Hybrid stress finite element model for non‐linear shell problems

The present paper describes a hybrid stress finite element formulation for geometrically non‐linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger‐Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi‐field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non‐linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton‐Raphson iteratioin. Numerical examples presented in the paper include complete snap‐through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non‐linear shell problems of high complexity.