Singularity of stresses at the top of an elastic wedge supported by a thin flexible coating on its sides

Abstract

A study of the problem of determining the asymptotic behavior order of stresses at the top of the wedge-shaped area in cases when a thin flexible coating is fixed on its sides (or on one of them) was conducted. On the other side of the wedge-shaped area, the conditions for the presence of the same coating are assumed either it is fixed, stress-free or in smooth contact with a rigid solid. Mathematically, the problem is reduced to the problem of determining the roots of characteristic transcendental equations arising from the condition for the existence of a nontrivial solution of a system of homogeneous linear equations. For various combinations of boundary conditions and wedge angles, the asymptotic behavior order are determined for components of the stress tensor. In particular, the values of the angles at which the singular behavior of the stresses occurs.A study of the problem of determining the asymptotic behavior order of stresses at the top of the wedge-shaped area in cases when a thin flexible coating is fixed on its sides (or on one of them) was conducted. On the other side of the wedge-shaped area, the conditions for the presence of the same coating are assumed either it is fixed, stress-free or in smooth contact with a rigid solid. Mathematically, the problem is reduced to the problem of determining the roots of characteristic transcendental equations arising from the condition for the existence of a nontrivial solution of a system of homogeneous linear equations. For various combinations of boundary conditions and wedge angles, the asymptotic behavior order are determined for components of the stress tensor. In particular, the values of the angles at which the singular behavior of the stresses occurs.