裂纹梁结构静力与动力分析的p型自适应有限元方法  

P-adaptive finite element method for static and dynamic analyse of cracked beams

作　　者：余志刚[1] 卢文秀[1] 褚福磊[1] 

机构地区：[1]清华大学精密仪器与机械学系

出　　处：《清华大学学报（自然科学版）》2008年第8期1306-1310,共5页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金重点项目(10732060);国家“八六三”高技术项目(2006AA04Z438);国家杰出青年科学基金项目(50425516)

摘　　要：为提高裂纹结构静力和动力分析问题的收敛速度和分析精度,将基于Legendre正交多项式的p型自适应有限元方法与断裂力学方法相结合,给出了p型自适应梁单元刚度矩阵和质量矩阵的显式积分表达式,同时建立了裂纹单元的刚度方程。数值仿真和实验案例表明,该方法与细化网格的h型有限元方法相比,在自由度减少的同时能够有效地提高计算精度。考虑到裂纹识别问题一般采用有限元方法建立精确辨识模型,该文提出的方法在降低识别复杂度和提高识别精度方面具有一定的工程实用价值。The convergence and accuracy of static and dynamic analyse of cracked beam structures are improved by a p-version adaptive finite method combined with fracture mechanics theory presented in this paper. The beam element shape functions are assumed to be Legendre orthogonal polynomials with conventional cubic shape functions so that the element stiffness and mass matrices can be integrated analytically. The crack stiffness matrix is derived using fracture theory and the energy method and can be easily assembled into the global stiffness matrix for the cracked beams. Numerical and experimental studies show the method efficiently improves the analysis accuracy with less degrees of freedom compared with methods using a refined finite element mesh. Since crack identification problems usually rely on precise predicts by finite element methods, the present method is of practical value in reducing the computation complexity and in improving identification accuracy.

关 键 词：动力分析 p型有限元 裂纹 梁结构 

分 类 号：TB123[理学—工程力学] O327[理学—力学]