摘要
利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了两个圆形奇异超级解析单元列式,这两个超级单元能够分别准确地描述Ⅰ型和Ⅱ型Dugdale模型平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的Ⅰ型或Ⅱ型裂纹基于Dugdale模型的裂纹尖端塑性区尺寸和裂纹尖端张开位移(CTOD)或裂纹尖端滑开位移(CTSD)的计算问题。对典型算例的计算结果表明方法简单有效,具有令人满意的精度。
From the Hamiltonian governing equations of an elastic sectorial domain, the variable separation and eigenfunction expansion techniques are employed to formulate two circular singular hyper-analytical -elements. The two hyper-analytical-elements give a precise description of mode Ⅰ and mode Ⅱ Dugdale crack tip fields respectively. The new analytical elements can be implemented into FEM program systems to compute the plastic zone sizes and crack tip opening or sliding displacement based on mode Ⅰ or mode Ⅱ Dugdale model for plane crack problems with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple and effective.
出处
《工程力学》
EI
CSCD
北大核心
2005年第6期37-40,68,共5页
Engineering Mechanics
基金
国家自然科学基金重点项目(50438010)
