Showing papers by "Antonio Rodríguez-Ferran published in 1997"

Two stress update algorithms for large strains: accuracy analysis and numerical implementation

Abstract: Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unied derivation of both algorithms in spite of their inherent dierences. Then the two algorithms are adapted from convected frames to a xed Cartesian frame and implemented in a small-strain nite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis. ? 1997 John Wiley & Sons, Ltd.

A note on a numerical benchmark test: an axisymmetric shell under ring loads

Abstract: In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range of eccentricities of the ring load. For a certain range of the eccentricity the response shows either snap-through or snap-back, depending on the controlled variable. Thus, in this range of eccentricities, the test can be used to verify implementations of arc-length algorithms, using the displacement controlled solution as a reference. Moreover, results are presented for large eccentricities beyond the applicability of displacement-controlled strategies.