【作者】 马少杰；

【导师】 刘承论；

【作者基本信息】 山东科技大学 ， 工程力学， 2006， 硕士

【摘要】 裂纹尖端附近应力场具有强奇异性，采用常规的数值方法分析断裂力学的效果往往较差，因此迫切需要另辟蹊径寻找有效方法，而边界元法的基本解也具有这种奇异性，所以通过恰当的单元划分、单元形状改良和数值积分处理技巧等可以明显提高裂纹尖端的计算精度。本文首先提出原常单元(平板单元)位移不连续法由于单元几何形状与裂隙尖端几何形状拟合效果差等原因，计算裂纹尖端附近应力场误差较大，借鉴克劳奇改进二维尖端单元的构想，引入三维抛物线形尖端单元改良原平板单元。如此，既能与边界单元几何形状基本拟合，又能高精度地模拟裂纹尖端附近位移和应力变化规律，并提高计算效率。对改良的抛物线尖端单元影响系数进行了详细推导，给出了计算公式和数值计算方法，特别是自影响系数借助已有的二维抛物线位移不连续法解析解(克劳奇解)求解，无需直接对单元自身积分，解决了奇异积分问题，计算精度提高。由于三维位移不连续法本身具有求解单元不连续位移的特点，因此依此求解裂纹尖端应力强度因子便捷而直接，模拟系统的选择是合理且优越的。 另外，本文还论述了三维位移不连续法求解裂纹问题的具体解题步骤，系统分析了三维边界元数值模拟系统的实现原理。更多还原

【Abstract】 Having adopted the familiar numerical solution to solve the crack tip issue, but the result generally lead to higher error in evaluated, then solution to nearby crack tip is required. Fortunately, the basis solutions of the boundary element method take on attributive haracter of singularity, so, through fel- icitously element division, shape improvement and dealing with numerical integral ingenious in technique. And else, crack tip precision in calculation can be improved highly. Firstly, demonstrating the original constant element (flat board element) displacement discontinuity method to resolve stress intensity factors and stress field nearby crack tip is inefficient, its arises from the geometrical shape of element is inconsistent with geometrical shape of crack tip, and so on. Use for reference crouch’s means to amend two dimensional crack tip, bring forward three dimensional parabolic crack tip element to improve original flat element. So such, both shape consistent with boundary element geometrical shape, and simulate crack tip close-by variety law of stress and strain with higher precision, and enhancing calculative efficiency. Deduce the influence coefficients of the amended parabolic crack tip element detailed, and provided the calculating equations and numerical calculational methods. Especially, by aid of analytical solution of two dimensional parabolic displacem- ent discontinuity methods to solve the self-influence coefficient,then avoiding of element self-integral directly, resolve the singular integral, enhance calcu- lative precision. Because of 3D-DDM is characteristic of solving the discon- tinuity displacement essentially, then adopting it on stress intensity factor close-by crack tip is convenient and directly, moreover, simulative pattern is reasonable and predominantly.In addition, dissertate the solution steps concretely for three dimensional displacement discontinuity methods, and analyze implementation principium to the three dimensional boundary element numerical simulative system.更多还原