用广义WKB方法解低Froude数的运动物体的水波问题

<正> 假定流体在x正方向以速度U运动,未扰自由表面位于x轴,y轴垂直向上,坐标原点位于物体内部,并使得物体与未扰自由表面的交点分别位于(-x_0,0)与(x_0,0),设所有的长度物理量已用物体的特征长度L无量纲化,问题的小参数E定义为

广义WKB方法及其对浅水波问题的应用

本文首先指出WKB方法可适用于更广泛的一类方程,并把它应用于线性化浅水波方程。对浅水波焦散区的非线性情形,用广义WKB方法进行了讨论,把文献[4]的结果推广到一般弯曲焦散线的情形。

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.