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一、前言 用断裂力学方法对重力坝坝踵进行初裂分析有可能改进重力坝的设计方法,这一课题的主要内容之一是计算重力坝坝踵区的应力强度因子。 杂交模型有限元法的理论基础是放松了连续性要求的变分原理。用杂交模型法计算应力强度因子,易于考虑邻近裂纹尖端或切口顶端单元的应力奇异性,可用较少数目的单元得到相当精确的计算结果。文献[2]用杂交模型法计算过V形切口的应力强度因子,但仅限于切口表面无荷载的Ⅰ型问题。重力坝坝踵区则属复合型问题且切口表面作用水压力,单元内作用重力。重力坝的另一特点是坝基为半无限平面。本文在坝踵区设置了反映坝踵区应力奇异性的特殊单元,用修正势能原理导出了特殊单元的刚度矩阵,用杂交模型有限元与半平面边界元耦合法计算了坝踵区的应力强度因子。典型算例表
I. Preface It is possible to improve the design method of gravity dam by using the method of fracture mechanics to analyze the initial crack in the gravity dam heel. One of the main contents of this subject is to calculate the stress intensity factor of the gravity dam heel. The theoretical basis of the hybrid model finite element method is to relax the principle of variational requirements for continuity. Using hybrid model method to calculate stress intensity factor, it is easy to consider the stress singularity of the adjacent crack tip or the top of the incision. A relatively small number of units can be used to obtain quite accurate calculation results. In [2], the stress intensity factor of the V-shaped notch was calculated by the hybrid model method, but it was limited to the type I problem of no load on the notch surface. Gravity dam heel area is a complex type of problem and the role of the surface pressure of water cut, the role of gravity within the unit. Another characteristic of the gravity dam is the semi-infinite dam foundation. In this paper, a special unit is set up in the heel area to reflect the stress singularity in the heel region. The stiffness matrix of the special element is deduced by the principle of modified potential energy. The stress intensity at the heel area is calculated by hybrid model finite element method and half-plane boundary element method factor. Typical example table