Boundary variational ’principles’ for inequality structural analysis problems and numerical applications. (English) Zbl 0597.73096

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

Comput. Struct. 25, 35-49 (1987).

Summary: The aim of the present paper is the derivation of boundary variational ’principles’ for inequality problems i.e. for problems having as variational formulations variational or hemivariational inequalities. Using first the principles of minimum potential and complementary energy we derive first saddle point formulations for the problems using appropriate Lagrangians. Then we eliminate by an appropriate elimination technique the internal degrees of freedom and we obtain two minimum principles having as unknowns the normal displacements and reactions of the boundary region, respectively. Analogously we treat the case of hemivariational inequalities. The theory is applied to the inclusion and inhomogeneity problem and is illustrated by numerical examples solved both by the F.E.M. and the B.E.M.

MSC:

74P99	Optimization problems in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
74A55	Theories of friction (tribology)
74M15	Contact in solid mechanics
49J40	Variational inequalities
49S05	Variational principles of physics
74E05	Inhomogeneity in solid mechanics

Keywords:

boundary variational principles; two minimum principles; Signorini- Fichera problem; constraints; convex; nonconvex; superpotential; unilateral contact problem; quadratic programming; problem; separability of contact contours; hemivariational inequalities; principles of minimum potential; complementary energy; saddle point formulations; Lagrangians; elimination technique; internal degrees of freedom; normal displacements; reactions of the boundary region