Reconstruction of Residual Stress in a Welded Plate Using the Variational Eigenstrain Approach

We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.Comment: 16 pages, 17 figure

Verse scored free: Scansion, recording, notation

Cet essai retrace les tentatives faites par les prosodistes pour noter (score) le rythme de la poésie, notamment à l’aide de systèmes de notations empruntés à l’harmonie diatonique. La notation articule deux impulsions contradictoires : l’enregistrement d’une voix posée comme préexistante, et la génération de mise en voix ultérieures. En outre, elle introduit un ensemble de disjonctions entre le corps des voix qui sont notées ou qui interprètent la notation, et le corps de la marque en tant que signe visuel, tout en pointant vers leur réconciliation. L’appel à la musique devient un moyen de réguler ces tensions en même temps qu’il tente d’évacuer les excès rythmiques auxquels la scansion traditionnelle n’a jamais été capable de rendre justice