# Finite Elements

## Presentation

The student develops the various phases of a finite element analysis using a modern computing code: geometrical modeling of structures, meshing, setting the boundary conditions, resolution, analyzing the results from a critical point of view. It operates various features offered by the codes: meshing techniques, assembling various components, using specific elements and particular algorithms devoted to nonlinear problems (contact ...), evaluating the approximation errors...

Teaching is divided into two periods. During the first step, training is oriented towards understanding and ownership of computer code that serves as a tool to support education. This period is very circumscribed. During the second step, the student must conduct the analysis of a mechanical device, with a partial autonomy, in the form of a project. A study practical case, and an operating framework defined in advance are provided to the student.

Reliability and Design of experiments module :

The contents are divided in two parts. The first part presents the role and objective of RAMS (Reliability, Avaibility, Maintainability, Safety) analysis. The second part presents the Taguchy method for the design of experiments.

Mechanics of vibrations module :

Dynamic mechanical systems are modeled using vectorial differential equations, or partial differential equations.

Their behaviour is studied in the time domain by solving these equations, and in the frequency domain using Frequency Response Functions.

Modal decomposition and superposition techniques are used to analyse and interpret this behaviour.

Bibliographic work module :

Initiation to bibliographic search tools. Awareness to the concept of "industrial property".

## Objectives

Finite element module :

-      Remember the principles and implementing rules of finite element analyses conducted from a reference finite element code (Abaqus for example).

-      Identify the features offered by these numerical tools and the associated potentialities.

-      Carry out relevant analysis models.

-      Operate the results obtained.

-      Analyze the impact of modelling assumptions.

-      Assess the risks inherent to a poor analyse of the results.

Reliability and Design of experiments module :

-      Apply to practical case analyses the basics of reliability and design of experiments.

Mechanics of vibrations module :

-      Develop a linear dynamic model of a mechanical structure: a lumped parameters model for a discrete elements structure, or a distributed parameters model for a continuous structure.

-      Determine the vibrations of these structures undergoing transient or permanent excitation.

Bibliographic work module :

-      Carry out a literature review and establish a state of the art on a research topic that will be developed in I4GMPJ21 formation unit.

This state of the art will present :

-      past history (previous studies, de facto situation, necessity of research)

-      the main results of these past studies

The elements that could guide future work in UF I4GMPJ21.

## Needed prerequisite

Finite element module :