A strain smoothing formulation for NURBS-based isogeometric finite element analysis  

作　　者：WANG DongDong ZHANG HanJie XUAN JunChang 

机构地区：[1]Department of Civil Engineering, Xiamen University, Xiamen 361005, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第1期132-140,共9页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10972188);the Program for New Century Excellent Talents in University from China Ministry of Education (Grant No. NCET-09-0678);the Fundamental Research Funds for the Central Universities of China (Grant No. 2010121073)

摘　　要：A strain smoothing formulation for NURBS (non-uniform rational B-splines) based isogeometric finite element analysis is presented. This approach is formulated within the framework of assumed strain methods and strain smoothing operations. The strain smoothing is defined through strain averaging in the element sub-domains which are subsequently used for numerical integration of the Galerkin weak form. This formulation satisfies the orthogonality condition of the assumed strain methods. Meanwhile the present formulation totally avoids the gradient computation of the rational NURBS basis functions in the formulation of stiffness matrix. A transformation method is employed to accurately enforce the displacement boundary conditions. Numerical results demonstrate that the present formation gives very satisfactory solution accuracy simultaneously with improved computational efficiency.A strain smoothing formulation for NURBS （non-uniform rational B-splines） based isogeometric finite element analysis is presented. This approach is formulated within the framework of assumed strain methods and strain smoothing operations. The strain smoothing is defined through strain averaging in the element sub-domains which are subsequently used for numerical integration of the Galerkin weak form. This formulation satisfies the orthogonality condition of the assumed strain methods. Meanwhile the present formulation totally avoids the gradient computation of the rational NURBS basis functions in the formulation of stiffness matrix. A transformation method is employed to accurately enforce the displacement boundary conditions Numerical results demonstrate that the present formation gives very satisfactory solution accuracy simultaneously with improved computational efficiency.

关 键 词：NURBS basis functions isogeometric finite element analysis meshfree method strain smoothing sub-domain integration 

分 类 号：O241.4[理学—计算数学] TP391.72[理学—数学]