Étude expérimentale de l'instabilité paramétrique de plaques géométriquement imparfaites

Historique de la recherche -- Approche théorique -- Équations de base utilisées -- Conditions aux limites -- Développement des équations de base -- Solution de l'équation de compatibilité et de l'équation d'équilibre -- Solution des équations temporelles du mouvement -- Approche expérimentale -- Étalonnage des instruments -- Élaboration des courbes de résonnance -- Résonances des plaques imparfaites -- Comportement dynamique -- Comportement statique -- Réponse temporelle : asymétrie des vibrations -- Zone d'instabilité paramétrique -- Résonnances paramétriques -- Influence des imperfections géométriques sur les fréquences naturelles -- Forme des modes de vibration -- Résonances internes -- Mécanismes d'interaction -- Interaction entre résonances forcées et paramétriques -- Interaction entre résonances

Instabilité dynamique et résonances paramétriques de plaques géométriquement imparfaites

Élaboration des équations temporelles du mouvement -- Équations de base -- Conditions aux frontières -- Développement des équations de base -- Solution de l'équation de compatibilité et de l'équation du mouvement -- Solution des équations temporelles du mouvement par la méthode d'intégration directe -- Méthodes de résolution -- Résonances paramétriques principales des plaques imparfaites -- Modélisation utilisée -- Description des plaques étudiées et chargement dynamique -- Type de vibration -- Forme de la réponse temporelle -- Diagramme de phase -- Influence de l'amplitude de l'imprefection -- Influence du chargement statique -- Influence du mode de vibration -- Influence du rapport de forme de la plaque -- Influence du type de condiitons aux frontières -- Validation des résultats obtenus -- Intéraction entre résonance paramétrique et résonance forcée -- Modélisation utilisée -- Résonances internes et simultanées des plaques imparfaites -- Rapport de forme optimal pour l'obtention des résonnances internes multiples -- Modélisation utilisée -- Résultats numériques -- Interaction entre résonance simultanée et résonance forcée -- Application de la méthode asymptotique en première approximation -- Résolution des équations décrivant la réponse stationnaire -- Comparaison entre méthode asymptotique et intégration directe -- Approche expérimentale pour l'étude des plaques géométriquement imparfaites -- Utilisation d'une plaque quelconque -- Modelage de la plaque

Optimization of friction stir welding tool advance speed via Monte-Carlo simulation of the friction stir welding process

Recognition of the friction stir welding process is growing in the aeronautical and aero-space industries. To make the process more available to the structural fabrication industry (buildings and bridges), being able to model the process to determine the highest speed of advance possible that will not cause unwanted welding defects is desirable. A numerical solution to the transient two-dimensional heat diffusion equation for the friction stir welding process is presented. A non-linear heat generation term based on an arbitrary piecewise linear model of friction as a function of temperature is used. The solution is used to solve for the temperature distribution in the Al 6061-T6 work pieces. The finite difference solution of the non-linear problem is used to perform a Monte-Carlo simulation (MCS). A polynomial response surface (maximum welding temperature as a function of advancing and rotational speed) is constructed from the MCS results. The response surface is used to determine the optimum tool speed of advance and rotational speed. The exterior penalty method is used to find the highest speed of advance and the associated rotational speed of the tool for the FSW process considered. We show that good agreement with experimental optimization work is possible with this simplified model. Using our approach an optimal weld pitch of 0.52 mm/rev is obtained for 3.18 mm thick AA6061-T6 plate. Our method provides an estimate of the optimal welding parameters in less than 30 min of calculation time

A Mesh-Free Solid-Mechanics Approach for Simulating the Friction Stir-Welding Process

In this chapter, we describe the development of a new approach to simulate the friction stir-welding (FSW) process using a solid-mechanics formulation of a mesh-free Lagrangian method called smoothed particle hydrodynamics (SPH). Although this type of a numerical model typically requires long calculation times, we have developed a very efficient parallelization strategy on the graphics processing unit (GPU). This simulation approach allows the determination of temperature evolution, elastic and plastic deformation, defect formation, residual stresses, and material flow all within the same model. More importantly, the large plastic deformation and material mixing common to FSW are well captured by the mesh-free method. The parallel strategy on the GPU provides a means to obtain meaningful simulation results within hours as opposed to many days or even weeks with conventional FSW simulation codes

Hybrid Thermo-Mechanical Contact Algorithm for 3D SPH-FEM Multi-Physics Simulations

Numerical simulation of complex industrial processes has become increasingly ommon in recent years. Depending on the nature of the industrial application, multiple types of physical phenomena may need to be considered as well as the interaction of multiple disjoint bodies. This paper is focused on industrial applications with large plastic deformation. Such processes are typically not well treated by finite element (FE) methods. For this reason, the smoothed particle hydrodynamics method (SPH) is used. In this work, we introduce a robust and straightforward thermo-mechanical contact algorithm for multi-physics SPH simulations in 3D

Crystallographic Orientation Relationship between α and β Phases during Non-Equilibrium Heat Treatment of Cu-37 wt. % Zn Alloy

The crystallographic orientation relationship between α and β phases during the non-equilibrium heat treatment of a Cu-37 wt. % Zn alloy was investigated. With this aim, Cu-37 wt. % Zn alloy plates with a thickness of 2 mm were heated at 810 °C for 1 h and then were quenched in water. The microstructure and texture of heat-treated samples were analyzed using optical microscopy and electron backscattered diffraction. By this non-equilibrium heat treatment, β phase was formed on both the grain boundaries and grain interiors. In addition, the Σ3 twin boundaries acted as preferred areas for α→β transformation. The orientation imaging microscopy results revealed a Kurdjumov–Sachs (K–S) orientation relationship between α and β phases. Furthermore, the details of microstructural evolution and texture analysis were discussed

Static and vibration analysis of an aluminium and steel bus frame

The transport sector is increasing day by day to satisfy the global market requirement. The bus is still the main mode of intercity transportation in Canada. Despite, an essentially unchanged conception, the total weight of the bus has increased by over 25% during the last three decades. To solve this problem, industrialists have moved to the use of light metals in the transportation field. Therefore, use of lightweight materials, such as aluminum is essential to reduce the total weight of bus. In this study, the focus is on the bus frame as it represents 30% of the total weight and it is the most stressed part of the bus. Its life duration is more important compared to that of all other elements. Thus, a study of the static and vibratory behavior would be very decisive. In this article, two types of analysis are carried out. First is the modal analysis to determine the natural frequencies and the mode shapes using a developed dynamic model of the bus. Because if any of the excitation frequencies coincides with the natural frequencies of the bus frame, then resonance phenomenon occurs. This may lead to excessive deflection, high stress concentration, fatigue of the structure and vehicle discomfort. In this case, the results analysis shows that the natural frequencies are not affected by the change of material. The second type of analysis is the linear static stress analysis to consider the stress distribution and deformation frame pattern under static loads numerically. For the numerical method, the frame is designed using SolidWorks and the analysis is made using Ansys WorkBench. The maximum Von Mises stress obtained for the static loading is in the same order for the three chassis frames studied. But in the case of the aluminium frame, the weight of 764 kg was reduced