Advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements

The paper deals with two main advantages in the analysis of slender elastic structures both achieved through the mixed (stress and displacement) format with respect to the more commonly used displacement one: (i) the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and (ii) the lower polynomial dependence of the problem equations on the finite element degrees of freedom when solid finite elements are used. The smaller extrapolation error produces a lower number of iterations and larger step length in path-following analysis and a greater accuracy in Koiter asymptotic method. To focus on the origin of the phenomenon, the two formats are derived for the same finite element interpolation. The reduced polynomial dependence improves the Koiter asymptotic strategy in terms of both computational efficiency, accuracy and simplicity