ENGSCI 343 : Mathematical and Computational Modelling in Mechanics
Engineering
2025 Semester One (1253) (15 POINTS)
Course Prescription
Course Overview
Course Requirements
Capabilities Developed in this Course
| Capability 3: | Knowledge and Practice |
| Capability 4: | Critical Thinking |
| Capability 5: | Solution Seeking |
| Capability 6: | Communication |
Learning Outcomes
- Have knowledge of the mathematical tools and language used in continuum and computational mechanics, including tensors, coordinate transformations and eigenvalue analysis (Capability 3.1)
- Be able to understand, demonstrate and apply concepts of kinematics, the description of motion, displacement, deformation and strain, including: Material coordinates, Spatial coordinates, motion, deformation gradient, linear approximations, homogeneous deformations, shear, stretch, rotation, rigid rotations, Polar decomposition, multiplicative decomposition, linear strain, Displacement, displacement gradient, 2D strains and rotations, strain-displacement relations, compatibility, principal strains. (Capability 4.1 and 6.1)
- Be able to understand and apply concepts of force transmission in physical systems, including the stress tensor, equilibrium and the equations governing continuum mechanics, internal stress, traction, the stress matrix, the stress tensor, Cauchy's Law, principal stress, surface forces, body forces, equations of motion, equations of equilibrium. (Capability 3.2 and 5.1)
- Be able to understand and apply in the solution of problems of static elasticity: material models, linear elasticity, linearised kinematics, isotropy, elastostatics, Navier's equations, plane stress, plane strain, stress function, axisymmetric problems, pressurised cylinders, rotating discs, stress concentrations. (Capability 3.2)
- Understand and apply the basic equations of fluid dynamics, including the Stokes and Navier-Stokes equations and the derivation of fundamental solutions. Describe the continuum hypothesis for fluids, explain the difference between an Eulerian and Langrangian description of a fluid flow. Define and explain total and advective acceleration. (Capability 3.1)
- Be able to derive the flow field for viscous flows in simple situations, such as thin film flow down a slope, or viscous channel\pipe flow. (Capability 4.1)
- Be able to calculate relatively complex irrotational flows, such as that around a circular cylinder, by superpositioning simple irrotational flow solutions, such as Point Sources, Line Vortices, Uniform Flow; find the surface pressure using the Bernoulli equation; Integrate surface pressure components to evaluate forces. Be able to explain the Magnus Effect and D’Alembert’s Paradox. (Capability 4.1)
- Be able to calculate and explain the behaviour of a hydraulic jump; use the Mach number to check for compressibility effects; find the wave speed in a propagation problem and use the compressible form of the Bernoulli Equation. (Capability 4.2)
- Be able to (for Boundary Layers) calculate thickness, momentum thickness, displacement thickness; use Blasius solution to calculate the skin drag on a flat surface; describe flow separation. (Capability 5.1)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Assignments | 20% | Individual Coursework |
| Tests | 30% | Individual Coursework |
| Final Exam | 50% | Individual Examination |
| 3 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
| Assignments | ||||||||||
| Tests | ||||||||||
| Final Exam | ||||||||||
Exam mode C: in-person . Students must sit the exam to pass the course. Otherwise, a DNS (did not sit) result will be returned.
late submissions for the assignments are penalised at 4% of the total mark for each hour.
Workload Expectations
This course is a standard 15 point course and students are expected to spend 10 hours per week.
For this course, you can expect an average weekly workload comprising 3 hours of lectures, a 1 hour tutorial, 4 hours of reading and thinking about the content, and 2 hours of work on assignments.
Delivery Mode
Campus Experience
Attendance is expected at scheduled activities including lectures/labs/tutorials to complete/receive credit for components of the course.
Lectures will be available as recordings. Other learning activities including tutorials will be available as recordings.
The course will not include live online events including group discussions.
Attendance on campus is required for the test
The activities for the course are scheduled as a standard weekly timetable.
Learning Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
Health & Safety
Students must ensure they are familiar with their Health and Safety responsibilities, as described in the university's Health and Safety policy.
Student Feedback
At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.
Your feedback helps teachers to improve the course and its delivery for future students.
Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework, tests and examinations as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Learning Continuity
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.