Numbering Code	U-ENG25 35051 LJ71	Year/Term	2022 ・ First semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Mon.1
Instructor name	BIWA SHIROU (Graduate School of Engineering Professor)
Outline and Purpose of the Course	While the methods of stress-strain analysis for elementary structural members are the main topics in the "Mechanics of Materials" courses, more general physical laws of the mechanical behavior of solids are dealt with in this course. Namely, fundamental principles of solid mechanics such as three-dimensional expressions of stress and strain, equilibrium equations, constitutive equations (Hooke's law) are treated together with mathematical analysis of static deformations in elastic bodies. These subjects are important for the understanding of basic principles of large-scale computational analysis of various mechanical/structural systems.
Course Goals	This course aims to establish the understanding of rigorous expressions of stress and strain and fundamentals of deformation analysis of solids and structures. It is also the aim of this course to re-examine the values of approximate theories given in the "Mechanics of Materials" courses from a rigorous viewpoint.
Schedule and Contents	The following topics are discussed in the lectures, but subject to possible change according to each year's situations. Week 1 [Preliminaries] Basis vecotrs; Kronecker's delta; Alternating symbol; Summation convention Weeks 2-3 [Deformation and strain] Description of motion; Material time derivative; Green-Lagrange strain; Infinitesimal strain; Transformation of strain components; Principal strains Weeks 4-6 [Stress and laws of motion] Stress vector, Euler's laws of motion; Cauchy's law; Transformation of stress components; Cauchy's laws of motion; Equilibrium equations; Principal stresses and stress invariants Week 7-8 [Stress-strain relations] Hooke's law; Elastic moduli; Voigt expression Weeks 9-10 [Fundamental equations of elasticity] Navier's equations; Plane stress and plane strain; Compatibility relation for strain Weeks 11-13 [Two-dimensional problems of elastic deformations] Airy's stress function; Biharmonic equation; Stress function in polar coordinates; Stress concentration around a circular hole; Stress function for torsion; Torsion of bars of elliptic cross-sections Weeks 14 [Principle of virtual work] Virtual displacement; Principle of virtual work; Principle of stationary potential energy Week 15 [Final examination/learning achievement evaluation] Week 16 [Feedback]
Evaluation Methods and Policy	Grading is made based on the examination (85%) and the reports (15%). The total score of the examination and the reports is evaluated between 0 and 100 points (the pass mark is 60). Occasional changes of grading criteria will be announced in the class.
Course Requirements	The enrolling students are expected to have knowledge in the Mechanics of Materials courses. Good understanding of calculus, linear algebra (eigenvalue problems) and vector analysis is also necessary.
Study outside of Class (preparation and review)	Contents of "Mechanics of Materials" courses should be fully reviewed. Homeworks (reports) will be assigned to review the lectures.
Textbooks	Textbooks/References	Textbooks are not assigned. The lecture is given in the blackboard style.
References, etc.	T. Inoue, "Fundamentals of elasticity" (Nikkan Kogyo) S. Kobayashi and K. Kondo, "Elasticity" (Baihu-kan) For references written in English, students are advised to contact the instructor directly.
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