三维磁电热弹材料裂纹问题的超奇异积分方法

Hypersingular Integral Equation Approach Method for Three-dimensional Crack in Electro-magneto-thermo-elastic Multiphase Composites

应用位移基本解,磁电热弹材料三维裂纹问题被转化为求解一组以裂纹表面位移间断为未知函数的超奇异积分方程问题。进而,采用主部分析法得到了裂纹尖端的应力奇异指数及奇性应力场的解析表达式。然后,通过将裂纹表面位移间断未知函数表达为位移间断基本密度函数,使用有限部积分方法对超奇异积分方程组建立了数值方法。最后,通过典型算例计算,得到广义应力强度因子的变化规律。

Using the Green＇s functions, the extended general displacement solutions of three-dimensional crack problem in electro-magneto-thermo elastic multiphase composites under extended loads are analyzed by boundary element method. Then, this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations. The singularity of the extended discontinuity displacement around the crack front terminating at the interface is obtained with the main-part analysis method of hypersingular integral equations. Also,the exact analytical solutions of the extended singular stresses and extended stress intensity factors near the crack front are given. In addition,the numerical method of the hypersingular integral equations for a rectangular crack subjected to extended load is proposed with the body force method, in which the extended crack opening dislocation is approximated by the product of basic density functions and polynomials. Finally,numerical solutions of the extended stress intensity factors of some examples are obtained.