In6 1. Engng Sci. Vol. 31, No. 6, pp. 967-988. 1993 W20-7225/93 $6.00 + 0.00 Printed in Great Britain. Al! rights reserved Copyright @ 1993 Pergamon Press Ltd zyxwvut A HIGHER-ORDER THEORY FOR THE ANALYSIS OF LAMINATED PLATES AND SHELLS WITH SHEAR AND NORMAL DEFORMATION V. G. PlSKUNOV Kiev Highway and Automobile Institute, Suvorova Street No. 1, Kiev 252010, Ukraine V. E. VERIJENKO, S. ADALIt and E. B. SUMMERS Department of Mechanical Engineering, University of Natal, Durban 4001, Republic of South Africa Abstract-An improved higher-order theory is developed for the stress analysis of laminated tranversely isotropic plates and shells subject to transverse shear deformation and normal compres- sion. The theory is capable of analyzing the stress-strain behavior of layered plates and shells with an arbitrary number and sequence of layers which may differ significantly in their physical and mechanical properties. New variables which have a clear physical meaning are introduced. Various loading and boundary conditions are considered which enable transverse shear and normal reduction to be fully taken into account, and the complete set of boundary conditions is derived. The closed-form solutions of some multilayered plates and shells are derived. Numerical results are compared with those given in the literature, in order to validate the analysis presented. The features of this theory and the implications of the numerical results are discussed. 1. INTRODUCTION The advanced composite constructions involving laminated thin-walled structures, such as plates and shells, are now widely used in many mechanical and civil engineering applications. The increased use of multilayered structures has created considerable interest in their stress and strain state analysis. It is well-known that the use of the classical theory of laminated plates and shells leads to substantial errors in the design of these structures. Therefore, in recent years, numerous approaches which take into account transverse shear have appeared. Surveys of these theories, usually referred to as “higher-order”, “nonclassical”, “refined” or “improved” theories may be found in the reviews by Dudchenko et al. [I], Librescu and Reddy [2], Reddy [3] and N oor and Burton [4f, and in the books of Bolotin and Novichkov [5], Grigorenko and Vasilenko [6] and Piskunov and Verijenko [7], where the specific features of various theories and the contributions of their authors have been outlined. The main directions in the development of higher-order theories of multilayered structures will now be discussed briefly. The two main approaches for deriving 2-D equations of plates and shells are the analytical method and the method of hypotheses. Analytical approaches were introduced by Reissner [8f, Mindlin 191 and Gol’denveizer [lo] and have been used subsequently by other authors [ll-131. In the derivation of theories using a method of hypotheses, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA two approaches have been employed: “discrete-structural” [l, 71 or “layer-wise” [2,37 theories; and “continuously-structural” [ 1,7] or “single-layer” [2,3] theories. Both have advantages and disadvantages as outlined in Refs [l, 4,7,14]. The first approach leads to a system of governing equations whose order depends on the type of hypotheses and number of layers. In the second approach the order of the governing equations depends only on the type of hypotheses. The generalization of the first approach is given in Refs [S, 61, and more recently in Ref. [14]. The second approach was introduced by Ambartsumyan [15], where the classical hypotheses of Kirchhoff-Love were used. He then used this approach to derive a higher-order theory of laminated plates and shells [16]. However in these and other more recent publications mentioned in the reviews in Refs [l, 41, there is no compatibility between the nonlinear kinematic model which considers the distortion of the - .-.._I__- ~_________..__~ $To whom correspondence should be addressed. 967