Lecture

Finite Element Method: Basics and Applications

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In course

ME-372: Finite element method

L'étudiant acquiert une initiation théorique à la méthode des éléments finis qui constitue la technique la plus courante pour la résolution de problèmes elliptiques en mécanique. Il apprend à appliquer cette méthode à des cas simples et à l'exploiter pour ...

Description

This lecture introduces the fundamental concepts of the finite element method, covering one-dimensional and two-dimensional boundary problems, basics of functional analysis, and examples of case studies. The course aims to equip students with the ability to apply the finite element method to simple problems, understand its practical applications, and gain a theoretical initiation to this technique. Topics include statics, stress analysis, numerical analysis, and structural mechanics. The lecture also delves into the classification of solving methods, spatial discretization, and application examples like temperature distribution on the surface of an A320 in flight.

Instructor

François Gallaire

google scholar https://scholar.google.ch/citations?hl=fr&user=T3OooAcAAAAJ François Gallaire earned his engineering degree from Ecole Polytechnique in 1998 and a master's in Liquids Physics from Université Pierre et Marie Curie in 1999. He completed his PhD in 2002 at LadHyX on swirling flow instabilities and vortex breakdown. After six years at the Mathematics department of Université de Nice, he joined EPFL in 2009, founding the Fluid Mechanics and Instabilities Lab (LFMI). He became an associate professo

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Related concepts (31)

Applied mechanics

Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life.

Structural analysis

Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships.

Structural engineering

Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of human-made structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site.

Statics

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather, is in static equilibrium with its environment. If is the total of the forces acting on the system, is the mass of the system and is the acceleration of the system, Newton's second law states that (the bold font indicates a vector quantity, i.e. one with both magnitude and direction). If , then .

Structural engineer

Structural engineers analyze, design, plan, and research structural components and structural systems to achieve design goals and ensure the safety and comfort of users or occupants. Their work takes account mainly of safety, technical, economic, and environmental concerns, but they may also consider aesthetic and social factors. Structural engineering is usually considered a specialty discipline within civil engineering, but it can also be studied in its own right.

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