Introduction to the Finite Element Method

Transition code to replace old course "CIE5123 Introduction to the Finite Element Method" with "Unit 2: Finite Elements for Structural Analysis" of the new module "CIEM5110 Structural Mechanics and Dynamics".

The unit needs to be followed in its entirety and can be followed without attending the other units in the module.

This unit provides students with a structural mechanics perspective on the finite element method. The derivation of the discrete system of equations from the governing equations is discussed and it is shown how different types of analysis for obtaining deformations, stability, vibrations and collapse are performed. Students will work with a lightweight finite element code to analyze the static and dynamic response of a simple structure (modelled as beam, truss or frame) and compare the results obtained with the different types of analysis. Specifically, the following topics will be covered:

Formulation of the finite element method

- From virtual work to discrete system of equations

- Timoshenko beam element formulation

- Numerical integration

- Shear locking and reduced integration

- Treatment of boundary conditions

- Alternative derivation from PDE to discrete system of equations

Geometric nonlinearity

- Nonlinear strain definition

- Solution algorithms for the nonlinear finite element method

- Linear buckling analysis

Physical nonlinearity

- Introduction into nonlinear constitutive laws

- Plastic hinges for frame analysis

Time dependent problems

- Mass matrix of Timoshenko beam elements

- Explicit and implicit time discretization for transient elastodynamics

- Free vibration analysis

- Modal analysis