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
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
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
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
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
In this paper,we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable.We apply the finite element approximations of the stress field ...In this paper,we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable.We apply the finite element approximations of the stress field and the displacement field constructed for the elasticity problem by Hu(J Comp Math 33:283–296,2015),Hu and Zhang(arXiv:1406.7457,2014)to solve the bending moment and the rotation for the Reissner-Mindlin Plate Problem.We propose two triples of finite element spaces to approximate the bending moment,the rotation,and the displacement.The feature of these methods is that they need neither reduction terms nor penalty terms.Then,we prove the well-posedness of the discrete problem and obtain the optimal estimates independent of the plate thickness.Finally,we present some numerical examples to demonstrate the theoretical results.展开更多
A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direct...A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.展开更多
In this paper we give the optimal selection of the bubble function in the linear scheme proposed by recent paper [1]for the Reissner-Mindlin plate problem，
A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete...A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete components.Each channel consists of an integrator,a pole-zero cancellation net,and a linear amplification stage,which can be adapted to accommodate either positive or negative input signals.The RMS equivalent input noise charges are 3.3 fC,the conversion gains are approximately±2 mV∕fC,and the intrinsic time resolution reaches 32 ps.In the prototype PPAC application,the CSA performs as well as the commercial FTA820A amplifier,providing a position resolution as good as 0.17 mm,and exhibiting reliable stability during several hours of continuous data acquisition.展开更多
A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The resu...A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The results show that cold-pressing produces intense plastic deformation near the corrugated surface of the Al plate,which promotes dynamic recrystallization of the Al substrate near the interface during the subsequent hot-pressing.In addition,the initial corrugation on the surface of the Al plate also changes the local stress state near the interface during hot pressing,which has a large effect on the texture components of the substrates near the corrugated interface.The construction of the corrugated interface can greatly enhance the shear strength by 2−4 times due to the increased contact area and the strong“mechanical gearing”effect.Moreover,the mechanical properties are largely depended on the orientation relationship between corrugated direction and loading direction.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding str...Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.展开更多
In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mes...In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.展开更多
In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'...In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.展开更多
A simple finite element method for the Reissner-Mindlin plate model in the primitive variables is presented and analyzed. The method uses conforming linear finite elements for both the transverse displacement and rota...A simple finite element method for the Reissner-Mindlin plate model in the primitive variables is presented and analyzed. The method uses conforming linear finite elements for both the transverse displacement and rotation. It is proved that the method converges with optimal order uniformly with respect to thickness.It is simpler and more economical than the Arnold-Falk element[1].展开更多
This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both com...This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.展开更多
This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stress...This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.展开更多
A numerical scheme for the Reissner-Mindlin plate model is proposed.The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold ...A numerical scheme for the Reissner-Mindlin plate model is proposed.The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk[SIAM J.Numer.Anal.,26(6):1276-1290,1989].The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement.The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element.The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.展开更多
In this paper,we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem.We derive robust a post...In this paper,we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem.We derive robust a posteriori error estimators for them and prove their reliability and efficiency.展开更多
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.
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.
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.
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In this paper,we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable.We apply the finite element approximations of the stress field and the displacement field constructed for the elasticity problem by Hu(J Comp Math 33:283–296,2015),Hu and Zhang(arXiv:1406.7457,2014)to solve the bending moment and the rotation for the Reissner-Mindlin Plate Problem.We propose two triples of finite element spaces to approximate the bending moment,the rotation,and the displacement.The feature of these methods is that they need neither reduction terms nor penalty terms.Then,we prove the well-posedness of the discrete problem and obtain the optimal estimates independent of the plate thickness.Finally,we present some numerical examples to demonstrate the theoretical results.
文摘A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.
基金The project was supported by Zhejiang Provincial Natural Science Foundation of China(198035)
文摘In this paper we give the optimal selection of the bubble function in the linear scheme proposed by recent paper [1]for the Reissner-Mindlin plate problem，
基金supported by the National Natural Science Foundation of China(Nos.U2167202,12225504,12005276)the Natural Science Foundation of Shandong Province(No.ZR2024QA172)the Fundamental Research Funds of Shandong University.
文摘A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete components.Each channel consists of an integrator,a pole-zero cancellation net,and a linear amplification stage,which can be adapted to accommodate either positive or negative input signals.The RMS equivalent input noise charges are 3.3 fC,the conversion gains are approximately±2 mV∕fC,and the intrinsic time resolution reaches 32 ps.In the prototype PPAC application,the CSA performs as well as the commercial FTA820A amplifier,providing a position resolution as good as 0.17 mm,and exhibiting reliable stability during several hours of continuous data acquisition.
基金supported by Guangdong Major Project of Basic and Applied Basic Research, China (No. 2020B0301030006)Fundamental Research Funds for the Central Universities, China (No. SWU-XDJH202313)+1 种基金Chongqing Postdoctoral Science Foundation Funded Project, China (No. 2112012728014435)the Chongqing Postgraduate Research and Innovation Project, China (No. CYS23197)。
文摘A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The results show that cold-pressing produces intense plastic deformation near the corrugated surface of the Al plate,which promotes dynamic recrystallization of the Al substrate near the interface during the subsequent hot-pressing.In addition,the initial corrugation on the surface of the Al plate also changes the local stress state near the interface during hot pressing,which has a large effect on the texture components of the substrates near the corrugated interface.The construction of the corrugated interface can greatly enhance the shear strength by 2−4 times due to the increased contact area and the strong“mechanical gearing”effect.Moreover,the mechanical properties are largely depended on the orientation relationship between corrugated direction and loading direction.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by the National Key R&D Program of China (No. 2018YFA0707300)the National Natural Science Foundation of China (No. 52374376)the Introduction Plan for High end Foreign Experts, China (No. G2023105001L)。
文摘Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.
基金Subsidized by the Special Funds for Major State Basic Research Projects G1999032804.
文摘In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.
文摘In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.
文摘A simple finite element method for the Reissner-Mindlin plate model in the primitive variables is presented and analyzed. The method uses conforming linear finite elements for both the transverse displacement and rotation. It is proved that the method converges with optimal order uniformly with respect to thickness.It is simpler and more economical than the Arnold-Falk element[1].
基金the National Natural Science Foundation of China (Grant No. 10601003)National Excellent Doctoral Dissertation of China (Grant No. 200718)
文摘This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171239 and 11226333)Scientific Research Foundation for the Returned Overseas Chinese Scholars and Foundation for Excellent Young Scholars of Sichuan University (Grant No. 2011SCU04B28)
文摘This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.
文摘A numerical scheme for the Reissner-Mindlin plate model is proposed.The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk[SIAM J.Numer.Anal.,26(6):1276-1290,1989].The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement.The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element.The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.
基金J.Hu was supported by the NSFC project 10971005A Foundation for the Author of National Excellent Doctoral Dissertation of PR China 200718+1 种基金Y.Q.Huang was supported in part by the NSFC Key Project 11031006Hunan Provincial NSF Project 10JJ7001.
文摘In this paper,we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem.We derive robust a posteriori error estimators for them and prove their reliability and efficiency.
