A variational differential quadrature solution to finite deformation problems of hyperelastic shell-type structures:a two-point formulation in Cartesian coordinates  

作　　者：M.FARAJI-OSKOUIE R.ANSARI M.DARVIZEH 

机构地区：[1]Faculty of Mechanical Engineering,University of Guilan,Rasht,3756,Iran

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第8期1219-1232,共14页应用数学和力学（英文版）

摘　　要：A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean materials based on the seven-parameter shell theory.A work conjugate pair of the first Piola Kirchhoff stress tensor and deformation gradient tensor is considered for the stress and strain measures in the paper.Through introducing the displacement vector,the deformation gradient,and the stress tensor in the Cartesian coordinate system and by means of the chain rule for taking derivative of tensors,the difficulties in using the curvilinear coordinate system are bypassed.The variational differential quadrature(VDQ)method as a pointwise numerical method is also used to discretize the weak form of the governing equations.Being locking-free,the simple implementation,computational efficiency,and fast convergence rate are the main features of the proposed numerical approach.Some well-known benchmark problems are solved to assess the approach.The results indicate that it is capable of addressing the large deformation problems of elastic and hyperelastic shell-type structures efficiently.

关 键 词：shell large deformation variational differential quadrature(VDQ)technique seven-parameter shell theory first Piola Kirchhoff stress tensor and deformation gradient tensor(P−F)formulation 

分 类 号：O347[理学—固体力学]