CIEM5110

This book is used for Unit 2 Finite Elements for Structural Analysis of the module CIEM5110.

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

• Self study (before lecture 1.2): 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 the module (slides)

  1. Tensor basics

  2. Linear algebra

  3. Tensor calculus

  4. Strong form for linear elasticity

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• Lecture 1.2 - MUDE recap, FEM for elastostatics (slides)

  1. Strong form for linear elasticity

  2. From strong to discrete form

Week 2

Contents

• Lecture 2.1 - Derivation of timoshenko beam elements. Shear locking (slides)

  1. Timoshenko Beam

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• Lecture 2.2 - Workshop: Introduction to pyJive (slides)

  1. Workshop: Introduction to pyJive

Week 3

Contents

• Lecture 3.1 - Nonlinear FEM(slides)

  1. Towards nonlinear problems

  2. Linearized discrete form

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• Lecture 3.2 - Workshop: framemodel, timoshenkomodel(slides)

  1. PyJive workshop: TimoshenkoModel

  2. PyJive workshop: FrameModel

Week 4

Contents

• Lecture 4.1 - Geometric nonlinarity. Linear buckling analysis (slides)

  1. Geometrically nonlinear problems

  2. ../solid_nonlinear/Exercises/pyjive_buckling

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• Lecture 4.2 - Arclength, plastic hinges. With workshop (slides)

  1. Incremental-iterative algorithms

  2. Equilibrium path following

  3. ../solid_nonlinear/Exercises/pyjive_plastic_hinges

Week 5

Contents

• Lecture 5.1 - Workshop: nonlinear frame analysis

  1. ../solid_nonlinear/Exercises/pyjive_frame_exercise

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• Lecture 5.2 - Introduction to nonlinear material models (slides)

  1. Material non-linearity

Week 6

Contents

• Lecture 6.1 - Workshop: Linearization and convergence (slides)

  1. ../solid_nonlinear/Exercises/pyjive_nonlinmodule

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• Lecture 6.2 - Dynamics with finite elements (slides)

  1. Semi-discrete form for elasto-dynamics

  2. Time stepping schemes for elasto-dynamics

  3. Modal Analysis

Week 7

Contents

• Lecture 7.1 - Workshop: frequency analysis (slides)

  1. ../dynamics/Exercises/pyjive_frequency

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• Lecture 7.2 - Workshop: transient analysis (slides)

  1. ../dynamics/Exercises/pyjive_transient

Week 8

Contents

• Lecture 8.1 - Workshop: hammer test analysis (slides)

  1. ../dynamics/Exercises/pyjive_hammer