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This is an English version of an article published as: David Dureisseix, Recyclez ! Le Pli 162:20,2021, the journal of the Mouvement Français des Plieurs de Papier (MFPP), the French paperfoldingassociation.

This is an English version of an article published as: David Dureisseix, Des mots en couleur, Le Pli 161:8-12, 2021, the journal of the Mouvement Français des Plieurs de Papier (MFPP), the French paperfolding association.

This is an English version of an article published as: David Dureisseix, Recyclez ! Le Pli 162:20,2021, the journal of the Mouvement Français des Plieurs de Papier (MFPP), the French paperfoldingassociation.

This is an English version of a part (due to copyright restrictions) of an article published as: David Dureisseix, Jérôme Cavoret, A-t-on raison de parler de pli « montagne » et de pli « vallée » ?, Le Pli, 157:3-5, 2020, the journal of the Mouvement Français des Plieurs de Papier (MFPP), the French paperfolding association.

National audience

Iso-area origami models and checkered patterns are highly symmetrical designs. Some challenging issues concern the double-faced models (that can be reversed), and the optimality design (folding from an as small as possible initial square sheet of paper). This study focuses on the case of a 4 x 4 checkerboard exhibiting probably the highest degree of symmetry among all flat-folded models and the best-known optimality degree. This is an English version of a preprint of "Un échiquier 4 x 4 reverso optimal", published in Le Pli, 154, pp. 12-15, 2019, the journal of the Mouvement Français des Plieurs de Papier (MFPP), the French paperfolding association.

International audience

International audience; Origami is the ancient art of paper folding. It started with traditional designs, and then came to creation of new models, and more recently transpires into scientific applications and researches. One of the first topic deals with geometry; apart from being used for educational purposes, it raises non trivial questions.The dedicated field of computational origami emerged since 1996, making use of algorithms for optimization and design. The folding process itself is linked to the kinematics of mechanisms and materials; it is also a source of innovation for designing deployable, foldable, and shape-adaptive structures: stents, airbags, temporary roofs, compliant mechanisms, spatial applications… Both these features and the artistic background of origami are also used for design of architectural structures.The aim of this presentation is to give an overview of the synergy of origami and scientific topics, to illustrate its potential source of innovation, and to present recent advances in engineering field.

International audience; The latest decade saw the emergence of a new approach to the ancient paperfolding art: the computational origami.Several complex planar geometry problems have been studied from their complexity and design efficiency point of view, such as the color changing. The checkered patterns are amonst the most challenging problems, especially when constrained by searching the most efficient design, i.e. with the less waste of paper.We propose herein the illustration of complexity on a pixel-matrix origami design, a complication of the chessboard: each board square should be able to change its color independently, using as many flapping mechanisms as necessary, but still using a single square sheet of paper with a minimal waste.

Design of compliant mechanism rely on several design criteria. For instance, mechanisms using folding motions may satisfy some stiffness, strength and controlability issues. Numerical tools may help in this design phase by separating the difficulties allowing a step-by-step procedure. Herein, this separation is made by using an asymptotic expansion technique.

This document is a short (and hopefully concise) introduction to dimensional analysis and is not expected to be printed. Indeed, it relies on URL links (in colored text) to refer to information sources and complementary studies, so it does not provide a large bibliography, nor many pictures.It has been realized with the kind help of Ton Lubrecht and Marie-Pierre Noutary.

This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from brute force enumeration, up to the equivalence to a dedicated problem in graph theory. This leads to algorithms starting from an untractable case on modern computers, up to a run of few seconds on a portable personal computer. This emphasizes the need for a prior analysis by humans before considering the assistance of computers for complex design problems. The graph problem is an enumeration of spanning trees from a grid graph, leading to a coarse scale description of the topology of the paper edge on the flat-folded state.

International audience; In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

International audience; Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward-backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.

National audience

Le projet support de l'étude présentée est la reconception d'un bras, pièce critique d'un robot parallèle à grande vitesse (voir première partie de l'article), menée en collaboration avec le Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM, unité mixte de recherche CNRS 5506, équipe DEXTER du département de robotique1) et la société Fatronik2, représentés par Sébastien Krut. L'objectif imposé est l'utilisation majoritaire de matériaux à faible impact écologique, en l'occurrence ici : le bois. Le bras d'origine est un tube de composite carbone stratifié à ±45°, assemblé par collage à des embouts plastiques ou métalliques (figure 1). Après avoir présenté dans une première partie de l'article le contexte détaillé, l'intérêt de l'utilisation du matériau bois, et la démarche de conception sélectionnée, on s'intéresse ici aux objectifs pédagogiques ainsi qu'à l'illustration de la mise en œuvre pratique de la démarche de conception choisie dans un cadre de formation.

International audience; A multiscale strategy using model reduction for frictional contact computation is presented. This new approach aims to improve computation time of finite element simulations involving frictional contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different frictional contact problems shows a great potential as far as reducibility for frictional contact problems is concerned. Time-space vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information.

The present invention provides a method, apparatus, and a machine for testing in pure bending, optionally in alternating bending. Two mutually identical testpieces are subjected to optionally alternating opposing bending movements while conserving mutual symmetry about a point, under drive from two controlled motor assemblies that are free to move relative to each other. Interfering forces induced in the two testpieces during testing are minimized, and the performance of the testpieces in pure bending can be studied with increased accuracy.