In this paper, we discusse the locking phenomenon of the finite element method for the pure displacement boundary value problem in the planar elasticity as Lame constant λ- ∞. The locking-free scheme of Crouziex-Rav...In this paper, we discusse the locking phenomenon of the finite element method for the pure displacement boundary value problem in the planar elasticity as Lame constant λ- ∞. The locking-free scheme of Crouziex-Raviart element was pro- posed and anaIyzed by Brenner et al.[2] and [3]. We firstly present the derivation of Brenner’s scheme, then propose and analyse a locking-free scheme of noncon- forming rectangle finite element.展开更多
The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotrop...The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.展开更多
In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also con...In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.展开更多
Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to A. The energy norm and L2 n...Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to A. The energy norm and L2 norm errors are proved to be O（h2） and O（h3）, respectively. Numerical tests confirm the theoretical analysis.展开更多
We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is r...We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is robust and optimal, in the sense that the convergence estimate in the energy is independent of the Lame parameter λ.展开更多
The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error est...The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.展开更多
In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finit...In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the L-2-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lame constant lambda. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible, Numerical experiments are given which are consistent with our theory.展开更多
In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the d...In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.展开更多
文摘In this paper, we discusse the locking phenomenon of the finite element method for the pure displacement boundary value problem in the planar elasticity as Lame constant λ- ∞. The locking-free scheme of Crouziex-Raviart element was pro- posed and anaIyzed by Brenner et al.[2] and [3]. We firstly present the derivation of Brenner’s scheme, then propose and analyse a locking-free scheme of noncon- forming rectangle finite element.
基金Acknowledgments. This work was supported by National Natural Science Foundation of China （No. 10971203）, Specialized Research Fund for the Doctoral Program of Higher Education （No. 20094101110006）, the Educational Department Foundation of Henan Province of China （No.2009B110013）.
文摘The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.
文摘In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.
基金Project supported by the National Natural Science Foundation of China (Nos. 10771198 and 11071226)the Foundation of International Science and Technology Cooperation of Henan Province
文摘Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to A. The energy norm and L2 norm errors are proved to be O（h2） and O（h3）, respectively. Numerical tests confirm the theoretical analysis.
基金Supported by the NSF of the Education Henan(200510078005)
文摘We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is robust and optimal, in the sense that the convergence estimate in the energy is independent of the Lame parameter λ.
基金The research is supported by NSF of China (10371113 10471133)
文摘The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.
文摘In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the L-2-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lame constant lambda. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible, Numerical experiments are given which are consistent with our theory.
文摘In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two.
