# Unit information: Finite Element Analysis in 2015/16

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Unit name Finite Element Analysis MENG33111 10 H/6 Teaching Block 1 (weeks 1 - 12) Professor. Wilcox Not open MENG11100 or MENG21100, or equivalent None Department of Mechanical Engineering Faculty of Engineering

## Description

 Finite Element Analysis (FEA) is the principle method of numerical analysis used by mechanical engineers to ensure their designs are fit for purpose. The FEA unit is divided into two components: Practical FEA and Theory of FEA. The Practical FEA component is run as a computing class using commercial FEA software. The students are first given some self-taught exercises to gain familiarity with the software and two assessed exercises. The first involves the design of a cantilever bracket and the second the design of a helicopter floor panel. The Theory of FEA component is a lectured course that gives students an insight into the underlying principles of FEA. The course begins with the analysis of pin-jointed structures using an FEA approach and then considers the application of FEA to stress analysis of continuous structures. The course includes element stiffness matrix formulation and also introduces dynamic and nonlinear simulations.

## Intended learning outcomes

On completion of the unit the student should be able to:

• Recall: that FEA is fundamentally about spatial discretisation to obtain an approximate solution to a boundary value problem (EX); that the basic FE calculation is concerned with the formulation and solution of linear simultaneous differential equations (EX); the main elements (pre-processor, solver, post-processor) of a commercial FEA programme (EX & CW); the salient information required in an input file for an FEA solver such as mesh, material properties, loading conditions, required outputs etc. (EX & CW); how to identify key parts (e.g. nodes, elements, boundary conditions, applied forces) of an FE model from a suitable visual representation (EX & CW); the definition of terms validation and convergence in the context of FEA; the nature of shape functions and stress/strain fields in constant strain elements (EX); the terms parent element, natural coordinates, physical coordinates and tangent stiffness matrix (EX).
• Explain: the purpose of performing FEA in the context of the mechanical engineering design process (EX & CW); the concepts of global and local stiffness matrices and that the former embodies the physical principles of compatibility & equilibrium (EX); the difference between plane stress and plane strain (EX + CW); the principle of energy-based derivation of element stiffness matrices, its extension to higher-order isoparametric elements and the need for numerical integration via, e.g., Gauss quadrature (EX); principles of good and bad meshing practice (EX & CW); the difference between time- and frequency-domain methods for dynamic FEA (EX); the need for stability criteria when performing time-domain dynamic FEA (EX); the main methods for solving nonlinear problems using FEA (EX); why many real situations require nonlinear FEA and the main sources of nonlinearity (EX).
• Apply their knowledge to: derive the stiffness matrix of a bar element from first principles; assemble an appropriate global matrix equation for simple bar and beam structures (EX); solve the global matrix equation to determine unknown displacements, reaction forces and loads within elements (EX); perform a convergence study using commercial FEA software (CW); derive the element stiffness matrix for simple elements using energy methods (EX); select appropriate plane stress and plane strain boundary conditions in 2D FEA (EX & CW); identify vibration modes and forced responses via frequency-domain analysis (EX); analyse transient problems using time-domain analysis (EX); solve simple nonlinear problems iteratively by calculating an appropriate tangent stiffness matrix (EX); identify appropriate boundary conditions to apply in an FEA analysis of a given structure and state the associated mathematical constraints, e.g. symmetry about y-axis requires no displacement of nodes in x direction on that axis (EX & CW); identify an appropriate model system with analytical solutions against which FEA data can be validated (EX & CW).
• Combine and apply the principles of FEA to unfamiliar situations by: formulating element and global stiffness matrices in other applications, e.g. heat flow, electrical conductance (EX); determining the most appropriate form of FEA and identifying appropriate validation cases for a specified problem (EX & CW).

Justify the validity of FEA results by: applying appropriate, physically-justifiable analytical models to obtain approximate solutions (EX & CW); performing convergence studies (EX & CW); forming a compelling and convincing argument to support their FEA results.

## Teaching details

The unit will be delivered through a combination of 11 x 1-hour lectures (1 per teaching week in TB1) and 11 x 1-hour computer classes (1 per teaching week in TB1). All lecture notes, together with additional material including example sheets and simple FE examples written in Matlab is provided through Blackboard. For the computer classes students will be provided with a structured set of exercises leading into the two assessed pieces of work. CW1 will be submitted at the end of Week 6 and CW2 at the end of Week 12. Formative feedback from CW1 will be provided before the end of Week 9

## Assessment Details

EX. 1.5 hour exam (50%)

CW1. Coursework assessment (25%)

CW2. Coursework assessment (25%)

Coursework Deadlines: Assuming the Practical part of the course runs in Weeks 1-12 the deadlines are at the end of week 6 (CW1) and the end of week 12 (CW2)