Implementing PGD technique in solving the problem of identifying Young's modulus of linear elastic isotropic material from full-field measurements by FEMU method

Abstract

This paper deals with implementing Proper Generalized Decomposition (PGD) technique in solving the problem of identifying Young's modulus of linear elastic isotropic material from full-field measurements by finite element model updating (FEMU) method. In this type of problem, using PGD technique enables reducing the computation cost as it helps to avoid performing the iterative process of computing the response of the mechanical structure by finite element method (FEM). The nature of PGD technique consists following important points: (i) – interested parameters are considered as extra variables for the response function; (ii) – sought multidimensional response function is approximated by the finite sum of modes, each is production of separated-variable functions; (iii) – This approximate solution is computed by the iterative solver using a variational formulation and a greedy algorithm. A numerical example of a tensile test was performed to verify this implementation. The obtained results confirm the correctness of PGD technique. Several comments were made on the use of this technique.