The influence of geometric effects on the behavior of strain softening frames

Abstract

This paper presents a mathematical programming based approach for the analysis of elastoplastic softening frames in the presence of geometric nonlinearity. Arbitrarily large deformations, albeit within a small strain regime, can be accommodated, if necessary. For the sake of efficiency, and without undue loss of accuracy, the algorithm processes the nonholonomic (path-dependent) problem in a stepwise holonomic (path-independent) fashion. This analysis capability has been used to investigate what level or order of geometric nonlinearity needs to be adopted to obtain sufficiently accurate results for practical frames. Two examples are provided for illustrative purposes.

An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

“…This can be easily achieved in a Lagrangian framework by introducing additional fictitious forces p (and deformations d p ) and nonlinear ''residuals'' R q (e.g. De Lloyd Smith, 1984-1985;Tangaramvong and Tin-Loi, 2010). It is of interest to note that such a description meaningfully preserves the dual nature of the Lagrangian static-kinematic relations.…”

“…The first two examples involve circular arch structures and the last two concern the multi-story frame structures adopted previously in the context of softening and large deformation effects (Tangaramvong and Tin-Loi, 2010).…”

“…This frame was recently used to investigate the influence of softening and nonlinear geometry effects (Tangaramvong and Tin-Loi, 2010). The structure was discretized into 126 elements, 261 degrees of freedom, 378 generalized stresses (or strain rates) and 504 yield functions.…”

“…The structure was also used by Tangaramvong and Tin-Loi (2010) to study the influence of strain-softening and nonlinear geometry . The finite element model constructed consists of 45 members, 90 degrees of freedom, 135 generalized stresses (or strain rates) and 180 yield functions.…”

“…Comi et al, 1991;Cocchetti and Maier, 2003; Le Van et al, 2003), often coupled with some iterative predictor-corrector type algorithm (e.g. Hellweg and Crisfield, 1998;Tangaramvong and Tin-Loi, 2010). The inherent numerical difficulties are well-known, and special care needs to be taken to ensure convergence and to capture the most critical equilibrium path.…”