## 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

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.