Course Details
Subject {L-T-P / C} : CE6001 : Applied Elasticity and Plasticity { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Shyamal Guchhait
Syllabus
Module I- Analysis of Stress: Introduction, Stress components at an arbitrary plane, Principal stresses, Stress invariants, Construction of Mohr’s circle, Differential equation of equilibrium, Plane stress problem, Boundary conditions
Module II- Analysis of Strain: Introduction, Principal strains, Strain deviator and its invariants, Plane strain problem, Compatibility conditions
Module III- Stress-strain relations: Introduction, Generalized Hooke’s law, Stress-strain relations for isotropic and orthotropic materials, Displacement equations of equilibrium
Module IV- Two Dimensional Problems in Elasticity: Stress function. Solution by polynomials, Saint-Venant’s Principle, Concentrated force acting on a beam, Effect of circular holes on stress distribution of a plate, Thick-walled cylinder subjected to internal and external pressure, Rotating disks of uniform thickness
Module V- Torsion: Introduction, Torsion of general prismatic bars, Torsion of circular and elliptical bars, Torsion of equilateral triangular bars, Membrane analogy, Torsion of a thin-walled tubes, Torsion of a thin-walled multiple-cell closed section, Torsion or rolled sections
Module VI- Introduction to Plasticity: Introduction, Nonlinear stress-strain behavior, Theories of failure, Criterion of yielding, Strain-hardening postulates, Rule of plastic flow.
Course Objectives
- To make students understand the concepts of stresses, strains and stress-strain relationships, basic theory of elasticity and plasticity and failure criteria.
- To expose students to two dimensional problems in Cartesian and polar coordinates .
- To make student familiar with problem formulations and solution techniques.
- To familiarize students with the principle of torsion of prismatic bars of non circular sections.
Course Outcomes
1. Students will be able to understand the concepts, theories about the stress and strain tensors for 2D and 3D elasticity problem. <br />2. Students will learn about the concept of different material constitutive relations for linear elastic system. <br />3. Students will be able to appreciate the broader 2D multidisciplinary context of the underlying theory of elasticity. <br />4. Students will be able to find out solutions for practical problems involving torsion in theory of elasticity. <br />5. Students will be able to learn applications of plasticity theorems to engineering design and analysis.
Essential Reading
- S P Timoshenko and J N Goodier, Theory of Elasticity, McGraw Hill,2006
- Mohammed Ameen, Computational Elasticity, Narosa Publishing House,2005
Supplementary Reading
- Chen and Han, Plasticity for Structural Engineers, Springer Verlag, 1998
- L S Srinath, Advanced Mechanics of Solids, Tata McGraw-Hill