On the elastic solution of frictional contact problems using variational inequalities

Abstract This article is devoted to the development and implementation of a variational inequalities approach to treat the general frictional contact problem. Unlike earlier studies which adopt penalty methods for the solution of the corresponding variational inequalities, the current investigation uses quadratic programming and Lagrange's multipliers to solve the frictional contact problem and identify the candidate contact surface. The proposed method avoids the use of user-defined penalty parameters, which ultimately govern the convergence and accuracy of the solution. To establish the validity of the method, a number of test cases are examined and compared with existing solutions where penalty methods are employed.

[1]  J. Böhm,et al.  A comparison of different contact algorithms with applications , 1987 .

[2]  D. A. Spence,et al.  Self similar solutions to adhesive contact problems with incremental loading , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[4]  K. Surana,et al.  Isoparametric line and transition finite elements with temperature and temperature gradients as primary variables for two dimensional heat conduction , 1986 .

[5]  Masaru Nakazawa,et al.  Finite element incremental contact analysis with various frictional conditions , 1979 .

[6]  Anil Chaudhary,et al.  A solution method for static and dynamic analysis of three-dimensional contact problems with friction , 1986 .

[7]  H. Parisch.  A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis , 1989 .

[8]  J. Mottershead,et al.  Linear elastic contact problems using curved elements and including dynamic friction , 1988 .

[9]  Byung Man Kwak,et al.  Analysis and applications of elasto-plastic contact problems considering large deformation , 1986 .

[10]  P. Panagiotopoulos,et al.  On the rigid body displacements and rotations in unilateral contact problems and applications , 1991 .

[11]  Klaus-Jürgen Bathe,et al.  ON THE TREATMENT OF INEQUALITY CONSTRAINTS ARISING FROM CONTACT CONDITIONS IN FINITE ELEMENT ANALYSIS , 1991 .

[12]  Moshe Eisenberger,et al.  Simple planar modeling of asymmetric shear buildings for lateral forces , 1986 .