AU3011 Computational Theory on Solid Mechanics Syllabus:
AU3011 Computational Theory on Solid Mechanics Syllabus – Anna University Regulation 2021
OBJECTIVES
The objective of this course is to make the students understand the principles of mechanics of rigid and deformable bodies in Engineering to learn nonlinear problems in solid mechanics and finite element method.
UNIT I STIFFNESS METHOD
Types of skeletal structures, internal forces and deformations. Introduction and applications of stiffness member approach to analyze beams, Trusses, plane frames and grids.
UNIT II STIFFNESS METHOD (SPECIAL TOPICS)
Various secondary effects like deformation of support, prestrain & temperature. Symmetry/Antisymmetry, Oblique, supports Elastic supports, Axial- flexural interaction. Analysis of Composite structures having combination of different type of members.
UNIT III NONLINEAR PROBLEMS IN SOLID MECHANICS
Material and geometric nonlinearities, Solution techniques for nonlinear equations: NewtonRaphson method.
UNIT IV FINITE ELEMENT METHOD
Theory of Stresses: State of stress and strain at a point in two and three dimensions, stress and strain invariants, Hook’s law, Plane stress and plain strain problems. Equations of equilibrium, boundary conditions, compatibility conditions. Introduction and Application of FEM to One dimensional (bar & beam) problems & two dimensional problems using Constant strain triangles.
UNIT V ENERGY METHODS
Principle of Stationary Potential Energy, Castigliano’s Theorem of Deflection, Castigliano’s Theorem on Deflection for Linear Load-Deflection, Strain Energy for Axial Loading, Strain Energies for Beams, Strain Energy for Torsion, Fictitious Load Method, Statistically Indeterminate Structures.
TOTAL : 45 PERIODS
COURSE OUTCOMES:
At the end of the course, the student will be able to
1. Apply equilibrium and compatibility equations to determine response of statically determinate and indeterminate structures.
2. Determine placements and internal forces of statically indeterminate structures by matrix methods.
3. Understand the concept of energy methods for solving problems.
4. Identify solution techniques for non linear equations
5. Apply the theory of stress in 2 and 3 dimensions
TEXT BOOKS:
1. Bhavikatti; Finite Element Analysis, New Age International Publishers
2. Gere & Weaver; Matrix Analysis of framed structures, CBS Publications
REFERENCES:
1. Desai & Abel; Finite Element Method, Tata Mcgraw hill
2. Meghre & Deshmukh; Matrix Analysis of Structures, Charotar Publication
3. A First Course in the Finite Element Method – D. L. Logan
4. Elements of Matrix and Stability Analysis of Structures by Manicka Selvam
5. Advanced Mechanics of Solids by L.S Srinath, Mcgraw Hill.
6. Mechanics of Materials by Beer & Johnston, Mcgraw Hill.