Condensed SFEs for nonlinear mechanical problems

Antoine Llau (1, 2, 3) , Julien Baroth (2, 4) , Ludovic Jason (1, 3) , Frédéric Dufour (2, 4)

1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 3SR - Laboratoire sols, solides, structures - risques [Grenoble]
3 LM2S - Laboratoire de Mécanique Systèmes et Simulation
4 RV - Risques, Vulnérabilité des structures et comportement mécanique des matériaux

This paper introduces a coupled approach between stochastic finite element methods and an adaptive condensation technique for the analysis of nonlinear mechanical problems under uncertainties. This coupling reduces the size of each individual nonlinear problem solved in SFE by the use of an adaptive condensation method. The reduced stiffnesses and other quantities necessary for the condensation technique are approximated using a second, low-order, polynomial expansion, thus taking advantage of the coupling with SFE. This approach also features a semi-analytical technique to compute accurately distributions of structural quantities of interest. This method is applied on an elasto-plastic steel bar with a small defect, and on a damaged beam under 4-point bending. In both cases it predicts the random behavior of the structure quite accurately, and is able to provide higher-order models than a state-of-the-art stochastic collocation method, for a reduced computation time.

Mots clés: Metamodels; Stochastic finite elements; Concrete cracking; Collocation; Static condensation

Domaines: Mécanique des matériaux [physics.class-ph]; Analyse numérique [math.NA]

Antoine Llau, Julien Baroth, Ludovic Jason, Frédéric Dufour. Condensed SFEs for nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 2016, 309, pp.434-452. ⟨10.1016/j.cma.2016.06.014⟩. ⟨hal-01348073⟩