【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 型弹性平面裂纹尖端场和 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 型裂纹应力强度因子和基于 型Dugdale模型的裂纹尖端张开位移的计算问题.对典型算例的计算结果表明该方法简单有效,具有令人满意的精度.更多还原

【Abstract】 From the Hamiltonian governing equations of plane elasticity for 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 the mode Ⅱ elastic crack tip field and mode Ⅱ Dugdale crack tip field respectively. The new analytical elements can be implemented in FEM program systems to compute the stress intensity factors and crack tip opening displacements by Dugdale model for antisymmetric plane crack problems with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.更多还原