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中文摘要：
提出了求解基于线性内聚力模型的平面裂纹扩展问题的半解析有限元法，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，推导了一个环形和一个圆形奇异超级解析单元列式，组装这两个超级单元能准确地描述裂纹表面作用有双线性内聚力的平面裂纹尖端场。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基于线性内聚力模型的平面裂纹扩展问题。典型算例的计算结果表明本文方法简单有效，具有令人满意的精度。
英文摘要：
A semi-analytical finite element method for crack propagation problems based on linear cohesive force model is presented. From the Hamiltonian governing equations of plane elasticity in sectorial domain, the variable separation and eigenfunction expansion techniques are employed to formulate a ring and a circular singular hyper-analytical-elements. The assembly of the two hyperanalytical-elements gives a precise description of the displacement and stress fields in the vicinity of crack tip for a cracked plane subjected to a bilinear cohesive force. The new analytical element can be implemented into FEM program systems to solve crack propagation for plane problems with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.
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