above are solved comletely. The optimized hybrid model shows a superior numerical behavior, i. e.1. It passed the patch test. 2. In comparision with 4-node axisymmetric displacement element, the present method yields more ideal results for both stresses and displacements and is espacially suitable for nearly incompressible materials without any locking phenomena. 3. The optimized hybrid element is universal for any types of meshes. 4. No false shears, no zero energy modes. ?. , ?-