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摘要

考虑了具有环形工艺孔洞并被裂纹削弱的结构构件的失效周期数的确定问题。假设结构受到给定频率和幅值的循环加载(拉-压)。本文提出了一种确定具有两个对称裂缝的结构单元的应力强度因子的方法。确定应力强度因子的问题已简化为求解一个奇异积分方程。对于该方程的数值解,采用了边界元法。给出了具有Cauchy型和Hadamard型奇异积分的有效数值模拟公式。研究了所考虑的奇异方程的解精度。考虑了不同密度近似的边界元。已经确定,使用密度近似为三次的边界元可以显著提高解的精度。密度在考虑的积分方程中表现为未知函数,用于计算应力强度因子。对所考虑的奇异方程的解析解和数值解以及应力强度系数的解析值和数值值进行了比较。利用应力强度因子的阈值确定了裂纹发展的初始裂纹长度。在巴黎准则的基础上计算了导致不可接受尺寸裂缝的加载循环的临界次数。这个临界循环次数是耐久性的一个特征。为了比较两者的耐久性特性,考虑了具有孤立单裂纹和裂纹链的板的临界循环次数的确定问题。在相同荷载水平下,最小临界循环数对应于工艺孔附近有裂纹的结构单元。
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Calculation model for assessing the durability of structural elements in the presence of holes and cracks
The problem of determining a number of cycles to failure for structural elements having technological holes of circular shape and weakened by cracks is considered. It is assumed that the structure is subject to cyclic loading (tension-compression) with given frequencies and amplitudes. A technique for determining stress intensity factors for the structural element with two symmetrical cracks adjoining a contour of hole has been developed. The problem of determining the stress intensity factor has been reduced to solving a singular integral equation. For the numerical solution of this equation, the boundary element method has been used. The formulas for the effective numerical simulation of singular integrals with singularities of the Cauchy and Hadamard type have been obtained. The solution accuracy of the considered singular equation is investigated. Boundary elements with different density approximations are considered. It has been established that the use of boundary elements with a cubic approximation of density leads to a significant increase in the solution accuracy. Densities appearing as unknown functions in the considered integral equations are used to calculate stress intensity factors. Comparison of the analytical and numerical solutions of the considered singular equation, as well as the analytical and numerical values of the stress intensity coefficients has been performed. The initial crack length starting crack development has been determined by using the threshold value of the stress intensity factor. The critical number of loading cycles leading to cracks of an unacceptable size has been calculated based on the Paris criterion. This critical number of cycles is a characteristic of durability. To compare the durability characteristics, the problems of determining the critical number of cycles for plates with single isolated cracks and with crack chains are considered. It has been established that at the same loading level, the smallest critical number of cycles corresponds to a structural element with cracks in the vicinity of technological holes.
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