1st order linear - Simply supported square slab

Problem definition

Calculate the mid span deflection of an 8x8 simply supported slab of 0.1 thickness under self-weight only. Take material properties E=2x10¹¹, G=7.7x10¹⁰ and ρ=7849.

Assumptions

A regular triangular finite element mesh is used with sufficient subdivision. Flexural and shear deformation is included, and the material is assumed to be isotropic.

Key results

The mid-span deformation is calculated using Navier's Method.

Result	Theoretical value	Comparison 1	Solver value	% error
Mid-span deflection	7.002x10^-3	6.990x10^-3	7.031x10^-3	0.43%
Mid-span Moment	23616	23708	23649	0.14%

Conclusion

An acceptable match is observed between the theoretical values and the solver results. An acceptable match is also observed between the solver results and those obtained independently.