Instructor: Anurag Gupta (ag@iitk.ac.in)
Office hours: Please email me to seek an appointment
Schedule: Tue (L9) 5-6pm; Wed (L9) 12-1pm; Fri (L8) 2-3pm
Teaching assistants: Saptarshi Paul (sapaul@iitk.ac.in); Akash Gupta (akashg21@iitk.ac.in)
Grading policy: Quizzes/Assignments (30%), Midterm (30%), Final (40%)
Attendance policy: No marks
Course objective: The purpose of the course is to expose the students to the fundamentals of elasticity. After attending this course, the students should be able to solve wide variety of boundary value problems in linear elasticity. The course will also prepare the students for advanced courses in solid mechanics.
Course Content: Review of strength of Materials and its limitations. Mathematical Preliminaries: Vector and tensors calculus; Indicial notation. The concept of strain: Finite deformation strain tensor; Linearized strain; Strain-Displacement relations; Physical interpretation of strain components; Principal Strains; Strain compatibility. The concept of stress: Cauchy’s principle and derivations of stress equilibrium equations; Stress components in 3D and their physical interpretations; Principal Stresses. Constitutive law for general linear elastic solid: Discussions on isotropic, orthotropic and transversely isotropic solid; thermoelasticity. Navier’s equations, stress and displacement based approaches. The isotropic linear elasticity boundary value problem; consequences of linearity (superposition, uniqueness, reciprocal relations). Plane Problems: plane stress, plane strain, anti-plane shear (also in axisymmetric coordinates). Solution methods for plane problems: Stress function approach/Series solutions. Circular hole in a shear/tensile field. Curved beam problems: End loadings; Inhomogeneous problem; Near Singular problem. Wedge problems: Power-law traction fields; Williams’ asymptotic method. Plane contact problems: The Flamant solution (distributed load over the half-plane); Frictionless contact problems (half punch, Hertz problem). Plane notch problems: Plane crack in a tensile field; Energy release rate. Planar problems in thermoelasticity: Steady state problems. Torsion of a prismatic bar: Prandtl’s stress function, Membrane analogy; Thin walled open sections; Rectangular bar; Multiply connected closed sections.
Notes, Assignments,...