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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.
Washington Accord (V4) Summary of Graduate Attributes attained in this course: WA1 – Engineering Knowledge WA2 – Problem Analysis WA4 – Investigation WA5 – Tool UsageCourse 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. Extension to distributed loading and development of equivalent nodal loading. 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.
EMTH210, EMTH271 or EMTH211, ENME202
Geoff Rodgers
James Hewett
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).
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 .