Int. J. Impact Engn# Vol. 9, No. 4, pp. 475~,84, 1990 0734-743X/90 $3.00+0.00 Printed in Great Britain Pergamon Press plc ON THE TRANSIENT RESPONSE OF CROSS-PLY LAMINATED CIRCULAR CYLINDRICAL SHELLS A. A. KHDEIR, J. N. REDDY and D. FREDERICK Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A. (Received 25 August 1989; and in revised form 26 June 1990) Summary--Transient response of simply-supported circular cylindrical shells is investigated using a higher-order shear deformation theory (HSDT). The theory is a modification of the Sanders' shell theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the bounding surfaces of the shell. The results obtained using the classical shell theory (CST) and the first-order shear deformation theory (FSDT) are compared with those obtained using the higher-order theory. The state-space approach is used to develop the analytical solutions to the equations of motion of the three theories. INTRODUCTION Laminated composite shells have found increasing application in many engineering structures. The applications range from machine elements to high performance space vehicles. The strength and light-weight requirements of space and under-water structures have created considerable interest in the study of composite circular cylindrical shells [1-11]. The study of transient response of composite laminates has received widespread attention in recent years. The classical separation of variables method in conjunction with the Mindlin-Goodman procedure was used by Sun and Whitney [12-15] and Dobyns [16]. Chou [17] employed the Laplace transform technique to study the dynamic response of orthotropic plates. Reddy [18-20] used the Newmark direct integration method in the dynamic analysis of the first and third order theories. The objective of this paper is to offer an exact solution based on the state-space technique to the dynamic response of cross-ply circular cylindrical shells. The solutions of the transient analysis of the third-order, first-order and classical laminate theories are presented in graphical form and the influence of lamination schemes on the center deflection and stresses is also investigated. GOVERNING EQUATIONS The governing equations of the third-order theory developed by Reddy and Liu [21,22] as applied to a circular cylindrical shell of length L, radius R and thickness h are: 0N 1 0N6 0~ 8x~ 0xx ON 6 + ON2= lqi) + r,2~2_ Tr,3 orb ox 1 Ox 2 Ox 2 coO, OQ2 \<~x, Ox2l+ ~C2\ ox~ + ox~ + 20x, Ox2} R - - F --ycl bq Oxl Ox2 R Oft + 7r5 + 7-F3- - + 7i-'5 + i, w- ~c2ITt~x2 + ~x22 ) = yr 3 dx I ox I Ox 2 Ox 2 475