ME 444 / PHYS 457 / TME 444:
Continuum mechanics may be the topic that best defines and unifies mechanical engineering. The topic considers motion, deformation, flow, stresses, forces, and heat transfer as determined by the laws of mechanics. Those phenomena may occur in any materials — solids, fluids, or things in-between — that can be well-modeled as continuous, not discrete (meaning quantization effects are negligible). To handle this wide variety of phenomena and materials, we use the language of tensor mathematics, which we will build up at the beginning of the course. Applications to ongoing research of the instructor and students will be incorporated wherever possible. The course will include
- indicial notation and tensor analysis,
- concepts of stress,
- both Eulerian and Lagrangian descriptions of deformation and strain,
- conservation of mass, momentum, energy, angular momentum, and
- constitutive equations to describe material response.
Basic ordinary and partial differential equations, linear algebra, undergraduate fluid mechanics (e.g., ME 225) and solid mechanics (e.g., ME 226).
- Introduction to Continuum Mechanics, Fourth Edition by W. Michael Lai, David Rubin, and Erhard Krempl; or an equivalent text.
- Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M. Schey.
- A Student's Guide to Vectors and Tensors by Dan Fleisch, and his video, What's a tensor?
Assignments & Grading
Students prevented from attending in person because of the covid-19 pandemic can nonetheless attend lectures remotely, submit Problem Sets via email, and take exams via Zoom (synchronously). Lectures will be recorded and posted on this page. Connection information for viewing lectures via Zoom is available from the instructor, by email.
All assignments and activities associated with this course must be performed in accordance with the University of Rochester's Academic Honesty Policy. In this course, students are allowed to collaborate on Problem Sets — provided that each collaborator takes the time to fully understand the material and write a separate copy of the assignment. On exams, use of all course resources is permitted, but collaboration with other students or outside aids, including services like Chegg.com, is prohibited. Facilitating dishonesty is dishonesty. Students must write and sign the Honor Pledge on all exams: “I affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own.”
- Problem Sets - 30%
- Roughly one assignment every two weeks (see Resources), due at 13:45 Eastern time, to be submitted via Gradescope. Late Problem Sets will not be accepted.
- Midterm - 35%
- 14:00 - 15:15, 2 March, Meliora 209
- Final exam - 35%
- 16:00 - 19:00, 3 May, Meliora 209.
I will distribute evaluations periodically to collect feedback. I typically check email frequently but cannot guarantee immediate response at all times. Quick questions can be effectively and efficiently addressed by email, but for in-depth questions a face-to-face discussion usually works better. The problem sets are intended to be hard enough to bring you into my office! Office hours take place Mondays 15:30-16:30 in Hopeman 218 and in my Zoom meeting room. Send email if you need to meet at another time.
This sequence may evolve as the course progresses.
- Introduction (Ch. 1)
- Tensors (Ch. 2)
- Kinematics of a Continuum (Ch. 3)
- Stress and Integral Formations of General Principles (Ch. 4)
- The Elastic Solid (Ch. 5)
- Newtonian Viscous Fluid (Ch. 6)
- Non-Newtonian Fluids (Ch. 8)
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