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Concept# Finite element method

Summary

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
The simple equations tha

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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 résoudre les problèmes de la pratique.

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Ce cours présente une introduction aux méthodes d'approximation utilisées pour la simulation numérique en mécanique des fluides.
Les concepts fondamentaux sont présentés dans le cadre de la méthode des différences finies puis étendus à celles des éléments finis et spectraux.

ME-373: Finite element modelling and simulation

L'objectif de ce cours est d'apprendre à réaliser de manière rigoureuse et critique des analyses par éléments finis de problèmes concrets en mécanique des solides à l'aide d'un logiciel CAE moderne.

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Reinforced concrete (RC) coupling beams are often used to transfer and resist the earthquake loads. Coupling beams can improve significantly the stiffness and the strength of the all lateral resistant structure. By performing inelastically they decrease the energy dissipation required by the walls piers granted a better seismic performance. Because of their importance, some experimental and modelling research has been conducted focusing on these important elements. While their behaviour is known to be different from that of conventional beams, in low-to–moderate seismic regions, such as Australia, coupling beams are often designed as an “ordinary beam” with standard longitudinal reinforcements and stirrups. This incorrect procedure may be potentially dangerous and lead to a premature and brittle failure in the event of an earthquake. A finite element modelling approach, which also considers the non-linear behaviour of the beam, is investigated, with the aim of obtaining a realistic and useful model for future research projects and new design procedures. This research presents the preliminary investigations for using finite element modelling to predict the response of coupling beams with ordinary detailing designed for low-to-moderate seismic regions. Some guidelines regarding the use and setting of different parameters of the model are given. A modelling for coupling beams designed for low-to-moderate seismic regions is proposed and compared with experimental model for validation.

2020The goal of the project is to study an optimal control problem for the Cahn-Hilliard equation. To this end, we proceed in three steps: we first introduce the Cahn-Hilliard equation and how it is derived, and describe some of its applications; then, we approximate it with the finite element method and solve it with FreeFem++. Finally, we formulate the optimal control problem and solve it with FreeFem++.

2015Related lectures (690)

Reinforced concrete (RC) coupling beams are often used to transfer and resist the earthquake loads. Coupling beams can improve significantly the stiffness and the strength of the all lateral resistant structure. By performing inelastically they decrease the energy dissipation required by the walls piers granted a better seismic performance. Because of their importance, some experimental and modelling research has been conducted focusing on these important elements. While their behaviour is known to be different from that of conventional beams, in low-to–moderate seismic regions, such as Australia, coupling beams are often designed as an “ordinary beam” with standard longitudinal reinforcements and stirrups. This incorrect procedure may be potentially dangerous and lead to a premature and brittle failure in the event of an earthquake. A finite element modelling approach, which also considers the non-linear behaviour of the beam, is investigated, with the aim of obtaining a realistic and useful model for future research projects and new design procedures. This research presents the preliminary investigations for using finite element modelling to predict the response of coupling beams with ordinary detailing designed for low-to-moderate seismic regions. Some guidelines regarding the use and setting of different parameters of the model are given. A modelling for coupling beams designed for low-to-moderate seismic regions is proposed and compared with experimental model for validation.

2020