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 ...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.展开更多
<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress ...<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress tensor T_(iL) and displacement gradient tensor u_(jM)in the paper.Then the specific expression of Φ_(iLjM) is derived by the comparison of theexpansion terms of Helmholtz free energy H.Finally,the coefficients (?)_(iLjM) related toΦ_(iLjM) are obtained by using ultrasonic measurement and the elastic tensor C_(iLjM) whichdepends on (?)_(iLjM) and initial stresses in the reference system are given.展开更多
文摘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.
文摘<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress tensor T_(iL) and displacement gradient tensor u_(jM)in the paper.Then the specific expression of Φ_(iLjM) is derived by the comparison of theexpansion terms of Helmholtz free energy H.Finally,the coefficients (?)_(iLjM) related toΦ_(iLjM) are obtained by using ultrasonic measurement and the elastic tensor C_(iLjM) whichdepends on (?)_(iLjM) and initial stresses in the reference system are given.
