板弯曲断裂计算的边界配置解法

王元汉; 伍佑伦; 余飞

板弯曲断裂计算的边界配置解法

华中科技大学, 土木工程学院, 武汉, 430074

详细信息

作者简介:
王元汉(1946- ),男,武汉人,教授,博士,博士生导师(E-mail:yhwang0062@163.Com).

中图分类号: O346.1
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- 被引次数: 0
出版历程
- 收稿日期: 2001-09-25
- 修回日期: 2003-02-19
- 刊出日期: 2003-06-15

Fracture Calculation of Bending Plates by Boundary Collocation Method

School of Civil Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

摘要

摘要: 采用复变函数理论和边界配置方法,分析计算了Kirchhoff板的弯曲断裂问题.假设了位移及内力的复变函数式,它们能满足一系列的基本方程和支配条件,例如域内的平衡方程、裂纹表面的边界条件、裂纹尖端的应力奇异性质.这样,仅板边界的边界条件需要考虑.它们可用边界配置法和最小二乘法近似满足.对不同边界条件和载荷情形进行了分析计算.数值算例表明,本文方法精度较高,计算量小,是一种有效的半解析、半数值计算方法.
- Kirchhoff板 /
- 断裂 /
- 边界配置解法 /
- 复变函数 /
- 应力强度因子
Abstract: Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it is only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi-analytical and semi-numerical method.
- Kirchhoff plate /
- fracture /
- boundary collocation method /
- complex variables function /
- stress intensity factors

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参考文献(12)

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