Analytical and Finite Element Modelling for Static Analysis of Doubly Curved Spherical and Cylindrical Laminated Composite Shells

Abstract

In this present work, the static analysis of multilayered laminated composite spherical and cylindrical shells by using an inverse hyperbolic shear deformation theory (IHSDT) is presented. A non-polynomial shear strain shape functions (combination of inverse hyperbolic function) is used in the present theory which more accurately maps the shear strain in the transverse direction. The present IHSDT also produce results for plate as a special case. By implementing the purposed displacement field along with the strain-displacement relations, and constitutive relations in the virtual work principle, the governing equation are obtained in terms of five field variables. These equations are then solved using Navier-type, closed form solutions. The bending results are presented for cylindrical and spherical shells for simply supported boundary conditions. These shells are subjected to sinusoidal, distributed and point loads in transverse direction. The results are provided for thick to thin as well as shallow and deep shells. The present results are compared with the layer wise theory and with several other well-known higher order shear deformation theories (HSDTs). Further, the finite element numerical solutions are also presented for various other boundary conditions and compared with present IHSDT results and as well with various other HDST theories. The comparison of the present results reveals the applicability and validity of IHSDT both in analytical and finite element framework.