Finite Element Analysis in Solid Mechanics

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Analyse and build FEA models for various engineering problems.
• Identify information requirements and sources for design and evaluation.
• Formulate finite element matrices
• Synthesise information and ideas for use in the evaluation process.

Full CEng Programme Level Learning Outcomes

Having successfully completed this module you will be able to:

• As part of the exam and coursework assignment students will apply theoretical structures concepts and new FEA simulation tools to evaluate structural analysis problems. In the coursework they will make critical arguments to support which tool is more appropriate for different aspects of an example problem.
• As part of the coursework assignment students will look for data to place their structural analysis predictions into real-world context, making arguments where this data may be incomplete.
• As part of the computing lab sessions and assessed in the coursework assignment, students will investigate structural analysis problems from multiple angles (e.g. deflection, stress, vibration etc.) using the practical application of structural analysis software.
• As part of the coursework assignment students will look for data to place their structural analysis predictions into real-world context, making arguments where this data may be incomplete. They may be asked to choose the most appropriate from a range of general analytical techniques
• As part of the exam and coursework assignment students will apply theoretical structures concepts and new FEA simulation tools to evaluate structural analysis problems. In the coursework they will make critical arguments to support which tool is more appropriate for different aspects of an example problem.

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

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

Knowledge and Understanding

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

• Fundamental concepts and method of FEA
• The computational implementation of these concepts in FEA software
• Direct stiffness and Energy approaches
• FEA formulation in solid mechanics

Introduction, Objectives

Recap of maths for FEA in solid mechanics:

• matrix algebra terminology
• adding, subtracting and multiplying matrices
• matrices to solve systems of linear equations
• manipulating matrices for computational FEA

General concepts of continuous solid mechanics:

• Variational principle in mechanics.
• The Principle of Minimum Total Potential Energy (PMTPE).
• Hamilton’s Principle, and Lagrange’s equations in dynamics of mechanical systems.
• A brief review of normal modes and natural frequencies in multi-degree-of-freedom discrete systems.

Finite Element Analysis in Theory:

• Application of the principle of minimum total potential energy (PMTPE) to approximate solution of elasticity problems
• Derivation of equations of motion and FE matrices in structural dynamics.
• Finite Element Formulation for 1D elastic springs and continua (rods, shafts)
• FE formulation for trusses in 2D, and the necessary coordinate transformations
• Beam bending elements.
• 2D Constant Strain Triangle (CST) elements for plane stress and plane strain
• 2D Quadrilateral elements

Finite Element Analysis in Practice:

• 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.
• Element selection

Teaching methods include:

• Lectures
• Class discussions
• Practical FEA model presentation

Learning activities include

• Directed reading
• Directed learning to use FEA software on computers, and example formative exercises
• Assignment, including writing of laboratory report

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.