Three-node triangular element for arbitrarily laminated general shells Humayun R.H. Kabir * , Khaled Al-Shaleh Department of Civil Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait Available online 28 June 2005 Abstract A spurious transverse stiffness-free, isoparametric-formulation-based three-node triangular finite element, suitable for both mod- erately-thick and very thin advanced fiber reinforced arbitrary laminated shells, is presented. The basic finite element formulations relate to the consideration of the effects of transverse shear deformations similar to the first order shear deformation theory that introduces five degrees of freedom, three translations and two rotations, at each node of the element. A full integration scheme nor- mally exhibits locking phenomenon among FSDT-based elements having the inherent property of C 0 -continuity. The three-node triangular element is the most discreditable one among all elements for thin situations. This isoparametric-based element is well known for its shear locking effects in thin situations when a full or reduced integration scheme is used. These shear locking effects are now eliminated by imposing a constant transverse shear strain criterion and introducing a shear correction expression in the formulations. The element has shown a robustness in all types of triangular mesh configurations and in coupling effects that arise due to the lamination sequences. The numerical results include convergence tests for transverse displacement and moment for shells of rectangular platform for moderately-thick and very thin situations. These numerical results are compared with the recently avail- able analytical solutions. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Three-node element; Shells; Arbitrary lamination; First order theory 1. Introduction Advanced fiber reinforced composite laminated shell structures are flexible in transverse shear, in comparison to their isotropic-material counter parts, due to the pres- ence of matrix that holds the fibers in place. As a result, consideration of transverse shear effects in laminated structures deserves due attention. The Love–Kirchhoff- based general finite elements that completely negate the effects of transverse shear deformations require C 1 -continuity (i.e., the solution functions and its deriva- tive are continuous) resulting in complications of devel- oping conforming elements as well as shortcoming in structural responses with transversely weak laminated materials. As a consequence, such elements have been losing their charms among the composite material users. They are now being replaced by the first order shear deformation (FSDT)-based finite elements, where the ef- fects of transverse shear deformations are incorporated into the shell formulations. These FSDT-based elements that necessitate C 0 -continuity are easy to develop using isoparametric shape functions, and are very popular among composite shell users. However, the FSDT-based elements are not free from flaws when full or reduced integration schemes are used, as laminates get thin these elements exhibit spurious transverse stiffness (spurious shear–strain energy) that results locking in convergence and posing difficulties in using directly such elements to thin shell situations. This spurious shear–strain energy generates from failing to satisfy the Kirchhoff conditions at thin situations: Composite Structures 77 (2007) 18–29 www.elsevier.com/locate/compstruct 0263-8223/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2005.05.013 * Corresponding author. E-mail address: kabir@civil.kuniv.edu.kw (H.R.H. Kabir).