An improved shear-membrane theory for multilayered shells

A new two-dimensional theory for the analysis of deep, doubly curved, multilayered shells is proposed. The theory is based on a kinematical approach in which the continuity conditions for displacements and shear stresses at layer interfaces and on the bounding surfaces of the shell are exactly satisfied, while, at the same time, refinements of the shear and membrane terms are taken into account, by means of trigonometric functions. The accuracy of the model is assessed in statics and dynamics through investigation of significant problems, for which an exact three-dimensional elasticity solution is known. In statics, the cylindrical bending of a cylindrical panel, of thickness h, and inner radius R, is examined. The results obtained are in good agreement with the analytical solution of Ren [Comput. Sci Technol. 29 (1987) 169¯187], and prove that no shear-correction factors are requested. In dynamics, wave propagation in a three-layered elastic cylinder is explored. The accuracy of the theory is assessed by comparison with the exact three-dimensional elasticity solution of Armenakas [J. Acoust. Soc. Am. 49 (5, Part 2) (1971) 1511¯1520]. The model is then applied to the exploration of the dispersive behavior of a viscoelastic cylinder.