Boundary minimum principles for the unilateral contact problems. (English) Zbl 0626.73123

Panagiotopoulos, P. D.; Lazaridis, P. P.

Int. J. Solids Struct. 23, 1465-1484 (1987).

The aim of the present paper is the derivation of boundary variational principles for the unilateral contact problem. Using the inequality constrained principles of minimum potential and complementary energy and the equivalent variational inequality formulations we derive first saddle point formulations for the problems using appropriate Langrangian functions. An elimination technique allows the formulation of two minimum “principles” on the boundary with respect to the unknown normal displacements and reactions of the contact region, respectively. It is also shown that these two minimum problems are equivalent to multivalued boundary integral equations involving symmetric operators. The theory is illustrated by numerical examples solved both by the FEM and the BEM.

MSC:

74A55	Theories of friction (tribology)
74M15	Contact in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
65K10	Numerical optimization and variational techniques
90C20	Quadratic programming
49J40	Variational inequalities

Keywords:

boundary element method; minimum principles; boundary variational principles; unilateral contact problem; inequality constrained principles of minimum potential; complementary energy; saddle point formulations; Langrangian functions; elimination technique; multivalued boundary integral equations; symmetric operators