Structural Analysis and Simulation under (Small and) Large Deformations

(ASG)

• Coefficient : 6^
• Hourly Volume: 150.0h (including 72.0h supervised)
  CM : 30h supervised
  CTD : 7.5h supervised
  Labo : 34.5h supervised (and 12h unsupervised)
  Out-of-schedule personal work : 66h

AATs Lists

Description

The purpose of this research module is to provide seventh-semester students with advanced theoretical and numerical knowledge to understand and implement numerical simulations in materials and structural mechanics, which are integral to the design process of mechanical systems in engineering design offices. This module focuses on three complementary aspects: (i) providing the fundamentals and practical application of the finite element method, which enables the numerical solution of field equations. In particular, special attention is given to the computer programming of the method, which is the best way to understand its various aspects. (ii) providing an introduction to geometric nonlinearities in order to develop a more realistic modeling approach for mechanical engineering problems, understand the basic theories implemented in commercial nonlinear computational codes, and recognize when conducting a nonlinear analysis becomes important. (iii) understanding the value of data in mechanics. In particular, we will focus on aspects related to the acquisition of experimental data through various testing and measurement methods, and the use of this data for the calibration of mechanical models.

The objective of this research module is also to provide the theoretical and numerical foundations necessary for students who wish to enroll in the Master 2 research program in mechanical modeling, offered jointly with ENSTA, while completing their final year of undergraduate study.

Learning Outcomes AAv (AAv)

• AAv1 [heures: 15, B2]: Derive the strong and weak formulations of a linear isothermal elastostatic problem in 1D and 3D.

• AAv2 [heures: 20, B3]: Program the finite element method in Python for linear isothermal elastostatic problems in 1D, using 1D elements with linear interpolation.

• AAv3 [heures: 35, B3]: Program the finite element method in Python for isothermal linear elastostatic problems in 2D, using linear triangular elements.

• AAv4 [heures: 20, B3]: Program an explicit integration algorithm of the centered-difference type for fast dynamics problems.

• AAv5 [heures: 15, B3]: Describe the kinematics of a motion in finite transformation, and describe the state of deformation

• AAv6 [heures: 15, B3]: Using a hyperelasticity model, calculate various stress tensors in finite transformations to design a mechanical system.

• AAv7 [heures: 15, B1]: Explain the challenges related to data in mechanics.

• AAv8 [heures: 15, B3]: Code a problem for identifying the parameters of a nonlinear (hyper)elastic behavior model.

Assessment Methods

Average of continuous assessment tests, homework assignments, practical exercises, and lab sessions.

Keywords

Finite Element Method, Numerical Simulation in Structural Mechanics, Geometric Nonlinearity, Data for Mechanics, Image Correlation, Calibration of Mechanical Models.

Prerequisites

• Basic mathematics: linear algebra, solving first- and second-order differential equations
• Course in numerical methods
• Courses in Continuum Mechanics (CM) and Deformable Solids (DS), Strength of Materials (SoM), and Design of Mechanical Structures (DSM)
• Course in thermodynamics

Resources

• Bonnet, M., & Frangi, A. (2007). Analyse des solides déformables par la méthode des éléments finis. Les éditions de l’Ecole Polytechnique.
• Hughes, T. J. (2003). The finite element method: linear static and dynamic finite element analysis. Courier Corporation.
• Ravelonarivo, L. R. (2022). Introduction à la mécanique des milieux continus déformables: Cours et exercices corrigés. Editions Ellipses.
• Bonet & Wood (2008). Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge press.