26. Summary of results#

The results obtained show that:

  • modeling DSQ provides a more accurate estimate of stresses and shear forces (< 5%) than modeling DKQ (= 20%). The estimation of the moments is equivalent for both models,

  • With an equivalent mesh, modeling DSQ obtains more accurate results than Q4G modeling (comparison of B and O models). The 2 models converge on the same results (comparison of J and P models). This is explained by the order of approximation of the rotations which is quadratic for DSQ and bilinear for Q4G,

  • the estimation of constraints is more accurate with modeling DKT (< 2%) compared to modeling DST (< 3.5%). On the other hand, the shear force is better estimated by DST (< 10% for DST and < 20% for DKT),

  • for COQUE_3D triangle or quadrangle configurations, the estimate of the transverse shear stress is constant in the thickness of the plate, in accordance with the modeling assumptions,

  • the results expressed in the user coordinate system for configurations DST and COQUE_3D are identical to those expressed in the global coordinate system,

  • the refinement of the mesh for configuration DSQ improves the estimation of stresses, shear forces and moments; the trend is reversed with respect to displacement,

  • the multilayer configuration makes it possible to visualize the distribution of plane and transverse shear stresses in the thickness of the plate, and to confirm the theory, namely a linear distribution for plane stresses and parabolic for shear stresses; on the other hand, the rotation of the coordinate system does not affect the stress values,

  • in general, at nodes where analytically zero stresses or efforts are expected, the numerical results obtained are not correct because the estimates are made mesh by mesh and then extrapolated to the nodes. Even the values averaged at the nodes in question are not necessarily zero.