Beam bending problems on a Pasternak foundation using reciprocal variational inequalities

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Abstract
The present study is concerned with a class of two-body contact problems in linear elasticity. The model problem is a bending problem of the beam resting unilaterally upon a Pasternak foundation. A variational formulation is given by the mini-max principle of the functional, and proof of the existence of saddle points is given by the compatibility condition for applied forces and moments on the beam. It has been found that the compatibility condition for equilibrium of the beam and foundation can be achieved by arguments of coerciveness of the functional on the admissible set. An approximation and example of the problem by finite element methods and a numerical method for its solution are also introduced.

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