The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conf...The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.展开更多
本文提出了一种新的格式,讨论了Reissner-Mindlin板问题的一种非协调三角形有限元逼近。取挠度空间为协调的一次元,角位移空间为非协调一次元,剪切力空间取分片常数元,证明了该格式对任意板厚都收敛,可以避免剪切闭锁现象,并有最优一致...本文提出了一种新的格式,讨论了Reissner-Mindlin板问题的一种非协调三角形有限元逼近。取挠度空间为协调的一次元,角位移空间为非协调一次元,剪切力空间取分片常数元,证明了该格式对任意板厚都收敛,可以避免剪切闭锁现象,并有最优一致误差估计,比Arnold("Analysis of a linear-linear finite element for the Reissner-Mindlin plate model")一文中的收敛结果好。最后还给出了零范数估计。展开更多
A new stabilized finite element method which is different from Hughes and Franco’s (1988) is presented for the Reissner-Mindlin plate model. The least square mesh-dependent residual form of the shear constitute equat...A new stabilized finite element method which is different from Hughes and Franco’s (1988) is presented for the Reissner-Mindlin plate model. The least square mesh-dependent residual form of the shear constitute equation is added to the Partial Projection scheme to enhance the stability. Using piecewise polynomials of order k≥1 for the rotations, of order k+1 for the displacement and of order k-1 for the shear, the kth order error-estimates are obtained. Besides, our computing scheme can be also applied to some lower order elements. All error-estimates are obtained independent of the plate thickness, and the stability parameter is an arbitrary positive constant.展开更多
A kind of stabilized mixed/hybrid scheme for Reissner-Mindlin plates is proposed with conforming isoparametric bilinear interpolations of de?ection/rotations. The choice of shear stress modes is discussed. It is shown...A kind of stabilized mixed/hybrid scheme for Reissner-Mindlin plates is proposed with conforming isoparametric bilinear interpolations of de?ection/rotations. The choice of shear stress modes is discussed. It is shown by numerical experiments that fulfilling an energy orthogonal condition for stress approximations is crucial to avoiding “shear locking”.展开更多
A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchoff ...A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchoff conditions at the interpolation points as the thickness of plate tends to zero, so the element is locking free. We construct two triangular elements by this method - a 3-node element and a 6-node element. The numerical results are provided.展开更多
Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compa...Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.展开更多
On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these meth...On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.展开更多
文摘The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.
文摘本文提出了一种新的格式,讨论了Reissner-Mindlin板问题的一种非协调三角形有限元逼近。取挠度空间为协调的一次元,角位移空间为非协调一次元,剪切力空间取分片常数元,证明了该格式对任意板厚都收敛,可以避免剪切闭锁现象,并有最优一致误差估计,比Arnold("Analysis of a linear-linear finite element for the Reissner-Mindlin plate model")一文中的收敛结果好。最后还给出了零范数估计。
文摘A new stabilized finite element method which is different from Hughes and Franco’s (1988) is presented for the Reissner-Mindlin plate model. The least square mesh-dependent residual form of the shear constitute equation is added to the Partial Projection scheme to enhance the stability. Using piecewise polynomials of order k≥1 for the rotations, of order k+1 for the displacement and of order k-1 for the shear, the kth order error-estimates are obtained. Besides, our computing scheme can be also applied to some lower order elements. All error-estimates are obtained independent of the plate thickness, and the stability parameter is an arbitrary positive constant.
文摘A kind of stabilized mixed/hybrid scheme for Reissner-Mindlin plates is proposed with conforming isoparametric bilinear interpolations of de?ection/rotations. The choice of shear stress modes is discussed. It is shown by numerical experiments that fulfilling an energy orthogonal condition for stress approximations is crucial to avoiding “shear locking”.
文摘A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchoff conditions at the interpolation points as the thickness of plate tends to zero, so the element is locking free. We construct two triangular elements by this method - a 3-node element and a 6-node element. The numerical results are provided.
基金supported by the Key Technologies R&D Program of Sichuan Province of China(No. 05GG006-006-2)
文摘Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.
基金supported by NSFC(11571266,91430106,11171168,11071132)NSFC-RGC(China-Hong Kong)(11661161017)
文摘On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.
