Louis Blanchard

Shape Gradient for Isogeometric Structural Design

The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows one to overcome these difficulties by using a unique geometrical representation, yielding a direct relationship between geometry and analysis. In this study, in the framework of linear elasticity problems, we investigate its use for sensitivity analysis and, more specifically, shape gradient computations.

Galerkin Strategy for Level Set Shape Analysis: Application to Geodesic Tube

In this paper, we consider the geodesic tube characterization using a Galerkin-Level Set strategy. The first section is devoted to the analysis of a geodesic tube construction between two sets through the definition of the shape metric. In the second section, we define the Galerkin-Level Set strategy in shape analysis. This new variational formulation associated to a Hilbert space metric for shape identification problem consists in parameterizing the level set function in a finite dimensional subspace spanned by linear independent functions. Consequently, this method is more focused on topological changes than on high accuracy for the boundary evaluation as in a traditional level set formulation. In the third section, we use the Galerkin-Level Set formulation applied to a geodesic tube construction between two sets, through the calculus of the shape derivative of the normal speed. Finally, this geodesic tube construction is validated by a numerical experiment.

Shape Optimal Conception of Antenna Arrays

The synthesis of an array antenna is an inverse problem. The solution of this problem is the optimization of the complex excitation law of the antenna’s radiating elements and the shape of the antenna which provides a specified radiation pattern.