Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection ope...Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.展开更多
In this paper,we study the accuracy enhancement for the frictionless Signorini problem on a polygonal domain with linear finite elements.Numerical test is given to verify our result.
In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we uti...In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we utilize the results presented in this paper to study the Signorini problem in mechanics.展开更多
In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field...In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes.The idea of the LMFS is similar to the localized domain type method.The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix.The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function(NCP-function).Numerical examples are carried out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.展开更多
In this paper, a new numerical method for the Signorini problem in three-dimensional elasticity is presented. The problem is reduced to a boundary variational inequality based on a new representation of the derivative...In this paper, a new numerical method for the Signorini problem in three-dimensional elasticity is presented. The problem is reduced to a boundary variational inequality based on a new representation of the derivative of the doublelayer potential. Furthermore, a boundary element procedure is described for the numerical approximation of its solution and an abstract error estimate is given.展开更多
We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of H2 regularity, then the converg...We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of H2 regularity, then the convergence rate can be improved from O（h3/4） to quasi-optimal O（h｜log h｜1/4） with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal O（h） as expected by the linear approximation.展开更多
In this paper, a exterior Signorini problem is reduced to a variational inequality on a bounded inner region with the help of a coupling of boundary integral and finite element methods. We established a equivalence be...In this paper, a exterior Signorini problem is reduced to a variational inequality on a bounded inner region with the help of a coupling of boundary integral and finite element methods. We established a equivalence between the original exterior Signorini problem and the variational inequality on the bounded inner region coupled with two integral equations on an auxiliary boundary. We also introduce a finite element approximation of the variational inequality and a boundary element approximation of the integral equations. Furthermore, the optimal error estimates are given.展开更多
In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a ...In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.展开更多
In this paper, we apply EQ rot 1 nonconforming finite element to approximate Signorini problem. If the exact solution u∈H5/2(Ω), the error estimate of order O(h) about the broken energy norm is obtained for quadrila...In this paper, we apply EQ rot 1 nonconforming finite element to approximate Signorini problem. If the exact solution u∈H5/2(Ω), the error estimate of order O(h) about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconvergence results of order O(h3/2) are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.展开更多
This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the ...This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method.We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions.For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law,we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space.This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries.Furthermore,we present perturbation results for two well-established approximations of the classical Signorini condition:The Signorini condition formulated in velocities and the model of normal compliance,both satisfying even a sharper version of our stability condition.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11101454)the Natural Science Foundation of Chongqing CSTC,China(Grant No.cstc2014jcyjA00005)the Program of Innovation Team Project in University of Chongqing City,China(Grant No.KJTD201308)
文摘Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.
文摘In this paper,we study the accuracy enhancement for the frictionless Signorini problem on a polygonal domain with linear finite elements.Numerical test is given to verify our result.
基金Supported by the National Natural Science Foundation of China
文摘In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we utilize the results presented in this paper to study the Signorini problem in mechanics.
基金supported by the National Science Foundation of China(No.52109089)support of Post Doctor Program(2019M652281)Nature Science Foundation of Jiangxi Province(20192BAB216040).
文摘In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes.The idea of the LMFS is similar to the localized domain type method.The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix.The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function(NCP-function).Numerical examples are carried out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.
文摘In this paper, a new numerical method for the Signorini problem in three-dimensional elasticity is presented. The problem is reduced to a boundary variational inequality based on a new representation of the derivative of the doublelayer potential. Furthermore, a boundary element procedure is described for the numerical approximation of its solution and an abstract error estimate is given.
文摘We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of H2 regularity, then the convergence rate can be improved from O（h3/4） to quasi-optimal O（h｜log h｜1/4） with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal O（h） as expected by the linear approximation.
文摘In this paper, a exterior Signorini problem is reduced to a variational inequality on a bounded inner region with the help of a coupling of boundary integral and finite element methods. We established a equivalence between the original exterior Signorini problem and the variational inequality on the bounded inner region coupled with two integral equations on an auxiliary boundary. We also introduce a finite element approximation of the variational inequality and a boundary element approximation of the integral equations. Furthermore, the optimal error estimates are given.
文摘In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.
基金supported by National Natural Science Foundation of China (Grant Nos.10971203 and 11271340)Research Fund for the Doctoral Program of Higher Education of China (Grant No.20094101110006)
文摘In this paper, we apply EQ rot 1 nonconforming finite element to approximate Signorini problem. If the exact solution u∈H5/2(Ω), the error estimate of order O(h) about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconvergence results of order O(h3/2) are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.
基金supported by the DFG Research Center MATHEON,"Mathematicsfor key technologies:Modelling,simulation,and optimization of real-world processes",Berlin
文摘This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover,it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method.We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions.For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law,we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space.This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries.Furthermore,we present perturbation results for two well-established approximations of the classical Signorini condition:The Signorini condition formulated in velocities and the model of normal compliance,both satisfying even a sharper version of our stability condition.
