1st order linear - Simply supported orthotropic square slab
Problem definition
Calculate the mid-span deflection of a 10m by 10m simply supported slab of 25mm thickness with 10N/m2 UDL applied to it. The material properties the slab were assumed to be as follow: Ex = 33.5 MPa, Ey = 33500 MPa, Gxy = 523 MPa, 𝜈x = 0.4000, and 𝜈y = 0.0004.
FEM model
A regular triangular finite element mesh is used with a mesh size of 0.25m.
Analytical solution
The deflection was calculated using the solution obtained by Timoshenko and Woinowsky-Kreiger. The solution uses Navier’s method, which employs the double trigonometric series equation:
where:
w - deflection,
a = b - side lengths
Results
Value | Analytical solution (mm) | Solver result (mm) | % Error |
---|---|---|---|
Mid-span deflection | 29.799 | 29.795 | 0.01 |
Conclusion
A satisfactory convergence of the analytical and solver’s results was observed.
References
Timoshenko, S. and Woinowsky-Krieger, S. 1987. Theory of Plates and Shells. 2nd Edition. McGraw-Hill Book Company, Inc. New York, NY, USA.