P7

Learning with PurposeLearning with Purpose

Mesh Density and Configuration Project

FEA Analysis I22.513

Fucheng Chen Tushar Dange

V. Bhargav HuanRan Liu

Learning with Purpose

A) Deformed beam with bending stress contour of 8-noded brick element

1 element through the thickness



2 elements through the thickness


B) Deformed beam with bending stress contour of 20-noded brick element



C) Deformed beam with bending stress contour of 4-noded brick element



D) 25 cubic beam element model

Two other beam similar models were created with 12 and 50 cubic element to investigate the effect of number of element along beam length on deflection and max bending stress in the beam


D) Comparison among 12, 25, and 50 cubic element model

Number of Elements

Deflection at the center of beam (in)

Maximum Bending stress at center of beam (psi)

Maximum Bending stress at the wall (psi)

12 -0.0410 -4687.5 -8984.38

25 -0.0410 -4687.5 -9187.50

50 -0.0410 -4687.5 -9281.25

• The deflection and bending stress at the center of 25 cubic element beam was calculated by taking the average of the deflection at node 13 and 14.

• The deflection and bending stress at the center of 50 cubic element beam was taken at node 26.

• The deflection and bending stress at the center of 12 cubic element beam was taken at node7.

• From the table shown above, it is found that the number of beam elements does not impact the deflection or max bending stress at the center of beam.

• However, the maximum bending stress at the wall increases as the increase of number of elements.


E) Comparison of deflection at center of the beam among different model

Tabular Representation

Deflection (in) at the center of Beam (x=25)Number of Elements 8-noded bricks 20-noded bricks 4-noded tets 2-noded beams

1 -0.0489 -0.0401 -0.0068 -0.0410

2 -0.0397 -0.0406 -0.0232 N/A

8 -0.0407 -0.0408 -0.0392 N/A


E) Comparison of deflection at center of the beam among different model

Graphical Representation

0 1 2 3 4 5 6 7 8 9-0.0600

-0.0500

-0.0400

-0.0300

-0.0200

-0.0100

0.0000

Comparison of deflection at the center of the beam among different models and the-oretical calculation

8-noded bricks20-noded bricks4-noded tets2-noded beamsTheoretical

Number of Elements through the thickness

Defle

ction

at t

he C

ente

r of t

he B

eam

(in)


Maximum Bending Stress (psi) at the center of beam (x=25)Number of Elements 8-noded bricks 20-noded bricks 4-noded tets 2-noded beams

1 2309.36 4687.59 1650.1 4687.5

2 3657.02 4687.49 3380.7 N/A

8 4451.53 4687.48 4122.43 N/A

F) Comparison of maximum bending stress at center of the beam among different models



F) Comparison of maximum bending stress at center of the beam among different models


0 1 2 3 4 5 6 7 8 90

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Comparison of maximum bending stress at the center of the beam among different models and theoretical calculation



Max

imum

Ben

ding

Str

ess a

t the

Cen

ter o

f Bea

m (p

si)


Maximum Bending Stress (psi) at the wall (x=0)Number of Elements 8-noded bricks 20-noded bricks 4-noded tets 2-noded beams

1 3870.3 8987.56 2780.54 9187.5

2 7423.11 9392.15 6262.97 N/A

8 9135.72 9368.27 8463.69 N/A

G) Comparison of maximum bending stress at the wall among different models



G) Comparison of maximum bending stress at the wall among different models


0 1 2 3 4 5 6 7 8 90

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Comparison of maximum bending stress at the wall among different models and the-oretical calculation



Max

imum

Ben

ding

Str

ess a

th th

e W

all (

psi)


H) 8-layer 8-noded brick model with poisson ratio ν=0


• When the Poisson’s ratio of 8-layer 8-noded brick model changed to 0, the bending stress at the wall decreased to 8910.04 psi. The reason is that the beam will shrink when Poisson’s ratio is not 0, and the stress at the wall will increase due to the Encastre constraint at the wall location.

• All models showed that the results gets closer to the theoretical values as the number of element through the thickness increases.

• Comparing with the results from models with different element type, it is found that the 20-noded brick element models have the most accurate results.

• Besides, the 20-noded brick element model shows the accuracy of results even with small amount of elements, which indicates that the 20-noded brick element is the most efficient and accurate method when modeling cantilever beam with rectangular cross-section with a tip load applied.

• The 2-noded beams model showed consistency and accuracy of bending stress at the center of beam despite the number of element used. However, the accuracy of bending stress at the wall depends on the number of element.

I) Disscussion


• For 8-noded bricks and 4-noded tets, the tables and figures in part EFG shows that it is necessary to use more than one element through the thickness, since there is a huge difference between the results from model with one element through the thickness and theoretical values.

• For 20-noded bricks, it is reasonable to use one element through the thickness only if the bending stress at the center of the beam is desired. However, more than one element through the thickness is required, when bending stress at wall or deflection is desired.

J) Is there any reason to use more than one element through the thickness to model this beam


•

K) Theoretical Calculations


1. “Mesh Density and Configuration Project.” INTRO TO FINITE ELEMENT ANALYSIS. Department of Mechanical Engineering, UMass Lowell, n.d. Web. <http://m-5.eng.uml.edu/22.513/>.

2. “Axial, Bending, Torsion, Combined and Bucking Analysis of a Beam Tutorial ABAQUS.” INTRO TO FINITE ELEMENT ANALYSIS. Department of Mechanical Engineering, UMass Lowell, n.d. Web. <http://m-5.eng.uml.edu/22.513/>.

3. “Finite Element Analysis of A Propped Cantilever Beam.” INTRO TO FINITE ELEMENT ANALYSIS. Department of Mechanical Engineering, UMass Lowell, n.d. Web. <http://m-5.eng.uml.edu/22.513/>.

L) References

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