BE Mechanical Engineering Semester 8 (BE Fourth Year)University of Mumbai
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# Finite Element Analysis Semester 8 (BE Fourth Year) BE Mechanical Engineering University of Mumbai Topics and Syllabus

SubjectFinite Element Analysis
CBCGS [2019 - current]
CBGS [2015 - 2018]
Old [2000 - 2014]

## Topics with syllabus and resources

100.00 Module 1
101.00 Introduction
• Introductory Concepts: Introduction to FEM, Historical Background, General FEM procedure. Applications of FEM in various fields. Advantages and disadvantages of FEM.
• Mathematical Modeling of field problems in Engineering, Governing Equations, Differential Equations in different fields.
• Approximate solution of differential equations-- Weighted residual techniques, Least squares, Galerkin methods, Boundary Value problems.
200.00 Module 2
201.00 Fea Procedure
• Discrete and continuous models, Weighted Residual Methods – Ritz Technique – Basic concepts of the Finite Element Method.
• Definitions of various terms used in FEM like element, order of the element, internal and external node/s, degree of freedom, primary and secondary variables, boundary conditions.
• Minimization of a functional. Principle of minimum total potential. Piecewise Rayleigh-Ritz method. Formulation of “stiffness matrix”; transformation and assembly concepts
300.00 Module 3
301.00 One-dimensional Problems
• One Dimensional Second Order Equations – Discretization – Element types- Linear and Higher order Elements – Derivation of Shape functions and Stiffness matrices and force vectors.
• Assembly of Matrices - solution of problems in one dimensional structural analysis, heat transfer and fluid flow (Stepped and Taper Bars, Fluid Network, Spring-Cart systems) 3.3 Analysis of Plane Trusses, Analysis of Beams.
• Solution of one Dimensional structural and thermal problems using FE Software, Selection of suitable Element Type, Modeling, Meshing, Boundary Condition, Convergence of solution, Result analysis, Case studies.
400.00 Module 4
401.00 Two Dimensional Finite Element Formulations
• Introduction, Three nodded triangular element, four nodded rectangular element, four nodded quadrilateral element, eight nodded quadrilateral element.
• Natural coordinates and coordinates transformations: serendipity and Lagranges methods for deriving shape functions for triangular and quadrilateral element
• Sub parametric, Isoperimetric, super parametric elements. Compatibility, Patch Test, Convergence criterion, Sources of errors.
500.00 Module 5
501.00 Two Dimensional Vector Variable Problems
• Equations of elasticity – Plane stress, plane strain and axisymmetric problems.
• Jacobian matrix, stress analysis of CST and four node Quadratic element
• Solution of 2-D Problems using FE Software (structural and Thermal), selection of element type, meshing and convergence of solution. (Can be covered during practical hours).
600.00 Module 6
601.00 Finite Element Formulation of Dynamics and Numerical Techniques
• Applications to free vibration problems of rod and beam. Lumped and consistent mass matrices.
• Solutions Techniques to Dynamic problems, longitudinal vibration frequencies and mode shapes. Fourth Order Beam Equation, Transverse deflections and Natural frequencies of beams.
• Finding frequencies of beam using FE Software (Can be covered during practical hours).
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