Pierre Villon

Surface remeshing by local hermite diffuse interpolation

We propose a method to build a three-dimensional adapted surface mesh with respect to a mesh size map driven by surface curvature. The data needed to optimize the mesh have been reduced to an initial mesh. The building of a local geometrical model but continuous over the whole domain is based on a local Hermite diffuse interpolation calculated from the nodes of the initial mesh and from the normal vectors to the surface. The optimization procedures involve extracting from the surface mesh sets of triangles sharing the same node or the same edge and then remeshing the outer contour to a higher criterion (size or shape). These procedures may be used in order to refine or coarsen the mesh but also in a final step to enhance the shape quality of the elements. Examples demonstrate the ability of the method to create adapted meshes of complex surfaces while meeting high-quality standards and a good respect of the geometrical surface.

Estimation of the strain field from full-field displacement noisy data

In this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches.

Comparison of two approaches for differentiating full-field data in solid mechanics

In this study, the issue of reconstructing the gradients of noisy full-field data is addressed within the framework of solid mechanics. Two approaches are considered, a global one based on finite element approximation (FEA) and a local one based on diffuse approximation (DA). For both approaches, it is proposed to monitor locally the filtering effect in order to adapt the uncertainty to the local signal to noise ratio. Both approaches are applied to a case study which is commonly considered as difficult in solid mechanics (open-hole tensile test on a composite laminate). Both DA and FEA are successful for detecting local subsurface damage from the measured noisy displacement fields. Indications are also provided about the compared performances of DA and FEA. It is shown that DA is more robust, but the downside is that it is also more CPU time consuming.

An Introduction to Moving Least Squares Meshfree Methods

We deal here with some fundamental aspects of a category of meshfree methods based on Moving Least Squares (MLS) approximation and interpolation. These include EFG, RKPM and Diffuse Elements. In this introductory text, we discuss different formulations of the MLS from the point of view of numerical precision and stability. We talk about the issues of both “diffuse” and “full” derivation and we give proof of convergence of both approaches. We propose different algorithms for the computation of MLS based shape functions and we give their explicit forms in 1D, 2D and 3D. The topics of weight functions, the interpolation property with or without singular weights, the domain decomposition and the numerical integration are also discussed. We formulate the integration constraint, necessary for a method to satisfy the linear patch test. Finally, we develop a custom integration scheme, which satisfies this integration constraint.

Dynamic programming approach for newborn's incubator humidity control

The anatomy, physiology, and biochemistry of the human skin have been studied for a long time. A special interest has been shown in the water permeability of the premature infants skin, which is known to be an important factor in the maintenance of a controlled water and heat balance. The rate of evaporative heat exchange between the skin surface of a very premature infant and the surrounding incubator air may be so high that evaporative heat loss alone may exceed the infants total metabolic heat production. However, it has been demonstrated in several investigations published in recent years that basal evaporative water loss can be consistently reduced by increasing the ambient humidity. Nevertheless, the passive humidification system (water reservoir) used in most incubators cannot achieve high and steady humidity levels. Here, the authors propose an active humidification system. The algorithm is based on a combination of optimal control theory and dynamic programming approach. The relative-humidity (R.H.) regulation is performed in range of 35-90% at 33/spl deg/ C with small oscillations (/spl plusmn/0.5% R.H.) around the reference value (i.e., prescribed R.H.).

Meshless method for shallow water equations with free surface flow

Solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves. In this paper the Natural element method (NEM) is used to simulate a 2D shallow water flows in the presence of theses strong gradients. This particle-based method used a fully Lagrangian formulation based on the notion of natural neighbors. In the present study we consider the full non-linear set of Shallow Water Equations, with a transient flow under the Coriolis effect. For the numerical treatment of the nonlinear terms we used a Lagrangian technique based on the method of characteristics. This will allow avoiding divergence of Newton-Raphson scheme, when dealing with the convective terms. We also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step. Two numerical test cases were performed to verify the well-founded hopes for the future of this method in real applications.

Performance analysis of permutation cross—over genetic operators

ABSTRACT We are interested here in the utilization of Genetic Algorithms (GA) as approximation methods for combinatorial optimization. They are stochastic methods using genetic operators on a population. For their design, two points must be worked: the general scheme of the algorithm with parameter adjustment and the design of chromosome contents and genetic operators. The first point poses globally no specific problem. The latter one involves difficulties when binary genes inside the chromosomes are replaced by more general information such as permutations, in this case, the performance of the genetic operators must be analyzed with respect to the considered specific problems and their specific criteria. As performance of mutation operators are analogous to those of neighborhood operators used in well known local search methods, we will focus here only on cross—over operator (COO) performances. The aims of this paper are first to design permutation cross—over performance indicators which express the prob...

Faisabilité en emboutissage: optimisation du matériau par surface de réponse

Resume Cette communication concerne loptimisation des proprietes du materiau pour des pieces obtenues en emboutissage. Deux proprietes du materiau sont considerees, lexposant decrouissage n (de la loi dHollomon) et le coefficient danisotropie moyenxa0 r . Une fonction objectif, visant le controle des defauts est definie. Son but est deviter toute rupture et de controler le plissement. Le risque de rupture est detecte grâce a la Courbe Limite de Formage (CLF). Un facteur de risque de plissement a ete developpe dans notre laboratoire [9]. Loptimisation est effectuee par une methode utilisant une surface de reponse construite sur un nombre limite devaluations de la fonction objectif. Cette surface est interpolee localement par approximation diffuse.

Identification of elastic properties from full-field measurements: a numerical study of the effect of filtering on the identification results

The use of full-field displacement measurements in mechanical testing has increased dramatically over the last two decades. This is a result of the very rich information they provide, which is enabling new possibilities for the characterization of material constitutive parameters for inhomogeneous tests often based upon inverse approaches. Nonetheless, the measurement errors limit the accuracy of the identification of the constitutive parameters and their possible spatial resolution. The question addressed by this work is the following: can a filtering of the displacement measurement improve the results of the identification of elastic properties? The discussion is based on the study of a numerical example where the elastic parameters of an elastic structure with inhomogeneous properties are sought from synthetic data representative of in-plane full-field data. The displacement data are first filtered through a diffuse approximation algorithm, based on a moving least-squares approximation. Then, the identification of the elastic parameters is performed by an inverse approach based on the minimization of a cost function, defined as the least-squares gap between the experimental data and their numerical counterpart (finite element model updating). Within this framework, a first-order analysis is proposed in order to characterize the errors in the identified parameters, the measurement error characteristics being known. Results from raw and filtered displacement data are compared and discussed, filtering improving the identification for lower spatial resolution. The choice of the norm to define the gap between the experiment and the calculation is also discussed. For practical use and to take advantage of the proposed first-order methodology, two different ways can be considered: applying the methodology to a numerical example, representative of the experimental setup, to determine whether or not a filtering is valuable, and estimating the uncertainties of the identified parameters at the end of the identification process of an experimental characterization.

Implicit constraint handling for shape optimisation with POD-morphing

In the former paper, we have introduced an original morphing approach based on Proper Orthogonal Decomposition (POD) of shapes, designed to replace parametrized CAD models in structural optimization. Here, we expand the method to interpolate exclusively between admissible instances of structural shapes, thus permitting a global understanding of the design domain and also reducing the size of the optimisation problem. The result is a bi-level reparametrization approach for structural geometries based on Diffuse Approximation in a properly chosen locally linearized space, and the geometric parameters are replaced with the smallest set of variables needed to represent a manifold of admissible shapes for a chosen precision. We demonstrate the approach in a typical shape optimisation problem. Notre article précédent a introduit le concept original de morphing basé sur la Décomposition Orthogonale aux valeurs Propres (POD) des formes, qui vise à remplacer la démarche classique, basée sur les modèles CAO paramétriques, par un méta-modèle géométrique permettant de diminuer le nombre de variables dans les problèmes d’optimisation de forme. Ici, on étend ce concept pour permettre d’interpoler entre les instances de la géométrie de manière à obtenir toujours des structures admissibles, et d’avoir une “compréhension” globale du domaine de conception tout en minimisant le nombre de paramètres. C’est une approche bi-niveau de réparamétrage basée sur l’Approximation Diffuse dans un espace linéarisé où les paramètres de conception sont remplacés par un nombre réduit de variables permettant de représenter la variété de formes admissibles pour une précision donnée. Nous illustrons l’approche proposée sur un cas typique d’optimisation de forme.