Noboru Kikuchi

Contact problems involving forces and moments for incompressible linearly elastic materials

Abstract Aclass of rigid punch problems for an incompressible linearly elastic body involving forces and moments is considered by the theory of variational inequalities. After showing a proof of existence of the solution under a compatibility condition of the applied force and moment, extensive discussions about the reduced constraint of incompressibility in the finite element approximation are given. The reduced constraint is an explanation of the so-called reduced integration technique to resolve the incompressibility. Finally, the contact condition is controlled pointwise. Some justifications of the pointwise control are given by the idea of numerical integration.

A Class of Rigid Punch Problems Involving Forces and Moments by Reciprocal Variational Inequalities

ABSTRACT This study is concerned with a reciprocal formulalion of a class of rigid punch problems involving forces and moments. The unilateral contact conditions impose variational inequalities on the formulation of the problem. The present study is a generalization of Duvauts work in the sense that not only forces but also moments are applied on the rigid punch. A solution method for the formulation is also introduced together with several numerical examples.