fea cantilever beam

8/13/2019 FEA Cantilever beam

1/8


2/8

PROGRAM FLOWCHART

User Input Data:

Mechanical

Properties,

Dimensions and

Force

Value assigning:

Formation of Global

Stiffness Matrix,

Displacement Matrix and

Force Matrix

Gaussian Elimination

Back Substitution

Print output:

Displacement

Reaction Force

Stress on bar

Start Program

End Program


3/8

SAMPLE OF PROGRAM INPUT

SAMPLE OF PROGRAM OUTPUT


4/8

SAMPLE OF PROGRAM OUTPUT

Displaying Global Stiffness Matrix


5/8

VALIDATION: HAND CALCULATION AND PROGRAMMING

u1=0

EA= EB= EC = ED= 200GPa

AA = 500 mm2 AB = 800 mm

2 AC = 1000 mm2 AD = 1000 mm

2

LA= LB= LC = LD= 0.5m

F1=R1 FA = FB = FC = 0 FD = 1000kN

Global Stiffness Matrix =

[

]

=

[

] X 106

OverallEquation

----- Equation (i)


6/8

Since u1=0 and F1=R1 is unknown, we can form a 4x4 matrix by neglecting the first row and

first column in Equation (i) for further calculation.

[

] [

]

Gaussian Elimination

Back Substitution

Next: Row2 = Row2 - Row1 (

)

Next: Row3 = Row3Row2 ( )

Next: Row3 = Row4

Row3 (

)

Lower triangle is formed.


7/8

From Equation (i):

Reaction force acts onto wallStress at each bar is given by

Output Parameter Manual Programming (Matlab)

u2 (m) u3 (m) u4 (m) u5 (m) R1 (kN) -1000 -1000

(GPa) 2 2(GPa) 1.25 1.25(GPa) 1 1(GPa) 1 1The results from manual calculation and programming are identical. The program is suitable

to perform finite element analysis for the above case.


8/8

REFERENCE

The Mathworks Inc. (2013). Mathworks Documentation. Retrieved from

http://www.mathworks.com/help on 14th October 2013.

Assoc. Prof. Dr.Rizal Zahari (n.d.). Lecture on EAS 4401 Finite Element Analysis. Personal

Collection of Assoc. Prof. Dr. Rizal Zahari, Universiti Putra Malaysia, Serdang,

Selangor.
http://www.mathworks.com/helphttp://www.mathworks.com/help

fea cantilever beam

Documents