This course focuses on the mechanics of solids. Topics include mathematical preliminaries – summation convention, Krönecker delta, alternating symbol, vectors and Cartesian tensors; stresses, traction vector, equations of equilibrium, strains, compatibility conditions, material symmetry and Hooke’s law, solution schemes in elasticity, elastostatic plane problems.
The fundamentals of solid mechanics is important and is essential for the study of engineering.
Students learn the basics of mechanics of materials and will be able to solve some problems in engineering.
By completing this course, students will be able to:
1) Understand index notation used in equations in any subject area.
2) Understand stresses and strains.
3) Understand linear elasticity.
4) Understand how to formulate and solve some fundamental problems in mechanics of solids.
Vectors and Cartesian tensors, stresses, traction vector, equations of equilibrium, strains, compatibility conditions, material symmetry and Hooke’s law, solution schemes in elasticity, elastostatic plane problems
✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Most of time in the class is devoted to fundamentals and the rest to advanced contents or applications. To allow students to get a good understanding of the course contents and practical applications, problems related to the contents of this course are given as homework assignments. Solutions to homework assignments are reviewed in the class.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of the course. Index notation. Vectors. | Review section 0.1-0.2, 1.1-1.2 of class notes. |
Class 2 | Cartesian tensors. Eigenvalues and eigenvectors, vector and tensor calculus | Review sections 1.3-1.5 of class notes. |
Class 3 | Cartesian tensors. Eigenvalues and eigenvectors, vector and tensor calculus | Review sections 1.3-1.5 of class notes. |
Class 4 | Force distribution and stresses. Equations of equilibrium. | Review section 2.1-2.5 of class notes. |
Class 5 | principal stresses. Stationary shear stresses, commonly used definitions of stresses, and strains. Rigid-body displacements. | Review sections 2.6-2.10 of class notes. |
Class 6 | compatibility conditions and cylindrical coordinates | Review sections 2.11-2.14of class notes |
Class 7 | compatibility conditions and cylindrical coordinates | Review sections 2.11-2.14 of class notes. |
Class 8 | Midterm Exam | |
Class 9 | Linear Elasticity. Isotropic elastic materials. | Review sections 3.1-3.4 of class notes. |
Class 10 | Linear Elasticity. Isotropic elastic materials. | Review sections 3.1-3.4of class notes. |
Class 11 | Linear Elasticity. Isotropic elastic materials. | Review sections 3.1-3.4 of class notes. |
Class 12 | Classification of two-dimensional elasticity problems. Isotropic elastic plane problems in cylindrical coordinates. | Review sections 4.0-4.3 of class notes. |
Class 13 | Examples of infinite plane problems | Review sections 4.4 of class notes. |
Class 14 | Final Exam |
Bower, A. F., 2010, Applied Mechanics of Solids, CRC Press.
Class notes are available in the Instructor’s HP.
Barber, J. R., 2002, Elasticity, 2nd edition, Kluwer, Dordrecht.
Students' knowledge of linear elasticity and their ability to apply them to problems will be assessed.
Midterm exam 30%, Final exam 50%, exercise problems 20%.
In 2020, Midterm exam and Final Exam will be take-home exams (24 hrs) - Submit answers by e-mail.
None
Class notes are available in the Instructor’s HP.
http://www.cv.titech.ac.jp/~anil-lab/