Uncertainty quantification in computational nonlinear elasticity

Evangéline Capiez-Lernout (1) , Christian Soize (1) , M. P. Mignolet (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 Fac Mech & Aerosp Engn

This work presents a methodology for the construction of an uncertain nonlinear computational model adapted to the static analysis of a complex mechanical system. The deterministic nonlinear computationalmodel is constructed with the finite element method using a total Lagrangian formulation. The finite element nonlinear response is then considered as a reference deterministic solution from which a reduced-order basis is constructed using the POD (Proper Orthogonal Decomposition) methodology. The mean reduced nonlinear computational model is thus obtained by projecting the reference deterministic solution on this basis. The explicit construction of the mean reduced nonlinear computational model is proposed for any type of structure modeled with three-dimensional solid finite elements. A procedure for the robust identification of the uncertain nonlinear computational model with respect to experimental responses is then given. Finally, the methodology is applied to a structure for which simulated experiments are given.

Mots clés: Uncertainty quantification; nonlinear elasticity; computational mechanics

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]

Evangéline Capiez-Lernout, Christian Soize, M. P. Mignolet. Uncertainty quantification in computational nonlinear elasticity. ASME 2012 11th Biennal Conference on Engineering Systems Design and Analysis, Jul 2012, Nantes, France. Paper ESDA2012-82246, Pages : 1-10. ⟨hal-00734157⟩