Linear theory of shells taking into account surface stresses

A study was conducted to obtain the equations of equilibrium and constitutive equations for the stress resultants and couples tensors while taking into account the surface stresses acting on the shell surfaces. The equations were obtained generalizing the results to the case of the linear theory of elastic shells taking into account the transverse shear. The effective shell stiffness, specifically the bending stiffness Deff depended on the surface elastic moduli, which is substantial for nanodimensional thicknesses. The variational method was used for the formulation of boundary-value problems of the theory of elasticity with surface stresses. Constitutive equations also made it possible to write the equilibrium equations for the shell and plate with taking into account surface stresses in terms of displacements and rotations.