Beams Comprising Unilateral Material in Frictionless Contact: A Variational Approach with Constraints in Dual Spaces

Abstract

In this paper, beam models accounting for non-linear elastic bimodular constitutive behavior and frictionless unilateral contact conditions are rationally deduced from three-dimensional elasticity by means of a variational constrained approach. Consistent internal constraints on both stress and strain dual fields are enforced through a modified Hu-Washizu functional, obtained by a non-standard application of Lagrange multipliers and constrained in the convex set of the admissible contact displacements. A bimodular strain energy density is adopted and for both no-shear and first-order shear deformable beam models a generalized variational formulation of Signorini’s problem is recovered. Finally, several simple study cases are investigated, highlighting the influence of the bimodular constitutive law.KeywordsElastic StressBeam TheoryBeam ModelNeutral AxisDisplacement FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.