Mathematical models and algorithms for studying strength and stability of shell structures

In this paper, we describe severalmathematical models of deformation of reinforced shell structures, including those that account for various properties of the material. For the structures composed of orthotropic and isotropicmaterials, we consider linearly elastic and physically nonlinear problems, as well as the problems of creep. All models are constructed on the basis of the functional of total potential energy of the shell deformation. Geometric nonlinearity and transverse shears are taken into account. Strengthening ribs are introduced both in the discrete way and by the method of structural anisotropy. Three different algorithms of studying the strength and stability of shells are presented each of which is most effective for a specific range of problems.