含弱界面结构断裂分析中辛方法

A symplectic method for fracture analysis of structure with weak interface

基于哈密顿体系,提出了一种分析含弱界面弹性材料断裂问题的辛方法.通过引入对偶变量,建立基本问题的哈密顿体系.在该体系下,问题的解可被辛本征解的级数形式所表示.利用辛本征解之间的辛共轭正交关系,以及裂纹面条件、弱界面条件和结构外边界条件,可确定辛本征解级数的待定系数,从而得到问题的解.这样,可以获得Ⅰ型和Ⅱ型广义应力强度因子解析表达式.数值结果揭示了各种边界条件对应力强度因子的影响,同时也表明该方法对复杂的混合边界条件问题更有效.

Based on Hamiltonian system,a symplectic method for analyzing the fracture problem of weak interface between two elastic media is presented.By introducing the dual variables,the Hamiltonian system is constructed,then the solution of the problem can be represented by series form of the symplectic eigensolutions.By means of the symplectic adjoint orthogonal relationship between symplectic eigensolutions,together with crack surface conditions,weak interfacial conditions and external boundary conditions of structure,the undetermined coefficients of the symplectic series can be determined.Therefore,the solution is obtained.In this way,the generalized stress intensity factors of ModeⅠand ModeⅡare expressed analytically.The numerical results reveal the influence of various boundary conditions on the stress intensity factors,and also show that the method is more effective for complex mixed boundary conditions.