8ME4.3-FINITE ELEMENT METHODS |
Units: I |
Introduction
Introduction to FEM and its applicability, Review of mathematics : Matrix algebra, Gauss
elimination method, Uniqueness of solution, Banded symmetric matrix and bandwidth.
Structure analysis : Two-force member element, Local stiffness matrix, coordinate
transformation, Assembly, Global stiffness matrix, imposition of Boundary conditions.
Properties of stiffness matrix.
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Units: II |
One-dimensional Finite Element Analysis
Basics of structural mechanics : stress and strain tensor, constitutive relation. Principle of
minimum Potential. General steps of FEM, Finite element model concept / Discretization,
Derivation of finite elements, equations using potential energy approach for linear and
quadratic 1-D bar element, shape functions and their properties, Assembly, Boundary
conditions, Computation of stress and strain. |
Units: III |
Two dimensional Finite Element Analysis :
Finite element formulation using three nodded triangular (CST) element and four nodded
rectangular element, Plane stress and Plain strain problems. Shape functions, node numbering
and connectivity, Assembly, Boundary conditions. Isoparametric formulation of 1-D bar
elements, Numerical integration using gauss quadrature formula, computation of stress and
strain.
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Units: IV |
Finite Element Formulation from Governiing Differential Equation :
Method of Weighted Residuals : Collocation, Subdomain method, Least Square method and
Galerkin’s method. Application to one dimensional problems, one-dimensional heat transfer,
etc. introduction to variational formulation (Ritz Method.)
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Units: V |
Higher order elements, Lagrange’s interpolation formula for one and two independent
variable.
Convergence of solution, compatibility, element continuity, static condensation, p and h
methods
of mesh refinement, Aspect ratio and element shape.
Application of FEM, Advantages of FEM. Introduction to concept of element mass matrix in
dynamic analysis.
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