Equations of equilibrium for a strongly heterogeneous shallow shell

Abstract

A linear set of equations is proposed for a strongly thickness-heterogeneous (in particular, multilayer) shallow shell. The model unifies the equations of the Mushtary−Donnell−Vlasov technical-theory and the Timoshenko−Reissner equations, which take into account transverse shear. The thickness-heterogeneous shell is replaced with an equivalent homogeneous transversally isotropic shell, the elasticity modula of which are chosen just as the previously determined elasticity modula for heterogeneous plates. In the test example for a multilayered cylindrical shell, the approximate solution according to the proposed model is compared with the exact solution of the three-dimensional problem. The model gives good results in accuracy for a reasonably wide level of inhomogeneity.