Finite Element Analysis

             Finite Element Analysis

Course objective: To learn and apply finite element solutions to a structural, thermal, dynamic problem to develop the knowledge and skills needed to effectively evaluate finite element analyses.

Text books

1. Reddy. J.N.,“An Introduction to the Finite Element Method”,4th Edition,TataMcGraw-

Hill,2020

2. Seshu, P,“Text Book of Finite Element Analysis”, Prentice – Hall of India Pvt. Ltd., New

Delhi, 2013.

                            Reference books

1. Bhatti Asghar M, "Fundamental Finite Element Analysis and Applications”, John Wiley &

Sons,2005 (IndianReprint2013)

2. Chandrupatla&Belagundu, “Introduction to Finite Elements in Engineering” ,3rd Edition,

Prentice Hall College Div, 1990 Logan, D.L., “A first course in Finite Element Method”,

Thomson Asia Pvt. Ltd., 2002

3. Rao, S. S., “The Finite Element Method in Engineering”,3rd Edition, Butter worth

Heinemann, 2004

4. Robert D. Cook, David S. Malkus, Michae l E. Plesha, Robert J. Witt, “Concepts and

Applications of Finite Element

Unit - 1

1. What is Finite Element Analysis?

2. Problem-solving methods in Finite Element Method

3. Partial Differential Equation inFEA

4. Discretization in FEA

5. Mathematical modeling in FEA

6. The key idea and basic steps in Finite Element Formulation

7. Governing Equation in FEA

8. How does the Finite element methodology works?

9. Discrete and continuous model in FEM

10. Initial value problem in FEA

11. Boundary value problem in FEA

12. Eigenvalue problem in FEA

13. weighted Residual Methods

14. Piecewise continuous trial function solution of the weak form

15. Potential Energy Approach in Finite Element Analysis

16. Potential Energy Approach with Direct Approach in Finite Element Method

17. Weighted Residual method with homogeneous boundary condition and trial function

18. Weighted residual method for two unknown parameters with known trial function

19. Trial functions in weighted residual method of FEA

20. Rayleigh Ritz method to solve the Beam problem

21. Conditions for Potential Energy equation Determination

UNIT - II

1. One dimensional problem - Temperature Effects

2. Simple Displacement problem

3. Truss formulae

4, Truss problem

Unit - 5
15. Iso-parametric Formulation - FEA

Assignment

1. Assignment Problem 1

Boundary Value Problem Assignment Submission Link

2. Assignment Problem 2

Eigen value Problem Assignment Submission Link

3. Assignment 3 - Weighted Residual Method

weighted residual method part 1 submission link

4. Assignment 4 Beam problem submission link

5. Assignment 5 Rayleigh Ritz method - bar problem

Assignment 5 BAR problem submission Link

6. Assignment 6 - Spring Problem

Assignment 6 Spring problem submission link

7. Assignment 7 Two dimensional Problem

For the constant triangular element shown in fig. Assemble strain displacement matrix. Take t = 20mm, and E= 2 X 10^5 N/mm^2

8. Assignment 8 plane stress problem

For the plane stress element shown in fig the nodal displacements are u₁ = 2.0mm, u₂ = 0.5mm_, u₃= 3.0mm_, v₁= 1.0mm, v₂= 0.0mm, v₃= 1.0mm

Determine the element stresses 1.  σ_{x ,} σ_y,  τ_xy, σ_1, σ₂ and the principal angle θ_p,  let E=210 Gpa, v= 0.25, and t = 10 mm, all coordinates are in mm.

9. Assignmen`t 9 element stress problem

calculate the element stresses σ_{x ,} σ_y,  τ_xy, σ_{1, and} σ₂and the principal angle θ_p 

_{for the element shown in fig} 

Assessment

  Unit -1 - Finite Element Analysis Introduction MCQ 1

FEA Introduction Assessment MCQ

Unit -2 -SECOND Assessment 

One Dimensional problem MCQ

Unit -3 Third Assessment submission link

Unit -4 Axisymmetric assessment submission link

Unit -3 & 4 Two dimensional MCQ

 FEA Case studies