非线性阻尼下裂纹非匀速扩展问题的零级近似解析解

探讨了非线性阻尼下无限岩板内张开型裂纹非匀速扩展的瞬态分析问题．在现有断裂动力学问题文献中，一般采用拉氏变换与积分变换方法，得到的回路积分最后还需借助于数值方法求解．作者在断裂动力学基本方程中引入一个非线性阻尼项来考虑能量损耗，采用小参数摄动，得到零级近似动力学方程组，而且自始至终采用解析方法进行计算，获得了问题的零级近似解析解．如果沿裂纹长度上有剪应力作用，采用本文方法也可获得其零级近似解析解．本文方法将有利于改善非线性断裂动力学中应用有限单元法求数值解的收敛性．因而本文为解决这类非线性断裂动力学问题提供了一条新的途径．

The Zero Order Approximate Analytic Solution of Non-Uniform Speed Propagating Finite Crack Under Non-linear Damping

The transient analysis of a non-uniform speed propagating finite crack of the opening mode in an infinite rock plateunder non-linear damping was explored for the first time. In present research on fracture dynamic problems, Laplace or integral transformation was generally used, and numerical methods had to be adopted to solve the loop integral. In the basic equations of the fracture dynamics, an item of nonlinear damping was introduced to consider the energy sopilage, a small parameter perturbation was used, and the zero order approximate analytic equations were obtained. In this research, the analytical method was adopted in the calculation, and the zero order approximate analytic solution was presented. If there is a function of the shear stress along the crack surfaces, the zero order approximate analytic solution will also be obtained using the method of this paper. It is good for the promotion of the convergence of numerical solution in finite element method applied for non linear fracture dynamics. Therefore, a new method for the research on the non-linear fracture dynamic problems is presented.