Contact problems for nonlinearly elastic materials: weak solvability involving dual Lagrange multipliers

Andaluzia Matei, Raluca Ciurcea

Abstract


A class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

doi:10.1017/S1446181111000629

Keywords


contact models; nonlinearly elastic materials; dual Lagrange multipliers; weak solutions



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.2212



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.