The Hu–Washizu variational principle for the identification of imperfections in beams

Abstract

This paper presents a procedure for the identification of imperfections of structural parameters based on displacement measurements by static tests. The proposed procedure is based on the well-known Hu-Washizu variational principle, suitably modified to account for the response measurements, which is able to provide closed-form solutions to some inverse problems for the identification of structural parameter imperfections in beams

Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams

“…According to the classification by Friswell and Penny (2002), the proposed approach falls in the broad category of ''discrete spring models'', being equivalent to an internal hinge coupled with a linear elastic spring, which is herein assumed to have constant rigidity independently of the loading direction. Although very simple, this ''always open'' model (Irwin, 1957) proves to be very efficient for static problems (Buda and Caddemi, 2007;Caddemi and Morassi, 2007;Caddemi and Di Paola, 2008); it can be also applied to dynamic problems when the amplitude of vibration is smaller than the static deflection (Chondros et al, 2001), while ''breathing in time'' models (Kirmsher, 1944) are mandatory when cracks open and close, in so causing more complicated nonlinear phenomena. Extended finite element method (e.g.…”

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

“…only. It has been applied by Caddemi and coworkers to identification problems [9][10][11][12] and equilibrium stability problems [13]. The method by Biondi and Caddemi, however, requires the first-and the second-order primitives of the loading functions to be continuous, respectively, at the deflection discontinuity locations [8] and at the rotation discontinuity locations [7].…”

Closed-form solution based genetic algorithm software: Application to multiple cracks detection on beam structures by static tests

“…More interestingly, entirely analytical procedures for crack identification, leading to explicit closed form solution of the inverse problem either based on the modified Hu-Washizu variational principle [38] or to the application of Betti-Maxwell reciprocity theorem [39,40] can also be considered. The latter, however, are conveniently applied only to beams with single or double cracks.…”