First ply failure analysis of stiened panels ± a ®nite element approach B.G. Prusty a,1 , C. Ray b , S.K. Satsangi a, * a Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, West Bengal 721302, India b Department of Civil Engineering, Bengal Engineering College, Sibpur, Howarh, India Abstract A ®rst-ply failure analysis method has been developed for predicting the failure load on the laminated composite stiened panels under various loading conditions. The present ®nite element formulation is generalised to analyse both laminated bare/stiened plate and shell panels elegantly. Eight noded isoparametric quadratic elements for shell and three noded curved beam elements for the stiener are used for the analysis of stiened panel. The stiness matrix of the stiener is computed independently and then transferred to that of the shell. The formulation eliminates the restriction on the location and orientation of the stiener within the shell element. Several prominent failure theories have been considered in the present work for the prediction of failure load. The results obtained by the present formulation have been compared with those available in literature and some parametric study has also been performed on the basis of variety in shell geometry. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Finite element method; First ply failure load; Isoparametric shell element; Laminated stiened panels 1. Introduction Composite materials have seen dramatic increase in usage because of their outstanding strength, stiness and lightweight properties. The structural panels commonly used for the construction of marine vehicles, spacecraft etc are made in the form of single skin laminates rein- forced by stieners. The purpose of the study is to pre- sent a ®nite element formulation for the prediction of ®rst-ply failure load of laminated stiened plate/shell panels, which are considered to be the building blocks of complicated marine structures. The failure of composite laminates starts gradually. It starts with the failure of the weakest lamina. The applied load should be below the speci®ed level to initiate damage to ensure reliability and safety in design, which necessitates the ®rst-ply failure analysis. The existing failure criteria are many in number [1]. Yeh±Stratton criteria [2,3] based on ductile as well as brittle material have been developed to examine the failure of composite materials. The unique feature of Y±S criteria is its ability to change its format depending upon the stress applied and the type of material strengths. The present study deals with failure theories based on macro-mechanical behaviour. Few investigations have been done on the failure analysis of laminated plates [4±7]. But investigation on the ®rst-ply failure of stiened shell panels are not readily available in literature. Ray and Satsangi [8] have made ®rst-ply failure analysis of laminated stiened plates using eight noded isoparametric plate bending element for plate and three noded beam element for stiener. They have computed failure loads with various failure criteria. Goswami [9] has computed ®rst-ply failure load based on Tsai±Wu criterion. To the author's knowledge, no published results are available on the ®rst-ply failure analysis of laminated stiened shell un- der any loading condition. In the present investigation, ®rst-ply failure analysis is done on the basis of various failure criteria based on the macro-mechanical behavior including the latest failure criterion, i.e., Yeh±Stratton criterion. 2. Finite element formulation 2.1. Shell element The formulation of shell element has been carried out using an eight noded isoparametric quadratic element with ®ve degrees of freedom, i.e., u; v; w; h s and h r . Based on the assumptions adopted by Mindlin and Reissnar, a www.elsevier.com/locate/compstruct Composite Structures 51 (2001) 73±81 * Corresponding author. Fax: +91-3222-55303. E-mail address: subir@naval.iitkgp.ernet.in (S.K. Satsangi). 1 Research scholar from Regional Engineering College, Rourkela 769008, India. 0263-8223/01/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 8 2 2 3 ( 0 0 ) 0 0 1 2 6 - 4