Differentiate Partial Differential Equation, Elliptic, Hyperbolic & Parabolic Pde

Differentiate Partial Differential Equation, Elliptic, Hyperbolic & Parabolic Pde

FILENAME:SMEC413.docx

SCHOOL OF ENGINEERING &TECHNOLOGY / MECHANICAL & AUTOMOBILE ENGINEERING DEPARTMENT / VIITERM / FOURTH YEAR
1 / Course number / MEC413
2 / Course Title / FINITE ELEMENT METHODS (DE 2-ME&AE)
3 / Credits / 4
4 / Contact Hours (L-T-P) / 4-0-0
5 / Course Objective / The aim of the course is to provide the participants an overview on Finite Element Method, Material models, and Applications in Mechanical Engineering.
6 / Course Outcomes / On successful completion of this module students will be able to
  1. Differentiate partial differential equation, elliptic, Hyperbolic & parabolic pde.
  2. ImplementRitz and Rayleigh Ritz methods, Method of weighed residuals approximate method. Introduction to FEM using one-dimensional problems
  3. Implement Finite Difference Method for the Solution of elliptic, Hyperbolic & parabolic partial differential equation.
  4. Understand Point collocation, Sub domain collocation, Least squares, Galerkin method.
  5. Understand variational calculus,
  6. Demonstrate Geometric & natural boundary conditions, Basic Concept of Finite Element Method.
  7. Compare approximate solution with Analytical results.
  8. Explain Solution of static problems and case studies in stress analysis of Mechanical component.
  9. ExplainIso-parametric Elements and Analysis using Iso-parametric Elements.
  10. Demonstrate Automatic meshing techniques.
  11. To ImplementFEA using 2D and 3D elements and Semi-discrete approach for unsteady problems

7 / Outline syllabus
7.01 / MEC413.A / Unit A / Approximate Solution Methods
7.02 / MEC413.A1 / Unit A Topic 1 / Ritz and Rayleigh Ritz methods
7.03 / MEC413.A2 / Unit A Topic 2 / Method of weighed residuals, General concept
7.04 / MEC413.A3 / Unit A Topic 3 / Point collocation, Subdomain collocation
7.05 / MEC413.A4 / Unit A Topic 4 / Least squares, Galerkin method
7.06 / MEC413.B / Unit B / Finite Difference Method
7.07 / MEC413.B1 / Unit B Topic 1 / Characteristics and classification of PDE
7.08 / MEC413.B2 / Unit B Topic 2 / Solution of elliptic, Hyperbolic & parabolic PDE using Finite Difference Method.
MEC413.B3 / Unit B Topic 3 / Introduction to FEM using one-dimensional problems
7.09 / MEC413.C / Unit C / Introduction to Finite Element Method
7.10 / MEC413.C1 / Unit C Topic 1 / Introduction to variational calculus
7.11 / MEC413.C2 / Unit C Topic 2 / The differential of a function; Euler-Lagrange equation, Geometric & natural boundary conditions
7.12 / MEC413.C3 / Unit C Topic 3 / Basic Concept of Finite Element Method, Principle of potential energy
7.13 / MEC413.C4 / Unit C Topic 4 / Derivation of Stiffness and Mass matrices for a bar, A beam and A shaft, Comparison with Analytical results.
7.14 / MEC413.C5 / Unit C Topic 5 / Interpolation and Shape functions; Solution of static problems and case studies in stress analysis of Mechanical component
7.15 / MEC413.D / Unit D / Isoparametric Elements
7.16 / MEC413.D1 / Unit D Topic 1 / Analysis using Isoparametric Elements. Element types.
7.17 / MEC413.D2 / Unit D Topic 2 / numerical integration, error analysis. FEA using 2D and 3D elements
7.18 / MEC413.D3 / Unit D Topic 3 / Plain strain and plain stress problems, FE using plate shell elements.
7.19 / MEC413.E / Unit E / Importance of Finite Element Mesh
7.20 / MEC413.E1 / Unit E Topic1 / Automatic meshing techniques
7.21 / MEC413.E2 / Unit E Topic2 / Case studies using FEM for design of simple element geometries such as a tapered bar
7.22 / MEC413.E3 / Unit E Topic3 / A plate with a hole. Semi-discrete approach for unsteady problems
8
8.1 / Course work: 30%
8.11 / Attendance / None
8.12 / Homework / Three best out of 4 assignments: 20 marks
8.13 / Quizzes / Two 30-minutes surprise quizzes: 10 marks
8.14 / Projects / None
8.15 / Presentations / None
8.16 / Any other / None
8.2 / MTE / One, 20 %
8.3 / End-term examination: 50%
9
9.1 / Text book /
  1. Reddy, J. N., An Introduction to the Finite Element Method, McGraw Hill (2001).

9.2 / Other references /
  1. Bathe, K. J., Finite Element Procedures, Prentice Hall of India (1996).
  2. Zienkiewicz, O. C., The Finite Element Method, McGraw Hill (2002)
  3. Rao, S.S., The Finite Element Method in Engineering, Elsevier, 4th edition. 2005.
  4. Software - Ansys 14.0 .

Mapping of Outcomes vs. Topics

Outcome no. →
Syllabus topic↓ / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11
MEC413.A / X / X / X / X
MEC413.A1 / X
MEC413.A2 / X
MEC413.A3 / X / X
MEC413.A4 / X
MEC413.B
MEC413.B1 / X
MEC413.B2 / X
MEC413.B3 / X / X
MEC413.C / X / X / X / X
MEC413.C1 / X
MEC413.C2 / X
MEC413.C3 / X
MEC413.C4 / X
MEC413.C5 / X
MEC413.D / X / X / X
MEC413.D1 / X
MEC413.D2 / X
MEC413.D3 / X
MEC413.E
MEC413.E1 / X
MEC413.E2 / X / X
MEC413.E3 / X
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