Elastic deformation of thick, laminated composite shells

Abstract

A rigorous theory is derived which governs the linearly elastic deformation of shells made of laminated composite materials, including shear deformation and rotary inertia effects. The equations presented are applicable to static and dynamic problems for shells of arbitrary curvature, but constant thickness. Non-principal shell coordinates (α,β) are used in order that shells with initial twist ( R αβ ≠ ∞) may be straightforwardly accommodated. Equations of motion, boundary conditions and energy functionals are given for laminates with arbitrary fiber stacking sequences. An accurate theory is developed based upon the assumptions that terms containing ζ 2/ R i R j ( i, j = α, β) are small in comparison with unity, where ζ is the thickness coordinate, and R α and R β are radii of curvature. A more simple but less accurate theory is also given, corresponding to ζ/ R i ⪡ 1 ( i = α, β). Shallow shell theories are obtained by setting the Lamé parameters equal to unity and using projected planform coordinates ( x,y) in place of the shell coordinates (α, β). Further simplification to a Donnell-type shallow shell theory is also made.