CIEM1301

This book is used for weeks 1-2 of the elective CIEM1301 Advanced Computational Mechanics.

Click the dropdown blocks below to find a schedule for module activities per week. Clicking the links will take you to the relevant content pages.

Week 1

Contents

• Self study (before lecture 1.1): MUDE recap + MUDE additional material

  1. Strong form of the 1D Poisson equation

  2. From strong to weak form

  3. From weak to discrete form

  4. Finite element implementation

  5. Elements and shape functions

  6. Numerical integration

  7. Poisson equation in 2D

  8. Isoparametric mapping

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• Lecture 1.1 - Introduction to multiphysics

  1. Key concepts

  2. Finite Element implementation

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• Lecture 1.2 - Fluid-Structure interaction

  1. FSI

Week 2

Contents

• Self study (before lecture 2.2): MUDE recap on machine learning

• Lecture 2.1 - Introduction to multiscale methods

  1. Key concepts

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• Lecture 2.2 - FE\(^2\)

  1. FE^2

  2. Surrogate model

Week 3-10

Foundational Literature

• Fluid-Structure Interaction

  1. Jean-Frédéric Gerbeau: Fluid-structure interaction in the cardiovascular system. Lecture 1

  2. Céline Grandmont: Mathematical and numerical analysis of some fluid structure interaction problems (advanced)

  3. Olivier Doare: Fluid-structure interactions - 2.4: Fluid at rest, inertial effect, added mass phenomenon(all lecture series interesting!)

  4. Causin, Paola, Jean-Frédéric Gerbeau, and Fabio Nobile. “Added-mass effect in the design of partitioned algorithms for fluid–structure problems.” Computer methods in applied mechanics and engineering 194.42- 44 (2005): 4506-4527.

• Multiscale methods

  1. Nguyen, V.P. et al. (2012) Multiscale continuous and discontinuous modeling of heterogeneous materials: A review on recent developments. Journal of Multiscale Modelling.

  2. Geers, M.G.D. et al. (2017) Homogenization Methods and Multiscale Modeling: Nonlinear Problems. In Encyclopedia of Computational Mechanics Second Edition.

• Surrogate Modelling

  1. Basic recap of ML concepts: Mude Q2 2023 Chapter 6

  2. Mirkhalaf, M., & Rocha, I. (2024). Micromechanics-based deep-learning for composites: Challenges and future perspectives. European Journal of Mechanics-A/Solids, 105, 105242.