Three discrete Kirchhoff elements for shell analysis with large geometrical non‐linearities and bifurcations

Abstract

The comparative efficiency of three flat triangular shell elements is being assessed for analysing non‐linear behaviour of general shell structures. The bending formulation of the three elements is based on a discrete Kirchhoff model (namely the well‐known 3‐node DKT element and a new 6‐node DKTP element). The in‐plane behaviour is defined by constant (CST), linear (LST)and quadratic (QST) strain approximations. The super‐position of bending and membrane elements leads to the 3‐node DCT element (DKT plus CST), the 3‐node DQT element (DKT plus QST) and the 6‐node DLT element (DKTP plus LST). The geometrically non‐linear formulation is based on an approximate updated Lagrangian formulation (AULF) and the solution is obtained by using the Newton‐Raphson method with an automatic arc‐length control method. Illustrative examples include pre‐ and post‐buckling of different shell structures showing, in particular, some bifurcation points, large rotations and displacements and very important membrane‐bending coupling.

Citation

Talbot, M. and Dhatt, G. (1987), "Three discrete Kirchhoff elements for shell analysis with large geometrical non‐linearities and bifurcations", Engineering Computations, Vol. 4 No. 1, pp. 15-22. https://doi.org/10.1108/eb023679