The document discusses a lesson on finite element analysis for one-dimensional problems. The lesson will cover defining the stiffness matrix for a linear bar element, deriving the bar element equation, and assembling the global stiffness matrix. The objectives are to understand stiffness matrices, finite element formulations, the generic finite element procedure, and modeling finite elements to verify results.

1. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-1
EML 3004C
Formulate finite element equation for 1-Dbar element
Session objectives
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Dr.M.SUBRAMANIAN ME402 Finite Element Analysis
At the end of this session, the learner will be able to
• Understand the concept of stiffness matrix
• define FEA in engineering;
• explain various methods of FE formulations;
• explain the generic FE procedure;
• explain various finite elements for modeling;
• verify FEA results.
Teaching learning material
•Board/White Board and Markers
•Presentation/PPT 1/15

2. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-2
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
Derivation- Stiffness matrix
2/15

3. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-3
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
3/30
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
3/15

4. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-4
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
4/15

5. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-5
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
1-D bar element equation
5/15

6. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-6
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
6/15

7. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-7
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
7/15

8. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-8
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
8/15

9. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-9
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
9/15

10. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-10
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
Global Matrix
10/15

11. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-11
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
11/15

12. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-12
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
12/15

13. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-13
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
13/15

14. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-14
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Unit-II- ME402 Finite Element Analysis- One dimensional problems
Linear Bar element
Stiffness matrix of a 1-D bar element
14/15

15. Namas Chandra
Introduction to Mechanical engineering
Hibbeler
Chapter 6-15
EML 3004C
Dr.M.SUBRAMANIAN 16ME 102 /Engineering Mechanics
ME402 Finite Element Analysis
Thank You
15/15
Unit-II- ME402 Finite Element Analysis- One dimensional problems