Displacement Response of Segmented-Stiffness Composite Cylinders
Authors: Hyer Michael W. , Riddick Jaret C. 
Published: January 2022

Abstract
With advanced manufacturing technology such as tow placement devices and filament winders, cylindrical composite structures may well be constructed in such a fashion that the lamination sequence varies with circumferential location around the cylinder. For example, the stacking sequence at the top and bottom of the cylinder may be axially stiff to resist bending and axial loads, while the sides of the cylinder may be designed to resist shear loads. The variation in stacking sequence may be continuous, with the stacking sequences on the top and bottom making a smooth transition to another stacking sequence on the sides. Alternatively, as a manufacturing convenience the cylinder may be constructed in circumferential sections, or segments, using more conventional manufacturing technology. There would then be discrete changes in laminate stacking sequence at specific locations around the circumference which would result in stepwise changes in laminate properties at the circumferential locations where the different segments join. In reality, there may be stiffeners incorporated into the cylinder, particularly at the locations where the segments join. For the present work stiffeners will not be considered and as a result of the discrete change in stiffness rather unusual displacement response will occur, even for simple loadings. The present paper examines the response of a segment-stiffness composite cylinder to compressive axial end shortening and internal pressure. For more conventional nonsegmented construction where the cylinder is constructed of a single laminate, these loadings cause axisymmetric response, at least in the range of linear response. The specific cylinder considered has its top and bottom segments made of the same laminate, and the sides made of another laminate. It is further assumed that the bending-twisting stiffnesses D16 and D26 are negligible. As a result, the problem exhibits quarter symmetry and this feature is exploited in the analysis.
For pedagogical reasons an infinitely long cylinder is initially studied. This problem can be solved in closed form and the solution indicates that the primary feature that distinguishes the response of an infinitely-long segmented-stiffness cylinder from that of a more conventional single-laminate cylinder is the existence of circumferential displacements. For the case of axial end shortening, it is the difference in Poisson’s ratios between the various segments that is responsible for the existence of circumferential displacements. For the case of internal pressure, it is the difference in the extensional stiffnesses that causes the circumferential displacements. In both cases the radial displacement is independent of circumferential location, and therefore an infinitely long round cylinder remains round.
Motivated by the results for an infinitely long cylinder, a finite-length cylinder is studied by using the principle of minimum total potential energy in combination with the Kantorovich approach. For the application of the latter approach, the dependence of the response on the circumferential coordinate is assumed to be harmonic, and the dependence on the axial coordinate is solved for from the resulting system of ordinary differential equations that are obtained by taking the first variation of the total potential energy. Like the infinite-length cylinder, circumferential displacements characterize the response, but the boundary conditions greatly influence the magnitude of the circumferential displacement. Also, unlike the infinite-length cylinder, the finite-length cylinder does not stay round, rather, the radial displacements are a function of the circumferential location. The eigenvalues of the system of ordinary differential equations indicate that the characteristic lengths (St. Venant effect) for the circumferential and radial displacements are not the same. There is a bending boundary layer associated with the radial displacements, as with nonsegmented construction, but there is no boundary layer associated with the circumferential displacements. These eigenvalues help explain the behavior of the finite-length cylinder.