ME 444 / PHYS 457:
Continuum Mechanics
Department of Mechanical Engineering
University of Rochester
Fall 2024 | Douglas H. Kelley
Lectures 16:50-18:05 Mondays and Wednesdays in Hylan 202. Advanced undergraduate students are welcome and can add the course by emailing me.
Course Goals
Continuum mechanics 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 (so that 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.
Prerequisites
Basic ordinary and partial differential equations, linear algebra, undergraduate fluid mechanics (e.g., ME 225) and solid mechanics (e.g., ME 226).
Materials
- 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?
- 3blue1brown, especially Essence of linear algebra
Assignments & Grading
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 and encouraged 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, neither collaboration nor outside aids are permitted unless the instructor explicitly states otherwise. Services like Chegg.com are uniformly prohibited on all assignments. 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.” Procrastination is a major source of dishonesty, so start assignments early and keep yourself organized.
- Problem Sets - 30%
- Roughly one assignment every two weeks (see Resources), due at 23:59 Eastern time, to be submitted via Gradescope. Late Problem Sets will not be accepted.
- Midterm - 35%
- Thursday, 10 October, 12:00-15:00, Hopeman 204.
- Final exam - 35%
- Sunday, 15 December, 08:30-11:30, Hylan 202.
Feedback & Availability
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 Tuesdays 13:30-14:30 in Hopeman 218. Send email if you need to meet at another time or via teleconference.
Course Sequence
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)
- Elastic Solids (Ch. 5)
- Newtonian Viscous Fluids (Ch. 6)
- Viscoelasticity (Ch. 8)
Accessibility Accommodations
The University of Rochester respects and welcomes students of all backgrounds and abilities. The University employs professional staff committed to assisting students with disabilities in the classroom, residence halls, libraries, and elsewhere on campus. In the event you encounter any barriers to full participation in this course due to the impact of a disability, please contact the Office of Disability Resources (disability@rochester.edu, 585-276-5075). The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. It is a personal decision to disclose the existence of a disability and to request an accommodation. A decision not to disclose will be respected. Students who request an accommodation must provide appropriate documentation to the Disability Coordinator. The University remains flexible regarding the types of reasonable accommodations that can be made. Students with disabilities are invited to offer suggestions for accommodations.
Title IX
All members of the University community have the right to learn and work in a safe environment free from all forms of harassment, including harassment on the basis of sex or gender. Students who have been subjected to sexual harassment, including sexual assault, dating/domestic violence or stalking, have the right to receive academic, housing, transportation or other accommodations, to receive counseling and health services and to make a report about such behavior to the University and to law enforcement. For more information please visit www.rochester.edu/sexualmisconduct or contact the Title IX coordinator.
This page is available at http://hajim.rochester.edu/me/sites/kelley/me444/.