A TRIANGULAR ANISOTROPIC THIN SHELL ELEMENT BASED ON DISCRETE KIRCHHOFF THEORY.

Abstract

The research work presented here deals with problems associated with finite element analysis of laminated composite thin-shell structures. The specific objective was to develop a thin shell finite element to model the linear elastic behavior of these shells, which would be efficient and simple to use by the practicing engineer. A detailed discussion of the issues associated with the development of thin shell finite element has been presented. It has been pointed out that the problems encountered with formulation of these elements stem from the need for satisfaction of the interelement normal slope continuity and the rigid body displacement condition by the assumed displacement functions. These difficulties have been surmounted by recourse to the discrete Kirchhoff theory approach and an isoparametric representation of the shell middle surface. A detailed derivation of the strain energy density in a thin laminated composite shell, based on a linear shear deformation theory formulated in a general curvilinear coordinate system, has been presented. The strain-displacement relations are initially derived in terms of the displacement and rotation vectors of the shell middle surface, and are subsequently expressed in terms of the cartesian components of these vectors to enable an isoparametric representation of the shell geometry. A three-node curved triangular element with the tangent and normal displacement components and their first-order derivatives as the final nodal degrees of freedom has been developed. The element formulation, however, starts with the independent interpolation of cartesian components of the displacement and rotation vectors using complete cubic and quadratic polynomials, respectively. The rigid-body displacement condition is satisifed by isoparametric interpolation of the shell geometry within an element. A convergence to the thin shell solution is achieved by enforcement of the Kirchhoff hypothesis at a discrete number of points in the element. A detailed numerical evaluation through a number of standard problems has been carried out. Results of application of the "patch test solutions" to spherical shells demonstrate a satisfactory performance of the element under limiting states of deformation. It is concluded that the DKT approach in conjunction with isoparametric representation results in a simple and efficient thin shell element.