【摘要】：基于半無限平面體頂邊集中力作用下的彈力應(yīng)力解析解,提出一種解析逼近方法,求解含單個(gè)任意形狀凸孔洞無限平面體在孔邊任意荷載作用下的彈性應(yīng)力場。將n邊形孔洞外域劃分為頂邊上作用待定面力分布的n個(gè)半無限平面體。對于每個(gè)半無限平面體的頂邊,其孔口部分外力已知,而兩側(cè)延伸部分上面力未知。提出一種有效的迭代方式依次計(jì)算所有延伸邊上的面力,直至收斂,同時(shí)得到孔洞外域的彈性應(yīng)力場。該方法原理簡單、計(jì)算過程明了;由于基于彈性力學(xué)解析解和一維高精度數(shù)值積分,其最終結(jié)果屬解析逼近解。算例表明,該方法獲得的工程尺度下的孔洞外域應(yīng)力場與復(fù)變函數(shù)方法、有限元方法計(jì)算結(jié)果非常吻合,表明方法的有效性。同時(shí),可計(jì)算孔洞角點(diǎn)處近場應(yīng)力,由孔洞角點(diǎn)處近場應(yīng)力值擬合得到的廣義應(yīng)力強(qiáng)度因子具有極高精度,且應(yīng)力奇異性次數(shù)與斷裂力學(xué)理論值一致。
[Abstract]:Based on the analytical solution of elastic stress under concentrated force at the top edge of a semi-infinite plane body, an analytical approximation method is proposed to solve the elastic stress field of an infinite plane body with a single convex hole with a single arbitrary shape under arbitrary loads on the edge of a hole. In this paper, the external region of an n-side hole is divided into n semi-infinite plane bodies with the force distribution of the undetermined plane acting on the top edge. For the top edge of each semi-infinite plane body, the external force of the orifice part is known, but the upper force of the two side extension part is unknown. An effective iterative method is proposed to calculate the surface forces of all the extended edges in turn until they converge and to obtain the elastic stress field outside the hole at the same time. The principle of the method is simple and the calculation process is clear, because of the analytical solution of elastic mechanics and one-dimensional high precision numerical integration, the final result is an analytical approximation solution. The numerical results show that the stress field of the external hole field obtained by the method is in good agreement with the complex variable function method, and the finite element method is in good agreement with the results obtained by the finite element method, which shows the effectiveness of the method. At the same time, the near field stress at the hole corner can be calculated. The generalized stress intensity factor fitted from the near field stress value of the hole corner has a high accuracy, and the number of stress singularities is in agreement with the theoretical value of fracture mechanics.
【作者單位】： 合肥工業(yè)大學(xué)土木與水利工程學(xué)院;合肥工業(yè)大學(xué)土木工程結(jié)構(gòu)與材料安徽省重點(diǎn)實(shí)驗(yàn)室;
【分類號】：TU45
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本文編號：2374000