ENME302-24S2 (C) Semester Two 2024

# Computational and Applied Mechanical Analysis

15 points

Details:
 Start Date: Monday, 15 July 2024 End Date: Sunday, 10 November 2024
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 28 July 2024
• Without academic penalty (including no fee refund): Sunday, 29 September 2024

## Description

Partial differential equations and their classification; boundary and initial conditions; analytical solution methods. Introduction to computational solution techniques and packages in solid mechanics (FEM), fluid dynamics (CFD) and heat/mass transfer.

To extend students’ exposure to, and understanding of the significance and solution of differential equations by adding partial differential equations (PDEs) to the already-familiar ordinary differential equations.  Based on this mathematical understanding of PDEs, students will then become familiar with the underlying principles of the numerical solution techniques of these same equations that are utilised in commonly-employed computational packages such as COMSOL, used not in a “black box” manner but, rather, with an appreciation of the underlying mathematics and numerical techniques that are embedded within them. This understanding of computational methods will be further augmented by the students’ own development and implementation of standard algorithms for numerical solution of PDEs.

## Learning Outcomes

• Washington Accord (V4) Summary of Graduate Attributes attained in this course:
 WA1 – Engineering Knowledge
 WA2 – Problem Analysis
 WA4 – Investigation
 WA5 – Tool Usage

• Course topics with Learning Outcomes (and Washington Accord (WA) and UC Graduate Attributes) identified.

1. Bar (2DOF), Beam (4DOF), and Frame (6DOF) Elements: derivation, shape functions, assembly to models
1.1. Understand and apply the basic FEA elements and formulations, including major method limitations (WA1)
2.1. Recognise and apply different numerical solution terminology and techniques (WA1)
3. Discussion on mathematical modelling and simulation
3.1. Appreciate properties and limitations of any numerical solution method (WA1)
3.2. Understand computational strategies to maximize efficiency and minimize processing time. (WA2) (EIE3)
4. Introduction to Partial Differential Equations (PDEs), Separation of variables method and Fourier series
4.1. Recognise and classify the different types of PDEs (elliptic, parabolic and hyperbolic) (WA1)
4.2. Use separation of variables solution method where applicable. (WA1)
5. Generating a computational domain (CAD and mesh generation)
5.1. Able to code, MATLAB or similar, basic FEA assembly and analysis, and apply to solve problems (WA5) (EIE4)
6. Spatial discretisation: FD technique for elliptic problems, Time discretisation: application to parabolic PDEs
6.1. Understand the essential components of the PDE models for classical mechanical systems (WA1)
6.2. Recognise & apply, Dirichlet and Neumann boundary conditions, for unsteady state and initial conditions (WA2)
7. Important properties of numerical methods
7.1. Understand and apply d’Alembert solution and characteristics (WA1)
7.2. Confidently apply standard analytic solution methods to classical PDEs used in mechanical analysis (WA1)
8. Post-processing results / visualisation
8.1. Productively and confidently use generic computational packages (e.g. COMSOL) in the solution of “real world” problems in solid mechanics, fluid flow, and heat or mass transfer. (WA4) (EIE4)
8.2. Appreciate both the benefits and the limitations of such packages by comparison of numerical solutions with analytical solutions in situations where this is possible. (WA4) (EIE4)

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

 Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject. Employable, innovative and enterprising Students will develop key skills and attributes sought by employers that can be used in a range of applications.

## Timetable 2024

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 10:00 - 11:00 A1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture B 01 Tuesday 12:00 - 13:00 A1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture C 01 Wednesday 09:00 - 10:00 E8 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture D 01 Friday 11:00 - 12:00 A1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Computer Lab A 01 Thursday 12:00 - 13:30 Civil - Mech E201 Mech Computer Lab 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Thursday 13:30 - 15:00 Civil - Mech E201 Mech Computer Lab 15 Jul - 25 Aug 9 Sep - 20 Oct 03 Thursday 15:00 - 16:30 Civil - Mech E201 Mech Computer Lab 15 Jul - 25 Aug 9 Sep - 20 Oct

## Notes

For detailed course, policy, regulatory and integrity information, please refer to the UC web site, or see relevant Course or Department LEARN pages, (which are available to enrolled students).

## Indicative Fees

Domestic fee \$1,059.00

International fee \$6,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mechanical Engineering .

## All ENME302 Occurrences

• ENME302-24S2 (C) Semester Two 2024