A REFINED THEORY OF LAMINATED SHALLOW SHELLS

A new refined but simple shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. To evaluate the new displacement field assumed which is justified in plates from the three-dimensional elasticity theory, classic types of shallow shells a re considered. The boundary value problem is formulated by making use of the principle of virtual power in conjunction with the assumed cons istent displacement field. The theory accounts for cosine distribution of the transverse shear strains through thickness of the shell and ta ngential stress-free boundary conditions on the boundary surfaces of t he shell. The theory also accounts for in-plane inertia and rotatory i nertia. The Navier type exact solutions are presented in statics and i n vibrations for cylindrical and spherical shells under simply support ed edge boundary conditions. The theory is of the same order of comple xity as the shear deformation theory but is very much more efficient w ithout needing shear correction factors. Some numerical comparisons wi th other works are made.