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Finite Element Methods

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Type: NoteInstitute: SAVITRIBAI PHULE PUNE UNIVERSITY Offline Downloads: 46Views: 776Uploaded: 3 months agoAdd to Favourite

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ME1401 – INTRODUCTION OF FINITE ELEMENT ANALYSIS CONTENTS UNIT – I Fundamental Concepts Syllabus General Methods of the Finite Element Analysis General Steps of the Finite Element Analysis Boundary Conditions Consideration during Discretization process Rayleigh – Ritz Method (Variational Approach) Problems (I set) Weighted Residual method Problems (II set) Matrix Algebra Matrix Operation Gaussian Elimination Method Problems (III set) Advantages of Finite Element Method Disadvantages of Finite Element Method Applications of Finite Element Analysis UNIT – II One Dimension Problems Syllabus One Dimensional elements Bar, Beam and Truss Stress, Strain and Displacement Types of Loading Finite Element Modeling Co – Ordinates
Natural Co – Ordinate (ε) Shape function Polynomial Shape function Stiffness Matrix [K] Properties of Stiffness Matrix Equation of Stiffness Matrix for One dimensional bar element Finite Element Equation for One dimensional bar element The Load (or) Force Vector {F} Problem (I set) Trusses Stiffness Matrix [K] for a truss element Finite Element Equation for Two noded Truss element Problem (II set) The Galerkin Approach Types of beam Types of Transverse Load Problem (III set) UNIT – III Two Dimension Problems – Scalar variable Problems Syllabus Two dimensional elements Plane Stress and Plane Strain Finite Element Modeling Constant Strain Triangular (CST) Element Shape function for the CST element Displacement function for the CST element Strain – Displacement matrix [B] for CST element Stress – Strain relationship matrix (or) Constitutive matrix [D] for two dimensional element Stress – Strain relationship matrix for two dimensional plane stress problems
Stress – Strain relationship matrix for two dimensional plane strain problems Stiffness matrix equation for two dimensional element (CST element) Temperature Effects Galerkin Approach Linear Strain Triangular (LST) element Problem (I set) Scalar variable problems Equation of Temperature function (T) for one dimensional heat conduction Equation of Shape functions (N1 & N2) for one dimensional heat conduction Equation of Stiffness Matrix (K) for one dimensional heat conduction Finite Element Equations for one dimensional heat conduction Finite element Equation for Torsional Bar element Problem (II set) UNIT – IV AXISYMMETRIC CONTINUUM Syllabus Elasticity Equations Axisymmetric Elements Axisymmetric Formulation Equation of shape function for Axisymmetric element Equation of Strain – Displacement Matrix [B] for Axisymmetric element Equation of Stress – Strain Matrix [D] for Axisymmetric element Equation of Stiffness Matrix [K] for Axisymmetric element Temperature Effects Problem (I set)
UNIT – V ISOPARAMETRIC ELEMENTS FOR TWO DIMENSIONAL CONTINUUM Syllabus Isoparametric element Superparametric element Subparametric element Equation of Shape function for 4 noded rectangular parent element Equation of Stiffness Matrix for 4 noded isoparametric quadrilateral element Equation of element force vector Numerical Integration (Gaussian Quadrature) Problem (I set)

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