hw2 benchmark z beam
DESCRIPTION
Plate element benchmark comparisonTRANSCRIPT
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 1 Portland State University
Plate element benchmark comparison
Problem Statement:
A cantilever beam of z-cross section with an end couple force of 0.6 MN is applied as shown in the figure.1 is a benchmark to test plate element type. The benchmark value by NAFEMS1 standard bench test reports the compressive axial stress at the plate mid-surface to be -108 MPa at point P shown in the figure.
Figure.1 Ref: 1 National Agency for Finite Element Methods and Standards, Rev. 3, 1990 http://www.nafems.org
Objective: The standard reported value is used to perform a convergence study of all the plate
elements available, namely linear and parabolic order triangle and quadrilateral elements.
Relevant data: Material properties: E = 210 GPa, = 0.3. Physical Properties: Mindlin plate element with thickness of 0.1m.
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 2 Portland State University
Loading: A torque load of 1.2 MN-m is equivalent to a couple force of 0.6 MN applied at each edge as a shear load is shown as the figure 2.
Constraints: One end of the beam is clamped so as to simulate a cantilever beam condition.
Figure 2
Check Points and Tips in this problem:
Check that you apply a shear force of 0.6 MPa in opposite directions at two edges of the Z cross-section.
Check that you have changed the thickness from the default value. Always start with a course mesh, if possible. Investigate whether the drilling degree of freedom has an effect Check that you are looking for axial (Z) stress results. Check that you are reading results at mid-layer of the plate element. Check that there are two stress values reported at point P while you query
the two adjacent elements related to the node at P. Average those two values manually before keying into convergence plot.
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 3 Portland State University
Convergence Study
Linear Quadrilateral Element
No. of Elements
Compressive Axial Stress at P, MPa
51 113 80 111.5
280 111 312 111 660 110.5
The linear quadrilateral elements have converged at a mesh density of 280 elements.
Convergence study for linear quad elements
110.5
111
111.5
112
112.5
113
113.5
0 50 100 150 200 250 300 350
No of elements
Axia
l stre
ss a
t P (c
omp)
MP
a
Linear Quad
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 4 Portland State University
Parabolic Quadrilateral Element
No. of Elements
Compressive Axial Stress at P, MPa
9 106.96 12 108.74 15 108.34 18 109.3 21 109.45 24 109.61 32 109.54
The parabolic quadrilateral elements reach convergence at a mesh density of 24 elements!
Convergence for Parabolic Quad
9
12
15
1821
24 32
106.5
107
107.5
108
108.5
109
109.5
110
0 5 10 15 20 25 30 35
No of elements
Com
p A
xial
Stre
ss a
t P, M
Pa
Parabolic Quad
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 5 Portland State University
Linear Triangle Element
No. of Elements
Compressive Axial Stress at P, MPa
30 39.4 182 78.26 320 79.83 596 95.61 1062 99.05 1346 100
Linear triangle element has converged with a higher mesh density of 1062 elements.
Parabolic Triangle Element
Convergence Study for linear Triangle
0
20
40
60
80
100
120
0 500 1000 1500
No of Elements
Com
pres
sive
axia
l str
ess
at P
, M
Pa
Linear Triangle
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 6 Portland State University
No. of Elements
Compressive Axial Stress at P, MPa
54 11882 117.7
182 112.6320 111.09596 111.05
1346 110.9
The convergence of parabolic triangle elements has improved compared to linear triangle elements. They converge at mesh distribution of 320 elements.
Convergence study for Parabolic Triangle
110
111
112
113
114
115
116
117
118
119
0 200 400 600 800 1000 1200 1400 1600
No of Elements
Com
pres
sive
axi
al s
tress
at P
, MPa
Parabolic Triangle
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ME 565 Advanced Finite Element Analysis Assignment #2 (plate benchmark)
2008 Hormoz Zareh 7 Portland State University
Conclusion: Use of parabolic quadrilateral elements saves computation time and will result in accurate results compared to other elements.
Comparison
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20
40
60
80
100
120
140
0 200 400 600 800 1000 1200 1400 1600
No of elements
Axi
al S
tress
at P
(com
p),M
Pa
Linear Triangle Parabolic Triangle Linear Quad Parabolic Quad
108 MPa Theoretical Value