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22 changes: 20 additions & 2 deletions Weeks/Week6.md
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---
title: Week 6
layout: default
parent: 2) Calender
nav_order: 6
parent: Calendar
nav_order: 7
---

# Week 6

At the end of this week you will be able to: <br>
Define numerical methods to analyse systems governed by nonlinear Partial Differential Equations. This entails:<br>
<i>1. Define the formulation that characterizes the dynamics of structures subject to large deformations</i><br>
<i>2. Define numerical methods to solve nonlinear systems of PDEs</i> <br>
<i>3. Analyse and justify the results</i><br>
{: .learningobjectives }

Week 6. Geometrically nonlinear structures [[pdf 1]](https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek6&files=6.1_Geometrically_nonlinear_structures.pdf),[[pdf 2]](https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek6&files=7.1_Geometrically_nonlinear_structures.pdf) :<br>
<i>1. Geometric nonlinearity [5.4](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/geometric_nonlinearity.html)</i> <br>
{: .content }

[Workshop 1 (Static String)](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/Exercises/geometric_nonlinear_exercises/Workshop_1_Static_String.html)<br>
[Workshop 2 (Expanded Static String)](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/Exercises/geometric_nonlinear_exercises/Workshop_2_Offset_Calc.html)<br>
[Workshop 6 (Dynamic String)](https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/str_elem_dyn_workshops/Workshop_Dynamic_String.html)<br>
{: .exercises }
37 changes: 37 additions & 0 deletions _modules/week-06.md
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---
title: "Week 6: Geometrically Nonlinear Structures"
---

<!-- This will make a piece of text, followed by a button that is a hyperlink that opens in a new tab -->
<!-- In-Class Session <a href="https://tudelft-citg.github.io/HOS-prob-design/homework/HW_05_assignment.html" target="_blank">HW 5 Due</a>{: .label .label-red } -->

Lecture
: Geometrically Nonlinear Structures
<br><em>Wednesday, 08:45-12:45, Flux Hall D</em>

Homework
: Study content of week 6

Workshop
: Workshop: Workshop 1 (Static String), Workshop 2 (Expanded Static String), Workshop 6 (Dynamic String)
<br><em>Wednesday, 08:45-12:45, Flux Hall D</em>
<br><em>Thursday, 13:45-15:45, Flux Hall D</em>

<!-- Holidays
: None -->

At the end of this week you will be able to: <br>
Define numerical methods to analyse systems governed by nonlinear Partial Differential Equations. This entails:<br>
<i>1. Define the formulation that characterizes the dynamics of structures subject to large deformations</i><br>
<i>2. Define numerical methods to solve nonlinear systems of PDEs</i> <br>
<i>3. Analyse and justify the results</i><br>
{: .learningobjectives }

Week 6. Geometrically nonlinear structures [[pdf 1]](https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek6&files=6.1_Geometrically_nonlinear_structures.pdf),[[pdf 2]](https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek6&files=7.1_Geometrically_nonlinear_structures.pdf) :<br>
<i>1. Geometric nonlinearity [5.4](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/geometric_nonlinearity.html)</i> <br>
{: .content }

[Workshop 1 (Static String)](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/Exercises/geometric_nonlinear_exercises/Workshop_1_Static_String.html)<br>
[Workshop 2 (Expanded Static String)](https://teachbooks.tudelft.nl/computational-modelling/solid_nonlinear/Exercises/geometric_nonlinear_exercises/Workshop_2_Offset_Calc.html)<br>
[Workshop 6 (Dynamic String)](https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/str_elem_dyn_workshops/Workshop_Dynamic_String.html)<br>
{: .exercises }
2 changes: 2 additions & 0 deletions calendar.md
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- Week 2: Computational methods for rigid body dynamics
- Week 3: Computational methods for Partial Differential Equations
- Week 4: Computational methods for Partial Differential Equations in 2D
- Week 5: Modal analysis for time-dependent Partial Differential Equations
- Week 6: Geometrically nonlinear structures

<!-- - Week 2:
- Week 3:
24 changes: 24 additions & 0 deletions public/Assessment.html
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<h1 id="assessment">Assessment</h1>

<p>The assessment of this <strong>unit</strong> will be embedded on the project/exercise portfolio and individual exam of each <strong>B module</strong>. The following percentages will be applied:</p>
<ul>
<li>Probabilistic Design: 20%,</li>
<li>Numerical Modelling: 25%</li>
<li>Marine Renewables / Dams, Dikes and Breakwaters / Floating and Submerged Structures: 55%</li>
</ul>

<p>The assessment for <strong>Computational Modelling</strong> is tailored for each B module as follows:</p>
<ul>
<li><strong>HOS-B1 Marine Renewables</strong>:</li>
<li>Stand-alone project on floating wind turbine. The description of the project can be found <a href="./assets/projects/CIEM4210-Project-2024.pdf">here</a>.</li>
<li>Specific questions in the multiple-choice exam</li>
<li><strong>HOS-B2 Dams, Dikes and Breakwaters</strong>:</li>
<li>Stand-alone project on structural analysis of a breakwater. The description of the project can be found <a href="./assets/projects/CIEM4220-Project-2024.pdf">here</a>.</li>
<li>Specific questions in the oral exam</li>
<li><strong>HOS-B3 Floating and Submerged Structures</strong>:</li>
<li>Embedded chapters on the floating-submerged tunnel project. The description of the project can be found <a href="./assets/projects/CIEM4230-Project-2024.pdf">here</a>.</li>
<li>Specific questions in the oral exam</li>
<li><strong>OE44090 Introduction to Computational Dynamics of Offshore Structures</strong>:</li>
<li>Stand-alone project on floating wind turbine. The description of the project can be found <a href="./assets/projects/OE44090-Project-2024.pdf">here</a>.</li>
<li>Written exam</li>
</ul>
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<h1 id="forms-of-instruction">Forms of instruction</h1>

<p>In this unit we will use a problem-based teaching approach. At each week we will provide theoretical material in form of lectures that will later be used in hands-on tutorials and exercises. You are expected to use the concepts practiced during the tutorials and exercises in your final group project.</p>

<p>Each week we will have a <strong>4 hours workshop</strong> where we will cover basic theory (~1h), work on a guided tutorial (~1h) and work on exercises with applications of interest (~2h). In addition, we will have a <strong>2h walk-in feedback session</strong> every week.</p>

<h1 id="lecture-and-study-materials">Lecture and study materials</h1>

<p>This course/unit will use the following materials: Lecture slides, lecture notes, papers and chapters from relevant literature.</p>

<p>We will use the <a href="https://interactivetextbooks.citg.tudelft.nl/computational-modelling"><strong>Computational Modelling in Civil Engineering and Geosciences</strong></a> book as a reference (link also available on the top-right corner of this page).</p>

<p>In the <a href="./Calender.md"><em>Calender</em></a> section of this page you will find the links to the material for each week.</p>

<p>For each week you will have the description of the theory, with links to the pre-recorded videos, some solved exercises applying the concepts given in the theory and tutorials with applications to examples relevant to the modules. You will also find a set of exercises to be developed in the workshop sessions. Other than the Python notebooks some comparisons are made using other programs and laguages suchs as <a href="https://www.maplesoft.com/">Maple</a> and <a href="https://julialang.org/">Julia</a>. If the installation of additional software is required, we will provide instructions on how to do it.</p>

<p><strong>A note on the course structure</strong></p>

<p>The course is built up of a series of theory pages, as well as tutorial notebooks. It is advised for students to look into the theory pages first. Here a series of texts and videos explains the course material. After that the tutorial pages show ways of implementing the theory lectures. Tutorials are either example-only, with the full example and implementation shown, or they are exercise-solution based. This is indicated in the title. While all exercises have an example solution directly availible at the bottom of the page, it is advised to try it yourself first. In coding there are always different possible paths, so discuss your approach with fellow students or your lecturers. The correctness and efficiency of the solution is key, and even the provided solutions have room for improvement.</p>
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<h1 id="week-1">Week 1</h1>

<p class="learningobjectives">At the end of this week you will be able to: <br />
Define and analyse numerical methods to solve Ordinary Differential Equations (ODEs). This entails:<br />
<i>1. Define a simple solver to approximate solutions of ODEs based on Taylor Series</i> <br />
<i>2. Quantify the numerical error of an approximated solution</i><br />
<i>3. Define adaptive time stepping approaches to control the numerical error</i><br />
<i>4. Distinguish between different ODE solvers</i><br /></p>

<p class="content">Week 1. Computational methods for ODEs <a href="https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek1&amp;files=1_1_Computational_methods_for_ODEs.pdf">[pdf]</a>:<br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/ODEs/Introduction.html">Introduction to numerical methods for ODEs</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/ODEs/Taylor-series.html">Taylor series</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/ODEs/Solvers.html">ODE solvers</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/ODEs/Error_stability.html">Error and stability</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/ODEs/Error_control.html">Error control</a><br /></p>

<p class="exercises"><a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/w1_t1.html">Workshop: ODE Solver</a><br /></p>
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<h1 id="week-2">Week 2</h1>

<p class="learningobjectives">At the end of this week you will be able to: <br />
Defining and solving an Equation of Motion using the Lagrangian approach. This entails:<br />
<i>1. Recognize structural elements and understand their contribution in the Equation of Motion</i><br />
<i>2. Deriving the Equation of Motion using Lagrangian approach</i> <br />
<i>3. Solve Equation of Motion using numerical methods</i><br /></p>

<p class="content">Week 2. Computational methods for rigid body dynamics <a href="https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek2&amp;files=2_1_Dynamics_of_rigid_bodies.pdf">[pdf]</a>:<br /></p>

<p class="exercises"><a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/Workshop_Linearizing_EOM.html">Workshop 2</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/Workshop_EOM_Pendulum.html">Workshop 3</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/Workshop_EOM_2DOF.html">Workshop 4</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/Workshop_EOM_4DOF.html">Workshop 5</a><br /></p>
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<h1 id="week-3">Week 3</h1>

<p class="learningobjectives">At the end of this week you will be able to: <br />
Define and analyze numerical methods to solve systems governed by Partial Differential Equations. This entails:<br />
<i>1. Define the system of PDEs that characterize the behaviour of structures composed by rods and beams</i><br />
<i>2. Define numerical methods to solve a system of PDEs</i> <br />
<i>3. Implement a solver for a system of PDEs</i><br />
<i>4. Analyse and justify the results</i><br /></p>

<p class="content">Week 3. Computational methods for time-dependent Partial Differential Equations <a href="https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek3&amp;files=3_1_Numerical_methods_for_PDEs.pdf">[pdf]</a>:<br />
<i>1. Introduction to Finite Differences for time-dependent PDEs</i><br />
<i>2. Introduction to Finite Elements for time-dependent PDEs (<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/semi_discrete.html">6.4</a> and <a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/time_steppers.html">6.5</a>)</i> <br />
<i>3. Theory: Beam equation <a href="https://teachbooks.tudelft.nl/computational-modelling/structural_linear/euler_bernouilli.html">4.1</a></i> <br />
<i>4. Theory: Space frames <a href="https://teachbooks.tudelft.nl/computational-modelling/structural_linear/space_frame.html">4.3</a></i> <br /></p>

<p class="exercises"><a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/Workshop_FEM_dyn_rod.html">Workshop 1</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/structural_linear/Exercises/Workshop_FEM_dyn_beam.html">Workshop 2</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/structural_linear/Exercises/Workshop_FEM_dyn_space_frames.html">Workshop 3</a><br /></p>
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<h1 id="week-4">Week 4</h1>

<p class="learningobjectives">At the end of this week you will be able to: <br />
Define and analyse numerical methods to solve systems governed by Partial Differential Equations in 2-dimensional domains. This entails:<br />
<i>1. Define the system of PDEs that characterize the behaviour of linear elastic structures in 2D</i><br />
<i>2. Define numerical methods to solve a system of PDEs</i> <br />
<i>3. Implement a solver for a system of PDEs</i><br />
<i>4. Analyse and justify the results</i><br /></p>

<p class="content">Week 4. Computational methods for time-dependent Partial Differential Equations in 2D <a href="https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek4&amp;files=4_1_Numerical_methods_for_PDEs_in%202D.pdf">[pdf]</a>:<br />
<i>1. Isoparametric mapping <a href="https://teachbooks.tudelft.nl/computational-modelling/introduction/isoparametric_mapping.html">2.8</a></i> <br />
<i>2. Numerical integration <a href="https://teachbooks.tudelft.nl/computational-modelling/introduction/numerical_integration.html">2.6</a></i> <br /></p>

<p class="exercises"><a href="https://teachbooks.tudelft.nl/computational-modelling/continuum_linear/Exercises/Workshop_FEM_Linear_Elasticity.html">Workshop 1</a><br /></p>
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<h1 id="week-5">Week 5</h1>

<p class="learningobjectives">At the end of this week you will be able to: <br />
Define numerical methods to perform a modal analysis of systems governed by Partial Differential Equations. This entails:<br />
<i>1. Characterize the modal properties of a system of PDEs</i><br />
<i>2. Define numerical methods that return characteristics eigenfrequencies and eigenmodes of a system of PDEs</i> <br />
<i>3. Analyze and justify the results</i><br /></p>

<p class="content">Week 5. Modal analysis for time-dependent Partial Differential Equations <a href="https://surfdrive.surf.nl/files/index.php/s/Jm8e95QGRS97bDq/download?path=%2FWeek5&amp;files=5_1_Modal_analysis.pptx">[pdf]</a>:<br />
<i>1. Modal analysis <a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/modal_analysis.html">6.6</a></i> <br /></p>

<p class="exercises"><a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/str_elem_dyn_workshops/Workshop_modal_sup_pos_jacket.html">Workshop 4</a><br />
<a href="https://teachbooks.tudelft.nl/computational-modelling/dynamics/Exercises/str_elem_dyn_workshops/Workshop_Full_FEM_sup_pos_jacket.html">Workshop 5</a><br /></p>
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