ME 321: Advanced Mechanics of Solids


Instructor: Anurag Gupta (ag@)

Schedule: MWF 8-9 am, L11


Teaching assistants: Ayan Roychowdhury (ayanrc@), Rajeev Kumar (rajek@), Bitanu Roy (bitanuro@)

Schedule for discussion session: F 6-7 pm, L11


Grading policy: Quizzes (6-8): 35%, Midterm: 25%, Final: 40%


Texts


[1]  Applied Mechanics of Solids by Allan Bower. The complete book is available at http://solidmechanics.org

                   

[2]  Mathematical Preliminaries: Lecture Notes on the Mechanics of Elastic Solids (Vol. 1), by R. Abeyaratne. This book is available online at http://web.mit.edu/abeyaratne/ElasticSolids-Vol.1-Math.pdf.


[3]  Structures or Why Things Don’t Fall Down, by J. E. Gordon: This immensely entertaining book can be read like a novel without bothering about the dry technicalities of the subject. It successfully attempts at bringing both curiosity and personal experience to our interesting subject.


[4]  Historical perspectives:

      History of Strength of Materials, by S. Timoshenko

      Rheology: An Historical Perspective, by R. I. Tanner and K. Walters   

      Essays in the History of Mechanics, by C. A. Truesdell 


Linear theory of elasticity:

[5]  The Linearized Theory of Elasticity, by W. S. Slaughter

[6]  Theory of Elasticity, by A. I. Lurie

[7]  Theory of Elasticity, by L. D. Landau and E. M. Lifshitz

[8] Elasticity, J. R. Barber







 

Course Outline:


Introduction and overview

Mathematical preliminaries (vector/tensor algebra and calculus, integral theorems)

The concept of strain (deformation gradient, compatibility)

The concept of stress (balance of linear momentum, Cauchy’s theorem, Noll’s theorem)

Constitutive relations: restrictions due to physical and material symmetry

Linear elasticity (governing equations)

   2D problems (stress function, axisymmetric problems, the wedge problem)

   Torsion (Saint- Venant problem)

Thermo-elasticity (internal stresses, simple problems)

Rod theory (basic theory, stability)



 

Course notes/handouts (updated with the progress of the course):


Introduction and Vector/Tensor algebra

              Ref: First three chapters of [2], where you will find several solved examples.

              [Deborah Number]

              [Handout from Ayan’s discussion]

           

Vector/Tensor algebra and calculus

              Ref: Ch. 5-6 from [2].

              [Some theorems related to tensors]

              [Derivatives]


Tensor calculus and integral theorems

               [Integral theorems]

               [Quiz 1 Solution]

               [Quiz 1 (make-up) Solution]


Deformation gradient and strain

              [Handout from Ayan’s discussion]


Small strain and strain compatibility

              [Problem Set]

              [Quiz 2 Solution]

              [Compatibility equations]


Balance laws and the concept of stress

              [Stress] 

              [Handout from Ayan’s Discussion]

              [Practice problem set]

              [Mid-term exam from last year]


Linear isotropic elasticity: Superposition, Uniqueness, reciprocal theorem, axisymmetric problems

              [Mid-term exam]


Anti-plane strain, plane strain, plane stress, stress function

              [Practice problem set]


The wedge problem

              [Quiz 3 Solution]


The torsion problem

              [Practice problem set]


Thermoelasticity (2D problems)

              [Notes from Barber [8] with problems]

              More problems, especially the axisymmetric ones, can be found in Bower [1], Ch. 4

              [Quiz 4 solution]


Rod theory

           [Quiz 5 solution]

           [Quiz 6 solution]