The University of Southampton
Courses

# FEEG3001 Finite Element Analysis in Solid Mechanics

## Module Overview

This module is aimed at providing the requisite background in solid mechanics and structural vibration. Then, the module concentrates on solving this problem by introducing the Finite Element Method, aiming at providing an understanding of fundamental knowledge and technique of FEM developing tools to analyse engineering problems using FEM and typical commercial FEA package.

### Aims and Objectives

#### Module Aims

- Provide background solid mechanics required for the FEA contents. - Provide an understanding of fundamental knowledge and technique of FEM. - Develop tools to analyse engineering problems using FEM and typical commercial FEA package.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Variational principles in statics and dynamics of structure
• Fundamental concepts and method of FEA
• Direct stiffness, Rayleigh-Ritz methods and FEA.
• FEA formulation in solid mechanics.
• Fundamental isoparametric elements.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Formulate finite element matrices variationally.
• Analyse and build FEA model for various engineering problems.
• Identify information requirements and sources for design and evaluation.
• Synthesise information and ideas for use in the evaluation process.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Choose a commercial FEA software to solve practical problems through workshops and a design assignment.

### Syllabus

1. General introduction, objectives The general continuous solid mechanics: - Variational principle in mechanics. Priniciple of minimum total potential energy. Hamilton’s Principle. - Lagrange’s equations in dynamics of mechanical systems. - A brief review of normal modes and natural frequencies in multi-degree-of-freedom discrete systems. - Constitutive equations: an overview Finite Element Analysis: - Application of the principle of minimum potential energy to approximate solution of elasticity problems Rayleigh-Ritz Method in statics. - Derivation of equations of motion and FE matrices in structural dynamics. - General FE formulation: aspects of derivation of the element matrices, assembly, application of boundary conditions, solution procedures. - Practical aspects of the use of FE codes: pre- and post-processing. The use of commercial codes e.g. ANSYS. - Finite Element Formulation for 1D elastic continua (rods, shafts, strings): statics and dynamics - FE formulation for trusses in 2D: coordinate transformations - Beam bending elements. Statics and dynamics. - Constant Strain Triangle (CST) elements for plane stress and plane strain, axi-symmetric elements. - 2D Quadrilateral elements - Isoparametric FE formulations. - Element selection

#### Special Features

A balanced mix of the theoretical and practical aspects of a tool commonly used in engineering design.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include: Lectures Class discussions Practical FEA model presentation ANSYS computer laboratory sessions (ANSYS not available on VPN) Learning activities include Directed reading Assignments Example exercises and writing of laboratory report Independent learning to use FEA software on computers

TypeHours
Teaching35
Independent Study115
Total study time150

K.J. Bathe (1996). Finite Element Procedures in Engineering Analysis.

R.D. Cook (1981). Concepts and Applications of Finite Element Analysis.

I.H. Shames and C.L. Dym (1985). Energy and Finite Element Methods in Structural Mechanics.

### Assessment

#### Summative

MethodPercentage contribution
Examination  (120 minutes) 70%
Laboratory Report 12%
Laboratory Report 8%
Test 10%

#### Referral

MethodPercentage contribution
Examination  (120 minutes) 100%

#### Repeat Information

Repeat type: Internal

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