An introduction to dimensional analysis

1 Goals of dimensional analysis2 Physical quantities and their units3 Physical laws do not depend on a particular system of units4 Some examples for practicing dimensional analysis: Train yourself5 Using small scale modelsA A future change in SI basic units definition?B Some not-so-clear uses and alternative solutionsC The temperature caseD For LaTeX or pdfLaTeX fansEngineering schoolThis 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

Chessboard: Optimal chessboard color change

International audienceThe color change allows the folder to make some patterns appear on a paper with one color on each side. One is used for the foreground, the other one, for the background. It is typically a folding sequence related to an 'edge effect': Usually, the color cannot change on a model without crossing one edge of the paper. There are some exceptions, but as an edge of the paper is hidden, it cannot be used anymore for color change; consequently, this situation is close to the previous one.When folding a chessboard from an initial square of paper, the color changes are numerous. There are several chessboards folded from a strip of paper, or using modular origami; much less models use a unique square of paper. It is not surprising that a large square is needed for folding (without cutting) a quite small chessboard. Can a 8x8 chessboard be folded from a small square of paper? What is the smallest one

An Overview of Mechanisms and Patterns with Origami

International audienceOrigami (paperfolding) has greatly progressed since its first usage for design of cult objects in Japan, and entertainment in Europe and the USA. It has now entered into artistic areas using many other materials than paper, and has been used as an inspiration for scientific and engineering realizations. This article is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, strength of material, and mechanisms. It does not provide an exhaustive list of applications nor an in-depth chronology of development of origami patterns, but exemplifies the relationships of origami to other disciplines, with selected examples

A reduced order modeling for uncertainty propagation in the coupled biomechanical model of bone–implant healing process

International audienceUncertainty quantification is a useful approach for robust design and prediction in numerical simulation of engineering problems. Indeed, once a reliable model is available, it can be subjected to variability or lack of knowledge on one or several input parameters, considered as random variables. The model output is then also a random variable and the user is therefore interested in obtaining stochastic information on this model prediction. Biomechanical problems are prone to such uncertainty, eventually with a large dispersion on the input parameters. The target problem is herein a transient chemical poromechanical coupled problem of parabolic non-linear convection-diffusion-reaction serving to predict the bone healing around an implant. The goal is to provide a tool for implant design and a help to surgical decision. In this contribution focus is on the case where the deterministic model is considered as a black box: the stochastic analysis should therefore be non-intrusive. Amongst non-intrusive approaches, Monte Carlo simulations and polynomial chaos expansions with collocation are reference approaches. The inputs are given with their cumulative density functions (cdf), and we wish to build the cdf of the output quantity of interest (QoI). A reduced order model (ROM) can serve as reducing the cost of the overall analysis. Its efficiency is strongly related to the capability of the QoI to be represented in a smaller subspace. This ability can be improved for geometrical input parameters using a morphing approach. We therefore propose to couple ROM with geometric morphing and stochastic analysis, and assess the effectivity of the approach on the bone healing problem, both from an accuracy and efficiency points of view

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

International audienceIn this article, a phenomenological numerical model of bone remodeling is proposed. This model is based on the poroelasticity theory in order to take into account the effects of fluid movements in bone adaptation. Moreover, the proposed remodeling law stands from the classical 'Stanford' law, enriched in order to take into account the loading frequency, through fluid movements. This coupling is materialized by a quadratic function of Darcy velocity. The numerical model is carried out, using a finite element method, and calibrated using experimental results at macroscopic level, from the literature. First results concern cyclic loadings on a mouse ulna, at different frequencies between 1 Hz and 30 Hz, for a force amplitude of 1.5 N and 2 N. Experimental results exhibit a sensitivity to the loading frequency, with privileged frequency for bone remodeling between 5 Hz and 10 Hz, for the force amplitude of 2 N. For the force amplitude of 1.5 N, no privileged frequencies for bone remodeling are highlighted. This tendency is reproduced by the proposed numerical computations. The model is identified on a single case (one frequency and one force amplitude) and validated on the other ones. The second experimental validation deals with a different loading regime: An internal fluid pressure at 20 Hz on a turkey ulna. The same framework is applied, and the numerical and experimental data are still matching in terms of gain in bone mass density

A beam to 3D model switch in transient dynamic analysis

International audienceTransient structural dynamic analyses often exhibit different phases, which enable one to use an adaptive modeling. Thus, a 3D model is required for a better understanding of local or non-linear effects, whereas a simplified beam model is sufficient for simulating the linear phenomena occurring for a long period of time. This paper proposes a method which enables one to switch from a beam to a 3D model during a transient dynamic analysis, and thus, allows one to reduce the computational cost while preserving a good accuracy. The method is validated through comparisons with a 3D reference solutioncomputed during all the simulation

Bascule d'un modèle poutre à un modèle 3D en dynamique des machines tournantes

National audienceLes problèmes de machines tournantes incluant un contact rotor-stator, nécessitent un maillage 3D de la zone de contact. Cependant, un modèle 3D pour toute la durée de simulation conduit à des temps de calcul rédhibitoires. Or un modèle poutre est suffisant pour décrire la dynamique de la machine tournante hors contact. Une stratégie qui permet d'utiliser un modèle poutre et un autre 3D, pendant deux phases différentes durant la même simulation, permet donc de gagner en temps de calcul pour une précision équivalente. Cet article propose une bascule d'un modèle poutre à un modèle 3D, en dynamique des rotors transitoire, avec une résolution par intégration temporelle implicite. Si on démarre la simulation avec le modèle poutre, on construit à l'instant de la bascule, une solution 3D, telle que les déplacements 3D soient la somme d'un déplacement corps rigide de la section correspondant à la solution poutre et d'une correction qui tient en compte des déformations dans la section. Cette correction résulte de la résolution d'un problème statique. Cette correction statique peut être cal-culée sur trois pas de temps consécutifs (l'instant de bascule, le pas temps qui la précède et celui qui la suit) pour l'obtention d'une correction en vitesses. La bascule est validée par comparaison avec une solution 3D de référence obtenue en effectuant la simulation entière sur le modèle 3D

Design and analysis of a foldable / unfoldable corrugated architectural curved envelop

11 pagesInternational audienceOrigami and paperfolding techniques may inspire the design of structures that have the ability to be folded and unfolded: their geometry can be changed from an extended, servicing state to a compact one, and back-forth. In traditional Origami, folds are introduced in a sheet of paper (a developable surface) for transforming its shape, with artistic or decorative intent; in recent times the ideas behind origami techniques were transferred in various design disciplines to build developable foldable / unfoldable structures, mostly in aerospace industry. The geometrical arrangement of folds allows a folding mechanism of great efficiency and is often derived from the buckling patterns of simple geometries, like a plane or a cylinder (e.g. Miura-Ori and Yoshimura folding pattern). Here we interest ourselves to the conception of foldable / unfoldable structures for civil engineering and architecture. In those disciplines, the need for folding efficiency comes along with the need for structural efficiency (stiffness); for this purpose we will explore nondevelopable foldable / unfoldable structures: those structures exhibit potential stiffness because, when unfolded, they cannot be flattened to a plane (non-developability). In this paper we propose a classification for foldable / unfoldable surfaces that comprehend non fully developable (and also non fully foldable) surfaces and a method for the description of folding motion. Then we propose innovative geometrical configurations for those structures by generalizing the Miura-Ori folding pattern to non-developable surfaces that, once unfolded, exhibit curvature

A micro-macro strategy for ship structural analysis with FETI-DP method

International audienceIn the analysis of ship structures at small scale, with structural details heterogeneities and because there is only one prototype produced, which is the final product, the designers rely on finite element simulations. The finite element discretization of such structure, leads to a huge global numerical model, that suffers for computational cost and memory resource that may be unaffordable. In such a case, a multi-scale analysis should be performed. The classical local-global analysis that is used by engineers has several limitations such as: - structure details are not periodic, therefore classical homogenization methods are not easily applicable; - edge effects are not take into account; - zooming techniques are not easy to use: the gluing they require with the global scale often introduces artificial edge effects. This paper presents a micro-macro strategy based on the domain decomposition FETI-DP method as the solver in analysis of ship structure. With this approach, the two scales (micro and macro) are coupled during the iterations of the solver and we can consider the structural details in areas of interest, area where the fine mesh is used and a sub-domain is located. Performances are discussed and results in term of convergence are presented for several examples

LOOKING FOR OPTIMAL BIOMECHANICAL CONFIGURATIONS IN WEIGHTLIFTING AND POWERLIFTING : THEORETICAL AND EXPERIMENTAL APPROACHES

This work is part of a big project whose goal is to combine mechanical principles with the physical characteristics of athletes to develop a personalized virtual model optimized to help lifters improve their performance while reducing their injury risks. This study concentrates on the qualitative comparison between a virtual skeleton model of a squatting athlete numerically designed on MATLAB and the squatting patterns of elite athletes of the French national team (n=15). Comparing the results of the two approaches revealed differences in the Center Of Pressure (COP) movement during the squat as well as motor behaviour and velocity. After discussion with the athletes and their coaches it seems that the model lacked reality and more studies are needed