Murat Vural
Assistant Professor of Mechanical & Aerospace Engineering
MMAE 530 Advanced Mechanics of Solids
Fall 2011, 5:00-6:15pm TR, PH-108
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Instructor: |
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Teaching Assistant: |
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Murat Vural Office: E1-253D (312)567-3181, vural@iit.edu Office Hours: TR 2:00-3:30 |
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Ludwig Chaudesaygues Office: TBA |
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WEEK |
TOPICS |
NOTES |
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1-2 |
Mathematical Foundations: Tensor calculus, direct/indicial/matrix notations, divergence theorem, matrices, basis transformation, eigenvalues and eigenvectors, characteristic invariants. |
Formula Sheet |
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3-6 |
Kinematics (strain): Analysis and physical understanding of deformation gradient, rotation, finite and infinitesimal strain tensors, homogeneous and inhomogeneous deformations, polar decomposition theorem, generalized "Set-Hill" form of strain with stretch tensor, examples of deformation, calculation of normal and shear strains in arbitrary directions, derivation of relations for maximum normal and shear strains, volumetric and deviatoric strains, strain compatibility. |
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| 7-8 |
Force and Equilibrium (stress): Concepts of traction and stress, Cauchy relation, equilibrium equations (linear and angular momentum), body and inertial forces, properties of stress tensor, principal stresses. |
HW#5 |
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Midterm Exam (10/13/11, Thursday) |
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| 8-9 |
Constitutive Laws: Elastic potentials, stress-strain relations, elastic moduli and stiffness tensors and their properties, linear elastic solids (orthotropic, transversely isotropic and isotropic), thermoelasticity. |
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| 10-11 |
Boundary Value Problems (BVPs): Type of BVPs (traction, displacement, mixed), general solution to BVP, issues of existence and uniqueness, superposition, examples of BVPs (tension, uniaxial strain, torsion, flexure). |
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| 12-14 |
Problems in Linear Elasticity: Plane stress and plane strain, Airy stress function, axisymmetric problems (thick walled cylinder, rotating disk). |
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| 15-16 |
Variational Methods: Fundamentals of variational calculus, principle of virtual work, theorem of minimum potential energy, reciprocal theorem of Betti and Rayleigh, Rayleigh-Ritz method. |
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Final Exam (TBA) |
Recommended Reference Books:
Mechanics/Strength of Materials (Basics)
1. E.P. Popov, Engineering Mechanics of Solids, Prentice Hall, (1990)
2. A.-R. Ragab and S.E. Bayoumi, Engineering Solid Mechanics: Fundamentals and Applications, CRC Press, (1998)
3. S.P. Timoshenko and J.M. Gere, Mechanics of Materials, Van Nostrand, (1972)
4. R. Parnes, Solid Mechanics in Engineering, Wiley, (2001)
5. A.P. Boresi and R.J. Schmidt, Advanced Mechanics of Materials, Wiley, (2002)
Continuum Mechanics
1. S. Nair, Introduction to Continuum Mechanics, Cambridge University Press, (2009)
2. P.C. Chou and N.J. Pagano, Elasticity: Tensors, Dyadic, and Engineering Approaches, Van Nostrand, (1967)
3. Y.C. Fung, Introduction to Continuum Mechanics, Prentice Hall, (1977)
4. A.J.M. Spencer, Continuum Mechanics Longman, (1980)
Elasticity
1. Y.C. Fung, Foundations of Solid Mechanics, Prentice Hall, (1965)
2. J. Lemaitre and J.-L Chaboche, Mechanics of Solid Materials, Cambridge, (1990)
3. I.S. Sokolnikoff, Mathematical Theory of Elasticity, McGraw-Hill, (1956)
4. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, (1951)
Homework: All homework must be completed in a neat an organized manner. Due dates for homework problems will be announced in class. No credit will be given for late homework.
Collaboration Policy: I encourage collaboration on homework assignments: you can learn a lot from working with a group. This means that you are permitted to discuss homework problems with classmates, and are permitted to seek help from other students if you run into difficulties. However, material submitted for grading should represent the work of its author. Any work done in collaboration should be clearly marked as such. Needless to say, it is not acceptable to copy the work of other students, and it is not acceptable for two students to submit identical copies of any part of an assignment (see IIT Code of Academic Honesty for further clarification, http://www.iit.edu/~osa/Handbook/FinePrint.html).
Exams: There will be one midterm exam and a final exam. All exams will be in-class, closed book, and closed class notes, but formulas will be supplied as required.
Grading Policy: Homework 20%, Midterm Exam 35%, Final Exam 45%.
Grade Change Request: If you find that your grades have been added incorrectly, or you would like a grade on your homework or examination reconsidered, you should
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Prepare a written statement explaining why you think your grade is incorrect;
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Leave your written request, together with the homework/exam in question in my office at E1-253D or mailbox at E1-247.
Grade change requests received later than one week after the graded assignment was returned to you will not be considered.
Attendance: Attendance in my sections of MMAE 530 is rigidly enforced. I will hand out a sheet with each student's name on it. You are required to put your initials in the box corresponding to your name, otherwise you will be marked as absent. The part of my evaluation of your grade will be based upon your attendance record. Therefore, it is imperative that you come to class. If for some reason you cannot attend class, please e-mail me the day before and explain why.
last modified: 25-Aug-2011