The nonlinear prebuckling response of short thin-walled laminated composite cylinders in bending

The geometrically nonlinear Donnell shell theory is used to determine the prebuckling response of short thin-walled laminated circular cylinders in bending. Bending is induced by a known rotation of the clamped cylinder ends. The equilibrium equations and strain-displacement equations are manipulated so the governing partial differential equations are in first-order form. Using the separation of variables technique, along with a harmonic expansion in the circumferential direction, these first-order partial differential equations are converted to first-order ordinary differential equations. These equations are solved numerically using a finite-difference procedure and prebuckling responses are computed for cylinders with a radius:thickness ratio of 160 and length:radius ratios of 2 and 5. The range of validity of the prebuckling solution is limited by the critical, or buckling, end rotation, which is estimated by the simple classical method. The use of the classical estimate is justified by comparing it with more rigorous approaches. Three laminated composite cylinders are considered: an axially stiff [-/+45/0(2)](s) layup, a circumferentially stiff [-/+45/90(2)](s) layup, and a quasi-isotropic [-/+45/0/90](s) layup. The displacement response is discussed for each cylinder as a function of axial and circumferential location, with particular emphasis on the character of the radial displacement and the boundary layer associated with the nonlinear response. Comparisons with a geometrically linear. analysis are made. An analog with the axial compression problem is developed and valuable information about boundary layer length as a function of laminate material properties and applied end rotation is presented. In addition, the role of the laminate Poisson's ratio nu(x theta) on the displacement behavior is discussed. (C) 1996 Elsevier Science Ltd.