A practicable and locking-free laminated shallow shell triangular element of varying and adaptable curvature

Abstract

The concerted effort aimed at the conception and evolution of simple triangular finite elements for the analysis of laminated composite structures continues in the present discourse with the presentation of a 3-node (18 degrees of freedom) multilayered anisotropic shallow shell triangular element. Essentially the triangular edges are represented by cubic polynomials thus allowing for linear curvatures which during the course of a geometrically nonlinear deformation are automatically modified (by the natural modes) so that the element adapts to the new shell geometry. The formulation is based on kinematical and geometrical arguments in combination with subtle physical lumping principles and basic assumptions of shallow shell theory - all elements of our ARTE shallow shell formulation which is specifically oriented towards finite element analysis. The Natural Mode Method provides the element's kinematical field through rigid-body and straining modes of deformation. The straining modes are assigned to the triangular edges and implicitly provide for the complete kinematical field. The 3-node composite triangular element combines accuracy and economy (it only necessitates the computation of a 12 × 12 natural stiffness matrix) and all numerical experiments show that is free from the usual deficiencies of isoparametric displacement shell elements (i.e. locking, spurious modes, excessive stiffness and reduced quadrature etc.). Throughout the formulation emphasis is placed on issues of economy, efficiency and practicality. Numerical examples for linear and nonlinear deformation of isotropic and composite shells demonstrate the accuracy of the theory and substantiate the element's physical, geometrical and mathematical bases. A full laminated cylinder comprising 1504 degrees of freedom is studied to show the potential of the present element in the analysis of real-type practical structures. The major advantage of the developed shallow triangular element is expected in the nonlinear analysis of large and complex composite shells.