# Solid Mechanics

IIT Delhi, , Prof. Prof. Ajeet Kumar

Updated On 02 Feb, 19

IIT Delhi, , Prof. Prof. Ajeet Kumar

Updated On 02 Feb, 19

This is the first course where deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study extension, torsion and bending of beams. The one-dimensional theory of beams are also introduced. We also discuss various theories of failure which are critical for design of machine elements in industry.

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4.1 ( 11 )

Week 1: Mathematical preliminaries and notation; Kinematics of deformation: rigid vs deforming solids; Lagrangian and Eulerian descriptions; Concept of Traction vector

Week 2: Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor

Week 3: State of stress in simple cases ; Principal stress components and principal planes; Maximizing shear component of traction at a point; Mohrs circle

Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor; ongitudinal, shear and volumetric strains

Week 5: State of strain in simple cases; Strain compatibility condition; Local infinitesimal rotation; Linear stress-strain relation:isotropic and orthotropic cases; Relation between material constants

Week 6: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system, Axisymmetric deformations: combined extension-torsion of a cylinder

Week 7: Belt friction, Review of particle dynamics, Circular motion

Week 8: Bending of beams having non-symmetrical cross-section; Shear center, Shear flow in thin and open cross-section beams

Week 9: Deflection of a beam: Euler Bernouli and Timoshenko beam models; Buckling of beams

Week 10: Reciprocal relations, Castiglianos theorem, Deflection of straight and curved beams using energy method

Week 11: Various theories of failure and their application

Week 12: Brief introduction to plasticity, Yield surface

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.