Problem of the periodic welding of anisotropic elastic plane with different materials

ＩｎｔｒｏｄｕｃｔｉｏｎＵｐｔｏｎｏｗ,ｔｈｅｒｅｈａｖｅｂｅｎｍａｎｙｒｅｓｅａｒｃｈｅｓｏｎｔｈｅｐｌａｎｅｗｅｌｄｉｎｇｐｒｏｂｌｅｍｏｆｉｓｏｔｒｏｐｉｃｍａｔｅｒｉａｌｓ．ｅ．ｇ．［１］ａｎｄ［２］ｅｔｃ．Ｈｏｗｅｖｅｒ,ｆｏｒｔｈｅｐｌａ...     

On the complex variable displacement method in plane isotropic elasticity

A modified formulation of the complex variable displacement method in plane isotropic elasticity is presented. It makes use of two equations deduced from the planar Navier equations in terms of the complex variable, which differs from England’s original formulation based on only one equation. This formulation is more direct and complements the one by England.     

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili's complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors (SIFs) for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.     

ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｃｏｎｖｅｎｔｉｏｎａｌｂｏｕｎｄａｒｙｅｌｅｍｅｎｔｍｅｔｈｏｄ (ＢＥＭ) ,ｓｉｎｇｕｌａｒｐｏｉｎｔｓａｒｅｄｉｓｔｒｉｂｕｔｅｄａｌｏｎｇｔｈｅｂｏｕｎｄａｒｙｏｆｔｈｅｄｏｍａｉｎｕｎｄｅｒｓｔｕｄｙ ,ｗｈｉｃｈｌｅａｄｓｔｏｓｉｎｇｕｌａｒｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｄｕｅｔｏｔｈｅｓｉｎｇｕｌａｒｉｔｙｏｆｆｕｎｄａｍｅｎｔａｌｓｏｌｕｔｉｏｎｓ .Ｔｈｅｒｅｆｏｒｅ ,ｓｉｎｇｕｌａｒｉｎｔｅｇｒａｔｉｏｎｍｕｓｔｂｅｈａｎｄｌｅｄｗｈｅｎｓｏｌ…     

OnJ-integrals in the plane fracture of composite materials

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.     

应用半权函数法计算界面裂纹的应力强度因子

应用半权函数法求解双材料界面裂纹的应力强度因子，得到以半权函数对参考位移与应力加权积分的形式表示的应力强度因子。针对特征值为复数λ的双材料界面裂纹裂尖应力和位移场，设置与之对应特征值为-λ的位移函数，即半权函数。半权函数的应力函数满足平衡方程，应力应变关系，界面的连续条件以及在裂纹面上面力为0；半权函数与裂纹体的几何尺寸无关，对边界条件没有要求。由功的互等定理得到应力强度因子KⅠ和KⅡ的积分形式表达式。本文计算了多种情况下界面裂纹应力强度因子的算例，与文献结果符合得很好。由于裂尖应力的振荡奇异性已经在积分中避免，只需考虑绕裂尖远场的任意路径上位移和应力，即使采用该路径上较粗糙的参考解也可以得到较精确的结果。     

插值矩阵法分析双材料平面V形切口奇异阶

对二维V形切口问题提出奇异阶分析的一个新方法.首先,以V形切口尖端附近位移场沿其径向渐近展开为基础,将其线弹性理论控制方程转换成切口尖端附近关于周向变量的常微分方程组特征值问题,然后将数值求解两点边值问题的插值矩阵法进一步拓展为求解一般常微分方程组特征值问题,插值矩阵法是在离散节点上采用微分方程中待求函数的最高阶导数作为基本未知量.由此,V形切口的应力奇性阶问题通过插值矩阵法获得,同时相应的切口附近位移场和应力场特征向量一并求出.     

A mathematical theory of materials with elastic range and the definition of back stress tensor

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｇｅｎｅｒａｌ,ｔｈｅｋｉｎｅｍａｔｉｃａｌｈａｒｄｅｎｉｎｇｂｅｈａｖｉｏｒｏｆｍａｔｅｒｉａｌｓｉｓｄｅｓｃｒｉｂｅｄｂｙａｖａｒｉａｂｌｅｃａｌｅｄｂａｃｋｓｔｒｅｓｏｒｓｈｉｆｔｔｅｎｓｏｒ．Ｉｔｓｖａｌｕｅｒｅｐ...     

A mixed problem of plane elasticity for a domain with partially unknown boundary

The paper addresses a problem of plane elasticity for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides. The neighborhoods of the vertices of the inner boundary are unknown equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center. It is assumed that this elastic body is inserted into a hole of a rigid body, with the hole boundary coinciding with the outer boundary of the elastic body. Absolutely smooth rigid punches with rectilinear bases are pressed into all the rectilinear sections of the inner polygonal boundary of the elastic body. There is no friction between the elastic and rigid bodies. The unknown arcs are free from external stresses. Complex variable theory is used to determine the unknown arcs and the stress state of the elastic body __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 110–118, March 2006.     

Influence of couple-stresses on stress concentrations around the cavity

ＩｎｔｒｏｄｕｃｔｉｏｎＳｔｒｅｓｓｃｏｎｃｅｎｔｒａｔｉｏｎｉｓｏｎｅｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｏｆｍｅｃｈａｎｉｃｓｒｅｓｅａｒｃｈｄｏｍａｉｎ .Ｉｎｔｈｅｍｉｃｒｏｐｏｌａｒｅｌａｓｔｉｃｉｔｙｔｈｅｏｒｙ ,ｉｔｉｓｍｏｒｅａｂｓｏｒｐｔｉｖｅ .Ｉｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｍｉｃｒｏｐｏｌａｒｅｌａｓｔｉｃｉｔｙｔｈｅｏｒｙｕｓｕａｌｌｙｇｉｖｅｓａｌｏｗｃｏｅｆｆｉｃｉｅｎｔａｎｄｃｈａｎｇｅｓｔｈｅｓｔｒａｎｇｅｎｅｓｓａｔｔｈｅｔｉｐｏｆｔｈｅｃｒａｃｋ .Ｔｈｅｓ…