Determine deflections at the center of a rectangular plate

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Reference no: EM133931810

PART A

Question 1: Determine the stiffness matrix K for the frame shown below. Assume "1" and "3" are pinned. Take E=200 GPa E=200GPa, I=280×10⁶ mm⁴ I=280×10⁶ mm⁴, A=12×10³ mm² A=12×10³mm² for each member.

PART B

Determine the support reactions at pins "1" and "3". Take E=200 GPaE=200GPa, I=280×10⁶ mm⁴ I=280×10⁶mm⁴, A=12×10³mm2A=12×10³mm² for each member.

PART C

Compare the hand calculations with the SpaceGass/ABAQUS software and comment on the comparison between them. You need to include software analysis results. Get expert online assignment help in the USA.

PART D

Compare the hand calculations with the Matlab calculations and comment on the comparison between them. You need to include screenshots of Matlab input and output files in your assignment.

Question 2:

Determine the deflections at the center of a rectangular plate (with dimensions a=700 mm×b=1400 mma=700mm×b=1400mm) under a uniformly distributed load (UDL) of q=1.0 N/mm2q=1.0N/mm2 for various boundary conditions, as illustrated in the figure below. Use E=200 GPaE=200GPa and v=0.3v=0.3. Obtain the deformation shape indicating the predicted deflection at the center of the plate for different boundary conditions. Compare the predicted deflections obtained from ABAQUS with the analytical results provided in Table 2 for the three cases outlined in Table 1:

(a) Thick plates with thickness h=140.0 mmh=140.0mm
(b) Moderate plates with thickness h=28.0 mmh=28.0mm
(c) Thin plates with thickness h=0.70 mmh=0.70mm

Table 1: Write the deflection in empty cell for different boundary conditions.
Plate Thickness (h) Boundary conditions
SSCC
Thick plate 140.0 mm
Moderate plate 28.0 mm
Thin plate 0.70 mm

Boundary Condition Keys:

SSCC: Edges 1 and 2 are simply supported (S), Edges 3 and 4 are clamped (C)

SSSC: Edges 1, 2, and 3 are simply supported, Edge 4 is clamped

SSSS: All four edges are simply supported

SSFC: Edges 1 and 2 are simply supported, Edge 3 is free (F) and Edge 4 is clamped

SSFS: Edges 1, 2, and 4 simply supported, Edge 3 is free

SSFF: Edges 1 and 2 are simply supported, Edges 3 and 4 are free

Table 2: Analytical results for nondimensional deflection w¯w¯ of the plate under UDL.
Plate Thickness (h) SSCC SSSC SSSS SSFC SSFS SSFF
Thick plate 140.0 mm 0.974 1.056 1.142 1.196 1.289 1.431
Moderate plate 28.0 mm 0.849 0.932 1.018 1.066 1.155 1.294
Thin plate 0.70 mm 0.844 0.927 1.029 1.065 1.149 1.288
w=100Dqa4w(a/2,b/2)with D=Eh312(1-v2)
w=qa4100Dw(a/2,b/2)with D=12(1-v2)Eh3

Reference no: EM133931810

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