Closed-Form Analytical Solutions for Thin-Walled Cylindrical Composite Shell Structures Subjected to Axial and Bending Loads Under Temperature Environment
Authors: Mahadev Sthanu , Chan Wen S. 
Published: March 2016

This research discourse presents the development of a holistic mathematical model that is dedicated to showcase a set of analytical expressions for predicting global stiffness (axial stiffness, bending stiffness) and a material response characterization based on ply-per-ply in-plane stress investigations relevant to open-celled multidirectional curved cylindrical shell configurations. Additionally, the analytical model is shown to present the capability to mathematically determine the location of the centroid for thin-walled, composite cylindrical shells. The resulting centroidal expression for a composite system is essentially shown to be a primary function of material properties, composite stacking sequence, fiber orientation angle and the structural geometry as opposed to metal counterparts whose centroidal point is solely governed by their geometry.

Analytical stress estimates are computed for thin-walled curved cylindrical shell constructions that are subjected to typical tension and longitudinal bending type loading conditions applied at the centroid under the presence and absence of a uniformly distributed thermal loading environment. A broad parametric investigation on the in-plane ply stresses (σx,σy,τxy) are conducted via choosing three fundamental parameters namely; varying mean radius of curvature, changing laminate thickness-to-mean radius ratio and increasing laminate thickness respectively. Three preferentially tailored variabilities in ply stacking sequence are established from a [(±45° / 0°]s symmetric-balanced composite lay-up to illustrate the effects on ply stresses.

An ANSYS based finite element analysis scheme is employed to numerically determine the location of centroid and further substantiate the analytically acquired centroid predictions including and excluding the effects of temperature. The centroidal point is identified and its location is progressively reported for a fully open cross-sectioned curved strip to a fully closed cylindrical composite tube configuration by examining their distribution pattern as a function of circumferential arc angle (2α). FE tool is additionally utilized to compare the analytical stiffness predictions and analyze the validity of the in-plane analytical stress estimates. Excellent agreement is achieved in comparison between analytical solutions and computationally generated FE results. The central goal of this work is to demonstrate the potential of the formulated mathematical framework in accurately predicting the key mechanical attributes that dictates the structural behavior of curved composite shell members. This analytical model is designed to serve as a robustly efficient tool towards assisting structural design engineers in quickly gaining a broad fundamental understanding on the physical characteristics and structural response of such configurations by accurately conducting simple parametric studies during preliminary design phase prior to performing complex FE analyses.