Two Variants of Stating Problems of Mechanics of a Strip with a Section of One-Sided Fixing of Finite Length on a Rigid Support Element

The equivalence of two variants of problem formulation for mechanics of a strip rod connected to a rigid and fixed support element on a finite-size section of one of its face surfaces is proved. The first formulation is based on the use of a transformation model of rod deformation based on the transformation of the relations of the simplest Timoshenko shear model by preliminary satisfying the conditions of kinematic conjugation of the rod with the support element on the fastening section with the subsequent formulation of the kinematic and static conditions of conjugation of the fixed rod section with the loose one. The second variant, corresponding to the contact formulation of the problem, is based on the use of uniform relations of the refined Timoshenko-type theory for the entire rod (for the fixed and loose sections), containing an unknown tangential contact stress at the points of the surface of the connection of the rod with the support element on the fixed section, which is included in the equations as an external load. To determine this, the conditions of kinematic conjugation of the rod with the support element are used.