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In this course you will learn :
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; Mohr’s 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, Castigliano’s 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
