# FINITE ELEMENT METHODS 5 students

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:
1. Stress Analysis of Plate With Cut-outs using ANSYS/ABAQUSSoftware
2. Modal Analysis Of Cantilever Beam using ANSYS/ABAQUSSoftware
3. Case Studiesetc.
###### Text /References:
1. Introduction to Finite Elements in Engineering, Tirupathi R.Chandrupatla and Ashok D. Belagundu, Pearson Education (Singapore) Pte Ltd,2006.
2. An Introduction to Finite Element Methods, J.N. Reddy, Tata Mc Graw Hill,2008.
3. A First Course in the Finite Element Method by Daryl L.Logan.
4. Concepts and Applications of Finite Element Analysis, Robert Cook, Wiley India, Pvt., Ltd., 4thEdition-2007.
5. An Introduction to Finite Element Methods, J.N. Reddy, Tata Mc Graw Hill,2008.
6. Finite Element  Procedures,  J.  Bathe,  PHI  Learning,2009.7.       The Finite Element Methods in Engineering / SS Rao /Pergamon.
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### Instructor Raheem khan Nizam Khan

Master in Agriculture sciences having India and abroad working experince in Horticulture industry.

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