Static and dynamic problems for anisotropic inhomogeneous shells with variable parameters and their numerical solution (review)

Studies on the static and dynamic deformation of isotropic and anisotropic elastic shell-like bodies of complex shape performed using classical and refined problem statements are reviewed. To solve two-dimensional boundary-value problems and eigenvalue problems, use is made of a nontraditional discrete-continuum approach based on the spline-approximation of the unknown functions of partial differential equations with variable coefficients. This enables reducing the original problem to a system of one-dimensional problems solved with the discrete-orthogonalization method. An analysis is made of numerical results on the distribution of stress and displacement fields and dynamic characteristics depending on the loading and boundary conditions, geometrical and mechanical parameters of elastic bodies. Emphasis is placed on the accuracy of the results © 2013 Springer Science+Business Media New York.