Calculate the peak UZ displacement and bending stress (SY or SX) at the
center of a simply supported square plate of side 10 m and thickness 0.05 m subjected to a
periodic pressure load defined with respect to time.
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File Name
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Open drive
letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS
version\samples\Simulation
Examples\Verification\NAFEMS_R0016_Test13P.SLDPRT.
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Study Type
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Three shell studies are created:
| Study Name |
Study Type |
| Modal_Damping |
Linear Dynamics - Transient (modal
damping) |
| Rayleigh_Damping |
Linear Dynamics - Transient (Rayleigh
damping) |
| Frequency |
Frequency |
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Mesh Type
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Shell mesh for all three studies. Shell thickness = 0.05 m - Thin
shell formulation. Element size is 60 cm.
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Material Properties
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Linear elastic isotropic. Modulus of elasticity (E) = 2 x
1011 N/m2, Mass density (ρ) = 8000 Kg/m3, Poisson's
ratio (ν) = 0.3.
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Load
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Steady state periodic load F = F0 (sin (ωt) - sin (3 ωt))
over the whole plate where: (a) F0 = 100 N/m2, (b) ω = 2 π f, (c)
f = 1.2 Hz, and duration of loading = 15 sec. Horizontal axis is time (sec) and vertical
axis is pressure (N/m2).
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Dynamic Options
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- Number of mode shapes =
16
- Solution time = 9.0
sec
- Time step = 0.002
sec
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Damping
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-
Modal_damping: 2% of critical damping for all 16 modes
-
Rayleigh_damping: Mass coefficient a0 = 0.299, Stiffness
coefficient a1 = 1.339 x 10 -3
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Results
The steady-state UZ displacement and bending stress
response graphs at the center of the plate are in agreement with the analytical results. The
graph depicts the UZ displacement time history at the center of the plate. Horizontal axis
is time (sec) and vertical axis is UZ (mm).
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Reference |
SOLIDWORKS Simulation with Modal _Damping |
SOLIDWORKS Simulation with Rayleigh_Damping |
| Peak UZ displacement at center |
2.863 mm |
2.99 mm |
2.99 mm |
| Peak SY bending stress at center |
2.018 N/mm2 |
1.95 N/mm2 |
1.95 N/mm2
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Reference
NAFEMS, Publication R0016, The International Association for the Engineering
Analysis Community, "Selected Benchmarks for Forced Vibration," Test 13P, 1989.