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.||Review section 1.1 of class notes.|
|Class 2||Vectors||Review sections 1.2.1-1.2.3 of class notes.|
|Class 3||Change of basis||Review sections 1.2.4-1.2.5 of class notes.|
|Class 4||Cartesian tensors||Review section 1.3 of class notes.|
|Class 5||Eigenvalues and eigenvectors, vector and tensor calculus||Review sections 1.4-1.5 of class notes.|
|Class 6||Force distribution and stresses||Review sections 2.1-2.3 of class notes|
|Class 7||Equations of equilibrium and principal stresses||Review sections 2.4-2.6 of class notes.|
|Class 8||Stationary shear stresses, commonly used definitions of stresses, and strains||Review sections 2.7-2.9 of class notes.|
|Class 9||Rigid-body displacements, compatibility conditions and cylindrical coordinates||Review sections 2.10-2.12 of class notes.|
|Class 10||Linear Elasticity||Review sections 3.1-3.2 of class notes.|
|Class 11||Isotropic elastic materials||Review sections 3.3-3.4 of class notes.|
|Class 12||Classification of two-dimensional elasticity problems||Review sections 4.0-4.2 of class notes.|
|Class 13||Isotropic elastic plane problems in cylindrical coordinates||Review sections 4.3 of class notes.|
|Class 14||Examples of infinite plane problems||Review sections 4.4.1-4.4.2 of class notes|
|Class 15||Examples of infinite plane problems - Infinite plane subjected to a uniform body force in a circular region.||Review sections 4.4.3-4.4.4 of class notes.|
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%.