Random field generation

Details

Supervisors

Legat, Vincent ; Zein, Samih

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées

Abstract

This thesis, done in collaboration with Cenaero, contributes to the MACOBIO project. It develops a numerical tool modelling the properties of heterogeneous materials based on random field generation and analysing the mechanical responses of the composite objects. After reviewing the different composite materials and mechanical laws based on homogenization methods, this thesis presents a numerical tool to simulate Gaussian random fields on 3D surfaces. It first defines the covariance function associated with the Gaussian random field. The random field is then discretised on finite elements using Karhunen-Loève expansion. The Karhunen-Loève expansion is computed by solving a Fredholm integral equation of the second kind. The integrals involved by the Fredholm equation are evaluated using Galerking methods. The integrals depend on discrete values of the covariance function, itself a function of the geodesic distances. The geodesic distances are evaluated using the fast marching method or the recursive fast marching method. The recursive fast marching method is applied on 2D and 3D surfaces and the errors of the method are characterized. The random field generation method is applied on a composite chair. Two uncertain properties are modelled: the fibre volume fraction and the angles of the plies. Two mechanical responses (the deflection and the Tsai-Wu criterion) are analysed by means of the Monte Carlo method.