A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto-plastic structures is constructed. A series of PQP formulae for contact problems and elastic-plastic structures is derived in the text, and some numerical examples are illustrated as well.

[1]  A. Klarbring.  A mathematical programming approach to three-dimensional contact problems with friction , 1986 .

[2]  C. Ramakrishnan,et al.  A finite element solution for the two‐dimensional elastic contact problems with friction , 1981 .

[3]  Zhong Wan-xie,et al.  Quadratic Programming with Parametric Vector in Plasticity and Geomechanics , 1987 .

[4]  Johann Kollegger,et al.  Nonlinear contact problems—A finite element approach implemented in ADINA , 1985 .

[5]  Nguyen Dang Hung,et al.  Frictionless contact of elastic bodies by finite element method and mathematical programming technique , 1980 .

[6]  Philippe A. Tanguy,et al.  Finite element solution of three-dimensional incompressible fluid flow problems by a preconditioned conjugate residual method , 1987 .

[7]  W. E. Haisler,et al.  A finite element solution method for contact problems with friction , 1987 .

[8]  E. J. Haug,et al.  Analysis of unbonded contact problems by means of quadratic programming , 1976 .

[9]  J. Tinsley Oden,et al.  Finite Elements: Special Problems in Solid Mechanics , 1984 .

[10]  K. Huebner.  The finite element method for engineers , 1975 .

[11]  Bo Torstenfelt.  An automatic incrementation technique for contact problems with friction , 1984 .

[12]  S. Timoshenko,et al.  Theory Of Elasticity. 2nd Ed. , 1951 .

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

[14]  J. T. Oden,et al.  Numerical analysis of certain contact problems in elasticity with non-classical friction laws , 1983 .