Advanced formulation for laminated composite shells: 3D stress analysis and rigid-body motions

The application of the sampling surfaces (SaS) method to laminated composite plates is presented in a companion paper (Kulikov GM, Plotnikova SV. Exact 3D stress analysis of laminated composite plates by sampling surfaces method. Compos Struct 2012;94:3654–3663). In this paper, we extend the SaS method to shells to solve the 3D elasticity problems for cylindrical and spherical laminated composite shells. For this purpose, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic kinematic variables. Such choice of displacements allows the derivation of strain–displacement equations, which are invariant under all rigid-body shell motions in any convected curvilinear coordinate system. This gives in turn the opportunity to find the 3D elasticity solutions for laminated composite shells with a prescribed accuracy utilizing a sufficiently large number of SaS, which are located at Chebyshev polynomial nodes and layer interfaces as well.