Unit I: Prerequisites to FEM-Application of FEM, Strain- displacement relations, Stress- strain relations, Differential equations of equilibrium, Co-ordinates, basic element shapes, interpolation function, Minimum potential energy. Properties of stiffness matrix, treatment of boundary conditions, solution of system of equations, shape functions and characteristics.
Unit II: 1-D structural problems-Analysis of axial Bar element – stiffness matrix, load vector, temperature effects, Quadratic shape function. Analysis of Trusses- Plane Truss elements, Transformation matrix, stiffness matrix, load vector Analysis of Beams – Hermite shape functions – beam stiffness matrix – Load vector – Problems
Unit III: 2-D stress analysis using CST-Plane stress, Plane strain, Force terms, Stiffness matrix and load vector, boundary conditions. Axi-symmetric body subjected to axisymmetric loading-Numerical problems, Isoparametric element – quadrilateral element, linear shape functions.
Unit IV: Scalar field problems-1-D Heat conduction through composite walls, fins of uniform cross section,
2-D heat conduction problems, Torsional problems.
Unit V: Dynamic considerations-Dynamic equations – consistent mass matrix – Eigen values, Eigen vector, natural frequencies – mode shapes – modal analysis.3-D problems- Tetrahedron element – Jacobian matrix – Stiffness matrix, CAD softwares and its applications, Brief description to analysis of Plates & Shells.
Practice:
- Stress Analysis of Plate With Cut-outs using ANSYS/ABAQUSSoftware
- Modal Analysis Of Cantilever Beam using ANSYS/ABAQUSSoftware
- Case Studiesetc.
Text /References:
- Introduction to Finite Elements in Engineering, Tirupathi R.Chandrupatla and Ashok D. Belagundu, Pearson Education (Singapore) Pte Ltd,2006.
- An Introduction to Finite Element Methods, J.N. Reddy, Tata Mc Graw Hill,2008.
- A First Course in the Finite Element Method by Daryl L.Logan.
- Concepts and Applications of Finite Element Analysis, Robert Cook, Wiley India, Pvt., Ltd., 4thEdition-2007.
- An Introduction to Finite Element Methods, J.N. Reddy, Tata Mc Graw Hill,2008.
- Finite Element Procedures, J. Bathe, PHI Learning,2009.7. The Finite Element Methods in Engineering / SS Rao /Pergamon.
