解析试函数法分析平面切口问题

本文利用平面切口问题的基本解析解构造单元,分析平面切口问题。通过分析平面切口问题的Williams特征方程的有解区间,使用分区加速lleruM&&法依序无漏地计算了平面V型切口特征值。从Williams应力函数出发,推导了V型切口尖端的应力场基本解析解列式。并用此根据分区混合能量原理构造了含切口解析单元ATF-VN的刚度矩阵。文中还对含切口解析单元的单元尺寸和应力项数等因素对分析结果的影响进行了系统的讨论。

ANALYSIS OF PLANE NOTCH PROBLEMS WITH ANALYTICAL TRIAL FUNCTIONS' METHOD

The basic analytical solutions of plane notch problem are used to formulate finite elements, and the proposed elements are used to analyze the plane notch structure in turn. Following the analysis to the existence intervals of the Williams equations, the subregion accelerated lleruM& method is used to calculate the eigenvalues of plane notch problems. From the Williams stress function, the basic analytical solutions of the stress field at the tips of V-notchs are first derived and then used as the trial functions to formulate the element: ATF-VN. Meanwhile, the Subregion mixed energy principle is used in the formulation of the stiffness matrix. In this paper, a systematic research is done to analyze the factors that influence the results, such as the element抯 size and the stress item number.