A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox

Yao Koutsawa (1) , Isabelle Charpentier (1) , El Mostafa Daya (1) , Mohammed Cherkaoui

1 LPMM - Laboratoire de physique et mécanique des matériaux

Sufficiently smooth nonlinear PDE problems may be addressed through the higher order derivative com- putations of the so-called Asymptotic Numerical Method (ANM). In this paper, we theoretically discuss the generic solution of nonlinear residual equations. We then propose a Matlab implementation of the ANM based on Automatic Differentiation which allows for significant improvements in genericity and ease of use. The Diamant toolbox we construct is applied to the study of the geometrical nonlinear behav- ior of a laminated glass beam. Numerical results and experimental performances demonstrate the efficiency of the Diamant tool.

Mots clés: Asymptotic Numerical Method; Automatic Differentiation; Diamant; Laminated glass; Geometrical nonlinearities

Domaines: Mécanique des structures [physics.class-ph]; Modélisation et simulation

Yao Koutsawa, Isabelle Charpentier, El Mostafa Daya, Mohammed Cherkaoui. A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox. Computer Methods in Applied Mechanics and Engineering, 2008, 198, pp.572-577. ⟨10.1016/j.cma.2008.09.003⟩. ⟨hal-00374092⟩