A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle ...A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.展开更多
Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number o...Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.展开更多
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problem...Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.展开更多
The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a ...The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.展开更多
Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in t...Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-ditnensicnal continua is derived, and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form tire obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.展开更多
The formulation of boundary element method for handling contact problems with friction and the technique for high speed contact analysis are presented. This formulation is based on the idea of modifying the length of...The formulation of boundary element method for handling contact problems with friction and the technique for high speed contact analysis are presented. This formulation is based on the idea of modifying the length of contact elements without altering the total number of elements. The high precision of solution and high speed analysis are verified according to the results of conventional method and analysis method.展开更多
We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric ...We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.展开更多
Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second ...Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a nondifferentiable term due to the frictional contact. We prove that these C^0 DG methods are consis tent and st able, and derive optimal order error estima tes for the quadratic element. A numerical example is presented to show the performance of the C^0 DG methods;and the numerical convergence orders confirm the theoretical prediction.展开更多
Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solut...Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solutions to the finite-dimensional models are proved.A minimum principle is developed and a minimization algorithm is presented.Numerical calculation shows that the algorithm is highly efficient,reliable and promising.展开更多
文摘A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.
基金The project supported by the National Natural Science Foundation of China
文摘Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.
基金The project supported by the National Natural Science foundation of china(10225212,50178016.10302007)the National Kev Basic Research Special Foundation and the Ministry of Education of China
文摘Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.
基金supported by the Minisitry of Science of the Republic of Serbia (No. 144005)
文摘The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.
文摘Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-ditnensicnal continua is derived, and the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form tire obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.
文摘The formulation of boundary element method for handling contact problems with friction and the technique for high speed contact analysis are presented. This formulation is based on the idea of modifying the length of contact elements without altering the total number of elements. The high precision of solution and high speed analysis are verified according to the results of conventional method and analysis method.
文摘We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.
文摘Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a nondifferentiable term due to the frictional contact. We prove that these C^0 DG methods are consis tent and st able, and derive optimal order error estima tes for the quadratic element. A numerical example is presented to show the performance of the C^0 DG methods;and the numerical convergence orders confirm the theoretical prediction.
基金Project supported by the National Natural Science Foundation of China.
文摘Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solutions to the finite-dimensional models are proved.A minimum principle is developed and a minimization algorithm is presented.Numerical calculation shows that the algorithm is highly efficient,reliable and promising.
