The effect of surface stresses on the stress-strain state of shells

The effect of surface stresses on the stress-strain state (SSS) of an elastic shell is investigated. The surface stresses are represented as a static pre-loading localized in ultra-thin layers of the shell close to its surface. It is assumed that the mechanical properties of the surface layers differ from the properties of the material far from the surface. The three-dimensional elasticity equations are analysed by an asymptotic method using several asymptotic parameters. Equations are obtained by the method of reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of shell theory in which surface stresses have to be taken into account for a sufficiently small shell thickness. Asymptotic estimates of the effect of surface stresses on the SSS are obtained as a function of the ratio of the elastic moduli of the shell material and of the layer close to the surface, the ratio of the shell thickness to the thickness of the surface layer and the type of SSS and its variability with respect to the coordinates.