幂函数型曲线裂纹平面问题的一般解

通过构造一个新的、精确的和通用的保角映射,利用Muskhelishvili复势法研究了任意自然数次幂的幂函数型曲线裂纹的平面弹性问题,给出了远处受单向拉伸载荷下裂纹尖端Ⅰ型和Ⅱ型应力强度因子的一般解.当幂次取不同的自然数时,可以退化为若干已有的结果.通过数值算例,讨论了幂函数型曲线裂纹的系数、幂次及在x轴上的投影长度对Ⅰ型和Ⅱ型应力强度因子的影响规律.

求解应力强度因子的样条虚边界元交替法

为求解平面裂纹问题的应力强度因子,提出基于Muskhelishvili基本解和样条虚边界元法的样条虚边界元交替法.该方法将平面内带裂纹有限域问题分解成带裂纹无限域问题与不带裂纹有限域问题的叠加.带裂纹无限域问题利用Muskhelishvili基本解法直接得出,不带裂纹有限域问题采用样条虚边界元法求解.利用该方法对复合型中心裂纹方板和I型偏心裂纹矩形板进行分析.数值结果表明该方法精度高且适用性强.

BOUNDARY BEHAVIOR OF CAUCHY-TYPE INTEGRALS IN CLIFFORD ANALYSIS

In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.

映射函数法求方形孔口角点裂纹的应力强度因子

用映射函数法和Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ方程对无限大板内方形孔口角点裂纹在不同外载下进行应力分析，决定了裂纹尖端的应力强度因子随裂纹长α和孔构形尺寸Ｌ的变化规律；探讨了外载变化对Ｋ因子的影响．并使刚度导数法（有限元法）进行了计算．结果表明，在板宽Ｗ和Ｌ之比等于或大于５时，两种方法的误差在６％以内．

Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.

界面裂纹奇异积分方程的极限法推导

采用Muskhelishivili复变函数的方法,将两相材料中倾斜裂纹应力场基本解,直接退化得到两相材料界面裂纹的应力场基本解,并尝试性地采用极限分析方法导出了两相材料界面裂纹的奇异积分方程。

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.

映射函数法求方形孔口角点裂纹的应力强度因子

用映射函数法和Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ方程对无限大板内方形孔口角点裂纹在不同外载下进行应力分析，决定了裂纹尖端的应力强度因子随裂纹长α和孔构形尺寸Ｌ的变化规律，探讨了外载变化对ｋ因子的影响；并使用刚度导数有限元法进行了计算．结果表明，在板宽Ｗ和Ｌ之比大于５时，两种方法的误差在６％以内．

磁电弹性体中多条位错与Griffith裂纹

根据本征方程,研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论,得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明:在裂纹的端点及位错点上仍然存在应力的奇异性,离位错点越远处广义力越小,结论与已有的结果相符,证明了结论的正确性.当位错点与裂纹端点距离越近时,裂纹与位错间的应力场越小,并逐渐趋近于零.

磁电弹性体中螺型位错与唇口裂纹的相互作用

研究磁电弹性体中螺型位错与唇口裂纹的相互作用。结合Muskhelishvili方法和干扰技术,在假定裂纹面具有不可渗透条件下得到磁电弹性体中由位错和唇口裂纹所诱导的应力场、电场和磁场的解析解。应用广义Peach-Koehler公式,得到作用在位错上的影像力。通过数值算例,得到场强度因子的变化规律及影像力和广义力随位错位置的变化规律。