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SLS 02: Simply supported square plate under uniform load

Description

Material Modulus of elasticity E = 210 000 N/mm^2
Poisson’s ratio \nu= 0,3
Geometry Cross-section Thickness e=10 mm
Boundary conditions Along all edges Simply supported
Loads On the entire surface p=0.7799kN/m^2
Mesh Maximum element size 0.10m
Minimum element size 0.00m

Results

Handcalculation

    \[D=\frac{E \cdot e^3}{12(1-\upsilon ^2)}=\frac{210 000N/mm^2 \cdot (0,01m)^3}{12(1-0,3^2)}=19,231kNm\]

From Timoshenko: \alpha=0,00406

    \[\delta_y=\frac{\alpha \cdot p \cdot z^{4}}{64 \cdot D}=\frac{0,00406 \cdot 0.7799kN/m^2 \cdot (1m)^{4}}{64 \cdot 19,231kNm} = 0,165mm\]

Deformation \delta_y in Diamonds

Point Which result Independent reference Diamonds Difference
A Deformation \delta_y 0,165mm 0,163mm -1,00%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 02: plaque carrée simplement supportée.
  • Timoshenko, S., & Woinowsky-Krieger, S. (1959, p. 177 equ. 141 and Table 8). Theory of plates and shells. McGraw-Hill Publishing Company.

  • Tested in Diamonds 2023r01.

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