Continuum mechanics

I. Rationale: 

Continuum Mechanics is the cornerstone of Mechanical Engineering disciplines. The material presented in this class will form the foundation for the remainder of your degree program. We begin with a thorough introduction to vector and tensor analysis, making use of indicial notation for compact representation of these important algebraic tools, and proceed with a comprehensive treatment of kinematics. This will be followed by a brief introduction to fluid and solid mechanics at the end of the course.

II. Course Aims and Outcomes: 

Aims

At the end of this class, you should be comfortable working with tensors and vectors to solve mechanics problems. The basics of fluid and solid mechanics will be covered, including the derivation of the equations for fluids and solids.

Specific Learning Outcomes:

By the end of this course, students will:

Perform elementary tensor and vector analysis, including the use of indicial notation to represent tensor and vector components concisely. Understand the material coordinate frame, the laboratory coordinate frame, and how to calculate velocities and accelerations in each frame of reference. Perform analysis of infinitesimal deformation. Calculate strains and strain rates. Determine the stress distribution along the faces of a body with a given internal state of stress. Write the stress in terms of strains for a linearly elastic solid. Solve simple problems in vibrations of elastic solids. Derive the Navier-Stokes equations from the stress components in a fluid. Solve simple viscous fluid flow problems.