A PRE-ANALYSIS OF THE CREATION OF TEACHER RESOURCES FOR DEVELOPING INSTRUCTION IN BASIC LOGIC IN FRENCH HIGH SCHOOLS

If everyone agrees that logic is needed to do mathematics, there are divergences concerning the role of mathematical logic in acquiring the necessary and sufficient knowledge in this area. We will try first to see what might be the students' difficulties in the acquisition of logic of mathematics and what can be Mathematical Knowledge for Teaching Logic of mathematics. A study of syllabuses and textbooks for high school in France shows strong constraints and ill-defined conditions for this teaching. In their answers to a questionnaire we proposed, some teachers expressed their lack of theoretical knowledge in mathematical logic and lack of resources to present to their pupils activities in order to address notions of logic. During a continuous training, we try to offer an approach of mathematical logic which support teaching of logic of mathematics

Stability of Pseudo-Funicular Elastic Grid Shells

International audienceThe paper presents some results on the influence of the pre-stress induced by the erection method of elastic grid shells on their buckling capacity. It starts with the numerical methods and their validation with the study of a prebuckled arch. Then, a form-finding scheme using low-speed dynamics is used to generate automatically a family of elastic grid shells, and their buckling capacity is compared to the one of grid shells with the exact same geometry, but without any pre-stress. The paper demonstrates finally that the pre-stress decreases by a few percent the buckling capacity of elastic grid shells

Infirmières et ambulanciers: quelle collaboration optimale ? : travail de Bachelor

Notre sujet de travail de Bachelor a pour thème la collaboration entre les infirmières et les ambulanciers. Nous nous intéressons aux éléments qui pourraient influencer leur collaboration ainsi que les moyens qu’ils utilisent pour pourvoir fonctionner lors de leurs rencontres aux urgences

Möbius Geometry and Cyclidic Nets: A Framework for Complex Shape Generation

International audienceFree-form architecture challenges architects, engineers and builders. The geometrical rationalization of complex structures requires sophisticated tools. To this day, two frameworks are commonly used: NURBS modeling and mesh-based approaches. The authors propose an alternative modeling framework called generalized cyclidic nets that automatically yields optimal geometrical properties for the façade and the structure. This framework uses a base circular mesh and Dupin cyclides, which are natural objects of the geometry of circles in space, also known as Möbius geometry. This paper illustrates how new shapes can be generated from generalized cyclidic nets. Finally, it is demonstrated that this framework gives a simple method to generate curved-creases on free-forms. These findings open new perspectives for structural design of complex shells

Instantaneous Wavenumber Estimation for Damage Quantification in Layered Plate Structures

This paper illustrates the application of instantaneous and local wavenumber damage quantification techniques for high frequency guided wave interrogation. The proposed methodologies can be considered as first steps towards a hybrid structural health monitoring/ nondestructive evaluation (SHM/NDE) approach for damage assessment in composites. The challenges and opportunities related to the considered type of interrogation and signal processing are explored through the analysis of numerical data obtained via EFIT simulations of damage in CRFP plates. Realistic damage configurations are modeled from x-ray CT scan data of plates subjected to actual impacts, in order to accurately predict wave-damage interactions in terms of scattering and mode conversions. Simulation data is utilized to enhance the information provided by instantaneous and local wavenumbers and mitigate the complexity related to the multi-modal content of the plate response. Signal processing strategies considered for this purpose include modal decoupling through filtering in the frequency/wavenumber domain, the combination of displacement components, and the exploitation of polarization information for the various modes as evaluated through the dispersion analysis of the considered laminate lay-up sequence. The results presented assess the effectiveness of the proposed wavefield processing techniques as a hybrid SHM/NDE technique for damage detection and quantification in composite, plate-like structures

Application of classical models of chirality to surface second harmonic generation

International audienceTwo classical models (Kuhn and Kauzmann) are extended to calculate the second-order nonlinear response of an isotropic layer of chiral molecules. Calculation of the various nonlinear susceptibilities (electric dipolar, magnetic dipolar, and electric quadrupolar) is performed and applied to the derivation of the second harmonic field radiated by the molecules. It is shown that the two models give strikingly different results about the origin of the chiral response in such experiments. Previously published results are analyzed in view of this calculation which allows to understand the different interpretations proposed. This calculation emphasizes the interest of surface second harmonic generation to access information about the microscopic origin of optical activity in chiral molecules. © 2001 American Institute of Physics

Isogonal moulding surfaces: A family of shapes for high node congruence in free-form structures

International audienceThe design of free-form structures is governed by structural and geometric considerations, the latter ones being closely linked to the costs of fabrication. If some construction constraints have been studied extensively, the question of the repeatability of nodes in free-form structures has rarely been addressed yet. In this paper, a family of surfaces that can be optimized regarding typical geometrical constraints and that exhibit high node congruence is proposed. They correspond to particular meshes of moulding surfaces and are called isogonal moulding surfaces by the authors. The geometrical properties of these surfaces are discussed. In particular, it is shown how to derive Edge Offset Mesh from them. It is also demonstrated that they represent all the possible meshes parallel to surfaces of revolution. Finally, the reader is introduced to some computational strategies linked to isogonal moulding surfaces

Generating high node congruence in freeform structures with Monge's Surfaces

International audienceThe repetition of elements in a free-form structure is an important topic for the cost rationalization process of complex projects. Although nodes are identified as a major cost factor is steel grid shells, little research has been done on node repetition. This paper proposes a family of shapes, called isogonal moulding surfaces, having high node congruence, flat panels and torsion-free nodes. It is shown that their generalization, called Monge's surfaces, can be approximated by surfaces of revolution, yielding high congruence of nodes, panels and members. These shapes are therefore interesting tools for geometrically-constrained design approach