Course Details
Subject {L-T-P / C} : CE6000 : Finite Element Method { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Shishir Kumar Sahu
Syllabus
• Basic Principles of Structural Mechanics: Equations of equilibrium, Strain displacement relations, Stress strain relations, Plane stress and Plane strain problems, Boundary Conditions.
• Basics of Finite Element Method: Different steps involved in finite element method (FEM), Different approaches of FEM, Direct method, Variational Principle and Weighted Residual method. Advantages and disadvantages of finite element method.
• Element Properties: Displacement models, Shape functions, Stiffness matrices, One dimensional bar element, two dimensional truss elements, three dimensional truss elements, two dimensional beam elements, three dimensional beam elements, analysis of framed structures using truss and beam elements with Numerical examples. Development of FEM programming for analysis of structures in MATLAB environment.
• Lagrangian interpolation, Pascal’s triangle, Convergence criteria.
• Plane Stress and Plane Strain Problems: Analysis of plates using triangular CST elements, Rectangular elements.
• Analysis of structures using axy-symmetric elements.
• Natural coordinate systems, Isoparametric Elements: four node, eight node elements, Numerical integration, Gauss quadrature, one, two and three point quadrature rules, order of integration.
• Bending of plates by rectangular elements, triangular elements and quadrilateral elements, Concept of 3D modeling.
• Hamiltons Principle, Lagrange’s equation for dynamic problems. Vibration and buckling analysis of structures using Finite element method.
Course Objectives
- Students are exposed to computationally efficient numerical method for analysis of a variety of structures
Course Outcomes
1. Students will be able to understand the application of the Finite Element method for analysis of complex engineering problems <br />2. Students will be able to develop and understand finite element based programs for computational analysis of variety of structures in MATLAB environment. <br />3. Students will be exposed to basic research on numerical analysis of static and dynamic analysis of variety of structures.
Essential Reading
- R. D. Cook, D S Malkus and M E Plesha, Concepts and Applications of Finite Element Analysis, John Wiley& Sons, New York , .
- C. S. Krishnamoorthy, Finite Element analysis-Theory and Programming, Tata McGraw Hill , .
Supplementary Reading
- O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, McGraw Hill Publishing Company , .
- J. N. Reddy, An introduction to Finite Element Method, Tata-Mc Graw Hill, New Delhi , .
Journal and Conferences
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