Triangular thin shell finite element for laminated general shells

The problems associated with the finite element\ud analysis of thin shell structures are discussed with the\ud objective of developing a simple and efficient thin\ud shell finite element. It has been pointed out that the\ud difficulties in the formulation of thin shell elements\ud stem from the need for satisfaction of the interelement\ud normal slope continuity and the rigid body displacement\ud condition by the displacement trial functions. These\ud difficulties have been surmounted by recourse to the\ud discrete Kirchhoff theory (DKT) approach and an\ud isoparametric representation of the shell middle surface.\ud A three node curved triangular element with simple\ud nodal connections has been developed wherein the\ud displacement and rotation components are independently\ud interpolated by complete cubic and quadratic polynomials\ud respectively. The rigid body displacement condition is\ud satisfied by isoparametric interpolation of the shell\ud geometry within an element. A convergence to the thin\ud shell solution is achieved by enforcement of the\ud Kirchhoff hypothesis at a discrete number of points in\ud the the element. A detailed numerical evaluation through\ud a number of standard problem has been carried out.\ud Results of application of a patch test solution to\ud a spherical shell demonstrates the satisfactory\ud performance of the element under limiting states of\ud deformation. It is concluded that the DKT approach in\ud conjunction with the isoparametric representation\ud results in a simple and efficient thin shell element