2020 Introduction to Solid Mechanics

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Academic unit or major
Graduate major in Civil Engineering
Instructor(s)
Wijeyewickrema Anil 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Tue5-6(M113)  Fri5-6(M113)  
Group
-
Course number
CVE.A401
Credits
2
Academic year
2020
Offered quarter
1Q
Syllabus updated
2020/5/4
Lecture notes updated
-
Language used
English
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Course description and aims

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.

Student learning outcomes

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.

Keywords

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

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

  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

Textbook(s)

Bower, A. F., 2010, Applied Mechanics of Solids, CRC Press.

Reference books, course materials, etc.

Class notes are available in the Instructor’s HP.
Barber, J. R., 2002, Elasticity, 2nd edition, Kluwer, Dordrecht.

Assessment criteria and methods

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.

Related courses

  • CVE.A402 : Advanced Course on Elasticity Theory

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None

Other

Class notes are available in the Instructor’s HP.
http://www.cv.titech.ac.jp/~anil-lab/

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