06ME63-Modelling And Finite Element Analysis |
PART – A |
UNIT I: |
INTRODUCTION: Equilibrium equations in elasticity subjected to body
force, traction forces, stress strain relations for plane stress and plane strain,
Boundary conditions, Initial conditions, Euler’s Lagrange’s equations of bar,
beams, Principal of a minimum potential energy, principle of virtual work,
Rayleigh-Ritz method, Galerkins method., Guass elimination Numerical
integration.
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UNIT II: |
BASIC PROCEDURE: General description of Finite Element Method,
Engineering applications of finite element method, Discretization process;
types of elements 1D, 2D and 3D elements, size of the elements, location of
nodes, node numbering scheme, half Bandwidth, Stiffness matrix of bar
element by direct method, Properties of stiffness matrix, Preprocessing, post
processing.
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UNIT III: |
INTERPOLATION MODELS: Polynomial form of interpolation
functions- linear, quadratic and cubic, Simplex, Complex, Multiplex
elements, Selection of the order of the interpolation polynomial,
Convergence requirements, 2D Pascal triangle, Linear interpolation
polynomials in terms of global coordinates of bar, triangular (2D simplex)
elements, Linear interpolation polynomials in terms of local coordinates of
bar, triangular (2D simplex) elements, CST element.
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UNIT IV: |
HIGHER ORDER AND ISOPARAMETRIC ELEMENTS: Lagrangian
interpolation, Higher order one dimensional elements- quadratic, Cubic
element and their shape functions, properties of shape functions, Truss
element, Shape functions of 2D quadratic triangular element in natural
coordinates, 2D quadrilateral element shape functions – linear, quadratic,
Biquadric rectangular element (Noded quadrilateral element), Shape function
of beam element. Hermite shape function of beam element.
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PART – B |
UNIT V: |
DERIVATION OF ELEMENT STIFFNESS MATRICES AND LOADVECTORS: Direct method for bar element under axial loading, trusses,
beam element with concentrated and distributed loads, matrices, Jacobian,
Jacobian of 2D triangular element, quadrilateral, Consistent load vector,
Numerical integration.
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UNIT VI: |
HEAT TRANSFER PROBLEMS: Steady state heat transfer, 1D heat
conduction governing equation, boundary conditions, One dimensional
element, Functional approach for heat conduction, Galerkin approach for heat
conduction, heat flux boundary condition, 1D heat transfer in thin fins.
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UNIT VII: |
APPLICATIONS I: Solution of bars, stepped bars, plane trusses by direct
stiffness method. Solution for displacements, reactions and stresses by using
elimination approach, penalty approach.
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UNIT VIII: |
APPLICATIONS II: Solution of beam problems, heat transfer 1D problems
with conduction and convection.
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REFERENCE |
TEXT BOOKS: |
1. Finite Elements in engineering, Chandrupatla T.R., 3rd Pearson
Edition.
2. The Finite Element Method in Engineering, S.S. Rao, 4th Edition,
Elsevier, 2006.
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Reference Books |
1. The FEM its basics and fundamentals: O.C.Zienkiewicz,
Elsevier, 6e.
2. Finite Element Method, J.N.Reddy, McGraw –Hill International
Edition.
3. Finite Element Methods, by Daryl. L. Logon, Thomson Learning
3rd edition, 2001.
4. Finite Element Analysis, C.S.Krishnamurthy,–Tata McGraw Hill
Publishing Co. Ltd, New Delhi, 1995.
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