板弯曲断裂计算的边界配置解法

采用复变函数理论和边界配置方法,分析计算了Kirchhoff板的弯曲断裂问题.假设了位移及内力的复变函数式,它们能满足一系列的基本方程和支配条件,例如域内的平衡方程、裂纹表面的边界条件、裂纹尖端的应力奇异性质.这样,仅板边界的边界条件需要考虑.它们可用边界配置法和最小二乘法近似满足.对不同边界条件和载荷情形进行了分析计算.数值算例表明,本文方法精度较高,计算量小,是一种有效的半解析、半数值计算方法.     

Fracture calculation of bending plates by boundary collocation method

IntroductionPlatesarecommonstructuresinaerospace ,civil,mechanicalandchemicalengineering .Duringtheproductionanduseofthestructures,flawsandcracksmayappearintheplates.Inordertoassurethesafetyofplatestructures,toavoidcleavagefractureandfatiguefailure,andtodesignsafetyandmakerationaluseofmaterials,itisnecessarytodofractureanalysisfortheplatestructures.Fractureproblemofabendingplateismorecomplexthanthatoftheplaneelasticity[1,2 ].Firstofall,therearedifferenttheoriesforplatebending ,suchasKirchhoff…