# ES4B5 - Finite Element Analysis

(15 Credits)

#### Aims

The main objective of the module is to provide a practical training in Engineering design using finite element methods. Design is at the heart of what professional engineers do. When components have complex construction, shape, and general boundary conditions (loading and restraint) the designer will often use finite element methods to determine their structural integrity. The first half of the module aims at introducing the fundamental principles of the modelling for statics and dynamics analyses. In the second half of the module the student’s will be taught how to use the method in practice and to critically assess and evaluate the results. The module aims to provide an introduction to this important stress analysis technique, and by way of case studies shows how it may be used to design components.

#### Learning Outcomes

By the end of the module the student should be able to:

• Recognise the significance and importance of finite element methods to the professional design engineer.
• Provide a theoretical understanding on the fundamentals of finite element methods for small displacement linear elastic analysis (statics).
• Provided an introduction of non-linear finite element method.
• Provide experience in analysing problems by commercial FE software (Abaqus).
• Provide experience on how to develop good models and how to interpret the numerical results in design.

#### Syllabus

• History of Finite Element (FE) methods and the place of computational methods in structural analysis.
• Small displacement linear elasticity (equilibrium, compatibility, stress-strain relationships, boundary conditions).
• Integral formulation for static analysis by the implicit FE method.
• Displacement functions and formulation of element stiffness and load characteristics (bar, membrane, flexure, and plate bending).
• Shape functions and the isoparametric element formulation, introduction to curved surfaces.
• Requirements for FE displacement fields.
• Methods to solve the matrix equations for the discretised structure.
• Introduction to the non-linear finite element method.
• Introduction to the explicit FE method.
• Practical aspects (e.g. mesh design, constitutive modelling, boundary conditions) for the FE modelling and simulation of real components.
• Application of commercial FE software (Abaqus) in engineering design.