CIEM42X0

This book is used for Unit 2 Computational Modelling of all HOS-B modules (CIEM4210, CIEM4220 and CIEM4230).

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

Week 1

Contents

• Week 1. Computational methods for ODEs

  1. Introduction to Numerical methods for ODEs

  2. Taylor Series

  3. Ordinary Differential Equation Solvers

  4. Numerical error

  5. Error control

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Week 2

Contents

• Week 2. Computational methods for Rigid body dynamics [pdf]

• Types of structural elements

• Lagrangian mechanics

• Linearization

  1. Workshop 2: Linearizing the Equations of Motion

  2. Workshop 3: Deriving the EOM of a pendulum

  3. Workshop 4: Deriving the EOM of a 2DOF system

  4. Workshop 5: Deriving the EOM of a 4DOF floating wind turbine

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Week 3

Contents

• Week 3. Computational methods for time-dependent Partial Differential Equations [pdf]

• Introduction to Finite Differences for time-dependent PDEs

• Introduction to Finite Elements for time-dependent PDEs

  1. Semi-discrete form for elasto-dynamics

  2. Time stepping schemes for elasto-dynamics

• Rod equation

  1. Workshop: Workshop 1: FEM for a rod

• Beam equation

  1. Theory: Euler-Bernoulli beam elements

  2. Workshop: Workshop 2: FEM for an Euler-Bernoulli beam

• Space frames

  1. Theory: 2D frame analysis

  2. Workshop: Workshop 3: FEM for a jacket wind turbine

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Week 4

Contents

• Week 4. Computational methods for time-dependent Partial Differential Equations in 2D [pdf]

• Isoparametric map

  1. Theory: Isoparametric mapping

• Numerical integration

  1. Theory: Numerical integration

• FEM for Linear Elasticity

  1. Theory: Linear elasticity

  2. Workshop: Workshop 1: Finite Elements for Linear Elasticity

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Week 5

Contents

• Week 5. Modal analysis for time-dependent Partial Differential Equations [pdf]

• Modal analysis

  1. Theory: Modal Analysis

• Workshops modal analysis for a space frame structure

  1. Workshop 4: Workshop 4: Modal superposition of a jacket wind turbine

  2. Workshop 5: Workshop 5: Full FEM or Modal superposition for a jacket wind turbine

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Week 6

Contents

• Week 6. Geometrically nonlinear structures [pdf 1], [pdf 2]

• Geometric nonlinearity

  1. Theory: Geometrically nonlinear problems

• Workshops

  1. Workshop 1 (Static String): Workshop 1: Static string

  2. Workshop 2 (Expanded Static String): Workshop 2: Offset calculation and theory

  3. Workshop 6 (Dynamic string): Workshop 6: Dynamic string

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