热机载荷下多边形夹杂角端部应力场的杂交元分析

Singular Stress Analysis near Corner of Polygonal Inclusion under Thermo-Mechanical Loads

开发了一种多边形夹杂角端部超级单元模型,并将其与传统四节点单元组装,用于分析热-机载荷下结构中多边形夹杂角端部的应力场.与机械载荷作用下超级单元模型的区别在于,该模型将夹杂角部邻域应力场分为奇异项和非奇异项,而奇异性项又可分解为热致部分和力致部分.在数值计算中,首先分析了单正方形夹杂问题,验证了模型的有效性,考察了材料匹配的影响;然后分析了双正方形夹杂的干涉问题,考察了夹杂间距的影响.结果表明,当前模型可避免局部网格的高度加密,从而提高有限元计算的效率.

A n-node super element, being compatible with common four-node elements, is developed to solve singular stress fields near comer of a polygonal inclusion under thermo-mechanical loads. Different from the super wedge tip element for pure mechanical loading, the thermo-mechanical coupling behavior is considered in the expression local stress fields, i.e., the stress fields near an inclusion comer is decomposed as singular terms and non-singular terms in which the singular terms include the homogeneous solutions of thermal and mechanical loadings. In the numerical analysis, a single square inclusion is considered firstly, the validity of the present model is proved, and generalized stress intensity factors at the inclusion comer are systematically calculated for various Young＇s modulus ratios; then the interaction of double square inclusions with different distances is considered. The present model can avoid highly enriched meshes, and improve the computational efficiency.