Basic Background Requirement to FEM
Basic Background Requirement to FEM: – Matrix Algebra, Gauss Elimination Method, Numerical Integration – Gaussian Quadrature Rule. Conformal Mapping, Jacobian Matrix.
Static Analysis – Solid and Structural Mechanics
Static Analysis – Solid and Structural Mechanics: – Basic of Solid Mechanics: Approximation of Displacement Function, Strain-Displacement, Hook’s Law, Stress-Strain Relations, Strain Energy, Work Done, Total Potential. Principle of Minimum Potential Energy. Euler – Lagrange equation for bar, Euler – Lagrange equation for beam, Raleigh’s Ritz method, Simple Problems on Springs, Bars and Beams using Rayliegh’s Ritz’s method.
Introduction to FEM
Introduction to FEM: – Introduction, Infinite to Finite, Coordinate System – Global, Local and Natural Coordinates System, Coordinates Transformation. Shape functions describing the unknown variable, Pascal Triangle, Iso-parametric, Sub-parametric and Super-parametric formulation. Symmetric conditions – Planar, Axisymmetric, Cyclic and Repetitive Symmetry.
Types of Elements and their Properties
Types of Elements and their Properties: Different types of basic elements, Higher order elements, Simplex, Complex and Multiplex elements and special elements. Interpolation functions, Convergence Criteria, Patch test, Conform and Non-conform Elements. Co and C1 continuity elements.
Steps in Finite Element Method
Steps in Finite Element Method: Discretization, Approximation of the Basic unknown, Elemental Characteristic Equation, Assembly of the Overall Continuum, Solution of the Basic unknown, Computation of the other unknown. Treatment of Boundary Conditions: Elimination Approach, Penalty Approach and Multi Point Constraint Approach.
One Dimension Bar/Rod Element
One Dimension Bar/Rod Element: Finite Element Formulation of 1-D (Basic and Higher Order) bar Element, Problems on uniform, tapered and stepped bars subjected to different types of loading and boundary conditions including Thermal Load. Formulation of Plane and Space Truss Element, Problems on Plane and Space Trusses subjected to different types of loading and boundary conditions. Formulation of 1-D Torsion Element.
Finite Element Formulation of Beams and Frames
Finite Element Formulation of Beams and Frames: Basics of Beam Theory Hermite shape functions, Derivation of elemental stiffness matrix and load vectors for different types of Loading. Numerical problems on beams subjected to concentrated loads, linearly varying loads, uniformly distributed load and bending moments. Finite Element Formulation of plane and space Frame Structures. Numerical problems.
Finite Element Formulation of Two-Dimensional Problems
Finite Element Formulation of Two-Dimensional Problems: Introduction to Two Dimension Elasticity – Plane Stress and Plane Strain: Stress-Strain Relations. Constant Strain Triangular (CST) membrane element (TRIM3), Linear Strain Triangular (LST) membrane element (TRIM6). Four node quadrilateral membrane element (QUAM4), Eight node quadrilateral membrane element (QUAM8). Axisymmetric Elements- three node triangular axisymmetric element (TRIAX3), six node triangular axisymmetric element (TRIAX6), Four node quadrilateral axisymmetric element (QUAX4), Eight node quadrilateral axisymmetric element (QUAX4).
Finite Element Formulation of Three-Dimensional Solid and Structural Mechanics Problems
Finite Element Formulation of Three-Dimensional Solid Mechanics Problems: Three Dimension Elasticity: Hook’s Law, Stress – Strain Relationship. Solid Element – Four node Tetrahedron elements (TETRA4). Eight node Hexahedron Element (HEXA8). Twenty node Hexahedron Element (HEXA20).
Dynamic Analysis: – Finite Element Formulation for Dynamic Analysis – Extracting Eigen Value and Eigen Vectors. One Dimensional Finite Element Formulation for Longitudinal Vibration, Problems on Longitudinal Vibration. One Dimensional Finite Element Formulation for Lateral Vibration and Problems on Lateral Vibration. One Dimensional Finite Element Formulation for Torsional Vibration. Numerical Problems on Torsional Vibration.
Heat Transfer Analysis
Heat Transfer: Basic equations of heat transfer: Energy balance equation, Rate equation: conduction,convection, radiation, 1D finite element formulation using vibration method, Problems with temperature gradient and heat fluxes, heat transfer in composite sections, straight fins.
Fluid Flow Analysis
Fluid Flow: Flow through a porous medium, Flow through pipes of uniform and stepped sections, Flow through hydraulic networks.