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Regularization of 3D shape measurements on given Finite Element meshes using multilevel splines.

Abstract : Stereo Digital Image Correlation is a method that allows measuring a 3D displacement field on 3Dsurfaces using cameras. Among other choices, the Finite Element (FE) discretization space seems toconstitute a convenient approximation space for the measured displacement, since it allows making adirect link between the measured data and a FE software. In FE Stereo Digital Image Correlation, thedisplacement along with the geometry are therefore defined by the FE mesh of the structure of interest.Prior to any experimentation, a calibration phase is necessary to determine the parameters of the camerasand the actual shape of the specimen. This phase uses a Gauss-Newton minimization. However, using afine FE mesh leads to an ill-posed problem when identifying the shape. A regularization is thus essential.To address this issue, we propose to project the FE space onto a smaller, more regular space. As in [1],we choose spline functions, which are the standard for Computer-Aided Design. They possess higherregularity, and can be refined automatically without any modification in the geometry. Accordingly, amultilevel approach is adopted, which lowers computational costs and improves the regularization [2].Similarly to [3], an explicit link between the spline geometry and the FE mesh enables us to use aFE software in a non-invasive way. An extension using the concept of Free-Form Deformation (FFD),applied, e.g., in aerostructural optimization [4], will be finally discussed to adapt to any input FE mesh.
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Contributor : Morgane Chapelier <>
Submitted on : Thursday, February 11, 2021 - 4:39:27 PM
Last modification on : Thursday, February 18, 2021 - 10:16:13 AM


  • HAL Id : hal-03129257, version 1


Morgane Chapelier, Robin Bouclier, Jean-Charles Passieux. Regularization of 3D shape measurements on given Finite Element meshes using multilevel splines.. 14th World Congress on Computational Mechanics (WCCM) and ECCOMAS Congress 2020 -- Virtual Congress 11-15 January, 2021, Jan 2021, Virtual Conference, France. ⟨hal-03129257⟩



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