平板断裂问题的多尺度扩展有限元法  

Multiscale Extended Finite Element Method for Modeling Fracture Problem in Reissner-Mindlin Plates

作　　者：胡凯[1] 尹硕辉[1] 

机构地区：[1]河海大学力学与材料学院,江苏南京211100

出　　处：《河南科技大学学报（自然科学版）》2016年第2期11-16,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(51179063)

摘　　要：采用渐进弯曲奇异函数和跨过裂纹面的不连续函数,加强常规的位移逼近空间,从而使计算网格独立于裂纹,建立了贯穿裂纹Reissner-Mindlin板的多尺度扩展有限元法。在裂纹附近区域采用小尺度网格,其他区域采用大尺度网格。在计算代价不大的情况下,考虑大型结构中小裂纹的存在或者提高裂纹附近的精度。所有尺度单元都采用四结点四边形板单元,四边形任意结点板单元连接不同尺度单元。用互作用积分法计算裂尖应力强度因子,算例分析检验了本文方法的精度和有效性。A multiscale extended finite element method for Reissner-Mindlin plate with through crack was proposed. The standard displacement approximation space was enriched by the asymptotic bending singular function and the discontinuous function across the crack,hence the computation mesh was independent of the cracks. The fine-scale mesh was used around the cracks,whereas the coarse-scale mesh was used far from the cracks. Thus small cracks in the analysis of large structure were considered and the accuracy around the cracks was improved in the case of low calculation cost. The four-node quadrilateral plate element was used for any scale element,and the arbitrary-node quadrilateral plate element was used to connect elements with different scales. Stress intensity factors were evaluated with the interaction integral method. Examples were given to illustrate the accuracy and efficiency of the proposed method.

关 键 词：REISSNER-MINDLIN板 贯穿裂纹 多尺度 扩展有限元法 四边形任意结点板单元 应力强度因子 

分 类 号：TU311[建筑科学—结构工程] P315.9[天文地球—地震学]