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Finite Elements in Civil Engineering and Geosciences
Fundamentals
1. Preliminaries
1.1. Tensor basics
1.2. Linear algebra
1.3. Tensor calculus
2. Introduction to finite elements
2.1. Strong form of the 1D Poisson equation
2.2. From strong to weak form
2.3. From weak to discrete form
2.4. Finite element implementation
2.5. Elements and shape functions
2.6. Numerical integration
2.7. Poisson equation in 2D
2.8. Isoparametric mapping
2.9. Exercises
Rod with elastic support
Coding isoparametric mapping
2.10. Tutorials
Solving PDEs with Gridap.jl
3. Theoretical analysis
3.1. Introduction to functional spaces
3.2. Well posedness of the variaitonal problem
3.3. Well posedness of the discrete problem
3.4. Galerkin Orthogonality
3.5. Convergence
3.6. Error Estimates
Solids and Structures
4. Linear elasticity
4.1. Strong form for linear elasticity
4.2. From strong to discrete form
4.3. Exercises
Workshop 1: Finite Elements for Linear Elasticity
Workshop: Introduction to pyJive
Pyjive workshop: Applying constraints
5. Structural elements for linear analysis
5.1. Euler-Bernoulli beam elements
5.2. Timoshenko Beam
5.3. Timoshenko Beam
5.4. 2D frame analysis
5.5. Tutorials
Solving the Euler-Bernoulli equation with Continuous/Discontinuos Finite Elements
Solving the Timoshenko beam equation: approaches to avoid shear locking
5.6. Exercises
PyJive workshop: TimoshenkoModel
PyJive workshop: FrameModel
6. Nonlinear solid mechanics
6.1. Towards nonlinear problems
6.2. Linearized discrete form
6.3. Incremental-iterative algorithms
6.4. Geometrically nonlinear problems
6.5. Material non-linearity
6.6. Exercises
Pyjive Workshops
Pyjive workshop: NonlinModule
PyJive workshop: material nonlinearity
PyJive workshop: buckling
PyJive workshop: plastic hinges
PyJive workshop: stability of a house-shaped frame
Workshops Geometric Nonlinearity
Workshop 1: Static string
Workshop 2: Offset calculation and theory
7. Time-dependent problems
7.1. Numerical Methods for ODE’s
Introduction
Taylor Series
ODE solvers
Error control
Numerical error
7.2. Semi-discrete form for diffusion
7.3. Time stepping algorithms for diffusion
7.4. Semi-discrete form for elasto-dynamics
7.5. Time stepping schemes for elasto-dynamics
7.6. Modal Analysis
7.7. Exercises
ODE Solvers Workshops
Workshop 1: ODE Solvers
Workshop 2: Linearizing the Equations of Motion
Workshop 3: Deriving the EOM of a pendulum
Workshop 4: Deriving the EOM of a 2DOF system
Workshop 5: Deriving the EOM of a 4DOF floating wind turbine
Structural Elements Dynamics Workshops
Workshop 1: FEM for a rod
Workshop 2: FEM for an Euler-Bernoulli beam
Workshop 3: FEM for a jacket wind turbine
Workshop 4: Modal superposition of a jacket wind turbine
Workshop 5: Full FEM or Modal superposition for a jacket wind turbine
Workshop 6: Dynamic string
Pyjive Workshops
Pyjive workshop: Poisson and diffusion problems
PyJive workshop: modal analysis
PyJive workshop: Time-dependent analysis
PyJive workshop: Reproducing dynamics experiments
Fluids
8. Fluid dynamics
8.1. Fluids
Advanced
9. Multiphysics
9.1. Key concepts
9.2. Finite Element implementation
9.3. FSI
10. Multiscale methods
10.1. Key concepts
10.2. FE
\(^2\)
10.3. Surrogate model
10.4. Exercises
PyJive workshop: FE
\(^2\)
11. Layout Optimization
11.1. Key concepts
11.2. Examples
12. Scientific visualisation
12.1. Open database for scientific visualisation
12.2. Paraview
Paraview basics
Improving visualisation
12.3. Exercise: Visualisation for mechanics and flow simulation
Practical information
Course schedules
CIEM1110
CIEM1301
CIEM5110
CIEM42X0
Codes
Gridap
Moose
PyJive
General structure
Exam information
CIEM1110
CIEM5110
.md
.pdf
Error Estimates
3.6.
Error Estimates
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