Computational Engineering Analysis

Module aims

  • To expose principal computational methods in civil engineering.
  • To illustrate the main application areas for each of these methods.
  • To engage in computer modelling of real engineering problems.
  • To assess the accuracy of computer-based solutions.

Learning outcomes

On successfully completing this course unit, students will be able to:

  • Analyse structural, geotechnical and hydraulic problems using appropriate numerical methods.
  • Understand the fundamentals of finite element analysis for structural and geotechnical analysis.
  • Apply finite element analysis to a range of structural and geotechnical problems.
  • Estimate the errors involved in finite element analysis.
  • Discretise partial differential equations using the method of lines.
  • Appreciate and evaluate the errors made in numerical approximations of PDEs.

Module syllabus

Topics covered in this module include:

  • Finite element analysis for linear problems in solid mechanics; assembly and solution of discrete systems.
  • Plane stress/strain elements: basic formulations.
  • Higher order elements.
  • Error estimation for finite element analysis.
  • Modelling issues.
  • Application of finite element analysis to structural problems.
  • Extension of finite element analysis and application to geotechnical problems.
  • Discretisation of the soil domain: types of continuum elements; design of an FE mesh for geotechnical analysis.
  • Constitutive models: general principles of constitutive model formulation for soils.
  • Basic soil constitutive models of Tresca and Mohr-Coulomb type.
  • Boundary conditions for geotechnical analysis.
  • Discretisation of advection-diffusion equations with the method of lines.
  • Application to various problems in fluid mechanics and heat transfer.
  • Implementation of boundary conditions.
  • Numerical stability, consistency, and convergence. Lax equivalence theorem.
  • Error analysis in the discretisation of PDEs.

No.

Topic

Staff

01

Introduction to Finite Element Analysis

LM

02

Plane Stress/Strain Basic Elements

LM

03

Higher Order Elements

LM

04

Error Estimation for Finite Element Analysis and Applications to Structural Problems

LM

05

Geotechnical Engineering Problems: Considerations, Discretisation and Boundary Conditions

KG

06

Geotechnical Engineering Problems: Constitutive modelling

KG

07

Geotechnical Engineering Problems: Coupled consolidation analysis

KG

08

(Delivered in five 2-hour slots) Numerical solution of advection-diffusion equations

MvR

Pre-requisites

CI1-121, CI2-221

Teaching methods

This course consists of lectures, supporting tutorials and workshops. Staff and GTAs will be available to answer specific questions.

Assessments

Assessment information will be provided separately.

Reading list

Module leaders

Dr Lorenzo Macorini