【摘要】 本文由Hellinger-Reissner原理出发,以附加内部位移参数作为Lagrange乘子,把应力平衡条件作为约束条件引入到泛函中。同时,在裂纹尖端附近的单元中,假设应力由两部分组成:一部分不包含奇异性,另一部分包含有表示裂纹尖端正确奇异形状的专门应力项;在假设位移时,在常规位移的基础上再叠加与奇异应力项相对应的位移,从而推导出杂交/混合奇异有限元模型。该方法具有网格划分简单,节点数少,效率高的优点。更多还原

【Abstract】 This paper starts from the Hellinger-Reissner principle,define appendent internal displacement paramentes as Lagrange multiplier. It is introduced into the functional that treats stress equilibrium conditions as fixed conditions. At the same time, in the elements near crack tip, assumed stresses are made up of two parts.one part doesn’t contain singularity and another part contains special stree-sses terms that express right singular appearance of the crack tip. At assumed displacement, based on regular displacements,the author adds again the displacements to the proper singular stresses terms,Hence the author obtained the model of hybrid/mixed singular finite element. This is a new method for calculations stress intensity factors. The numerical results obtained by this method show central as well as single-edlge cracks in tension plates, or internal double cracks as well as double edge cracks in tension plates. Excellent accuracy has been obtained with available solutions in all the case. At the same time, the method has the advantages of the mesh division being simple and nodes numbers being few and efficiency being high, comparing with other singular finite element methods.更多还原