受热载荷两相材料界面端应力场的新型有限元分析

基于一种特殊有限元特征分析方法获得两相材料界面端奇异性应力和位移场数值特征解, 据此开发了一种新型超级单元模型, 用于分析热载荷作用下两相材料界面端的应力场. 与机械载荷作用下超级单元模型的区别在于, 该模型在能量泛函中考虑了热-机耦合的影响, 将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. 模型的有效性通过了经验解和传统有限元方法的验证；模型可以避免在界面端邻域网格高度加密, 提高了计算速度, 对于分析多奇异性点应力干涉问题有重要意义.

A NOVEL FINITE ELEMENT ANALYSIS OF STRESSES NEAR APEX OF A BI-MATERIAL WEDGE SUBJECTED TO THERMAL LOADING

A super wedge tip element for application to bi-material wedge is develop utilizing the numerical stress and displacement field eigen-solutions based on an ad hoc finite element eigenanalysis method. Singular stresses near apex of arbitrary bi-material wedges under thermal loading can be obtained from the super wedge tip element. Different from the super wedge tip element for pure mechanical loading, the thermal-mechanical coupling behavior is considered in the expression of total potential functional, and the thermal-mechanical stress field is decomposed as singular terms and non-singular terms in which the singular terms include the homogeneous solutions of thermal and mechanical loadings. The validity and applicability of this novel element are established through existing asymptotic solutions and conventional detailed finite element analysis. All numerical examples show that the novel finite element method yields satisfactory solutions with few elements, and is applicable to the problem of multiple singular points.