Boundary Problem of Thin Shells Theory

Abstract

A boundary problem for thin elastic shells is formulated. The generally acceptable geometrical (straight normal) and physical (linear elasticity) hypotheses which underlie the relations are considered. Geometrical nonlinearity of shell deformation is taken into account. Equilibrium equations expressed via the displacements of shell middle surface are presented as governing relations. Tangent and bending boundary conditions along the arbitrary shell contour (free and clamped edge, free-hinge and fixed-hinge, elastic support) are formulated. A set of previously satisfied conditions (regularity of shell surface and material, piecewise continuity of shell contour and of boundary support parameters) is implemented and the concept of a generalized solution is introduced. The small perturbation of a vector-function of a generalized solution is considered, becoming the basis of investigation of non-uniqueness of the generalised solution, and of branching of the solutions.