This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 1 (2006), pp. 43 - 55 NON-LINEAR ANALYSIS OF LAMINATED COMPOSITE DOUBLY CURVED SHALLOW SHELLS DAO HUY BICH Vietnam National University, Hanoi Abstract. This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell. 1. INTRODUCTION Linear analysis of laminated composite plates and shells was investigated by many :.·_:-::-_ors. However for non-linear analysis of these structures we are concerned with more ::_--=.culties, because the non-linearly partial differential equations governing composite :~:iates of arbitrary geometries and boundary conditions cannot be solved exactly. Ap; : - : :·2mate analytical solution to the large deflection theory of laminated composite plates :.=.:::. ::.on-linear bending and buckling analysis of cylindrical composite shells were consid-=::--:-:::. :or example, in [2-6, 8-11,19,22 .]. For plates of complicated geometries and shells : ::::.-"- ·.:'. ewlops non-linear finite element models of laminated structures, more results were ::-::.:~:. especially results of Reddy and the others [1, 7, 12-18, 21. ] . Tf: problem of postbuckling behaviour of shell structures under loading and non_ ::-_o~::- Yibration of shells is of significant practical interest. The present paper is conerned • --:. ~:::. ;owrning equations and approximate analytical solutions based on some wellknown .'.:~-_:_"::.;Hions to the non-linear buckling and vibration problems of laminated composite : : ·_:·::,::.· curYed shallow shells. Obtained results will be presented by analytical expression : : ~::-:- ~ower critical load, the postbuckling .
