A PRACTICABLE AND LOCKING-FREE LAMINATED SHALLOW SHELL TRIANGULAR ELEMENT OF VARYING AND ADAPTABLE CURVATURE

The concerted effort aimed at the conception and evolution of simple t riangular finite elements for the analysis of laminated composite stru ctures continues in the present discourse with the presentation of a 3 -node (18 degrees of freedom) multilayered anisotropic shallow shell t riangular element. Essentially the triangular edges are represented by cubic polynomials thus allowing for linear curvatures which during th e course of a geometrically nonlinear deformation are automatically mo dified (by the natural modes) so that the element adapts to the new sh ell geometry. The formulation is based on kinematical and geometrical arguments in combination with subtle physical lumping principles and b asic assumptions of shallow shell theory - all elements of our ARTE sh allow shell formulation which is specifically oriented towards finite element analysis. The Natural Mode Method provides the element's kinem atical field through rigid-body and straining modes of deformation. Th e straining modes are assigned to the triangular edges and implicitly provide for the complete kinematical field. The 3-node composite trian gular element combines accuracy and economy (it only necessitates the computation of a 12 x 12 natural stiffness matrix) and all numerical e xperiments show that is free from the usual deficiencies of isoparamet ric displacement shell elements (i.e. locking, spurious modes, excessi ve 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 a nd composite shells demonstrate the accuracy of the theory and substan tiate the element's physical, geometrical and mathematical bases. A fu ll laminated' cylinder comprising 1504 degrees of freedom is studied t o show the potential of the present element in the analysis of real-ty pe practical structures. The major advantage of the developed shallow triangular element is expected in the nonlinear analysis of large and complex composite shells.