 FAQ 003158 EN-US

06/13/2019

# Is it sufficient to perform the calculation with surface elements or is it better to use the solids elements?

When components are calculated with the Finite Element Method (FEM), you can choose between surfaces and solids in RFEM. The big advantage of surfaces is the calculation time, because the FE elements are only defined in the surface plane. The third dimension, that is the thickness, is considered as a physical property in the calculation. Thus, a surface can be considered as a mathematical simplification. In addition, surfaces can be meshed more easily than solids (Jacobi Matrix).

Plate elements are divided into two types of elements. Whereas in the classical thin plate theory (Kirchhoff) shear deformations due to shear forces are neglected, special extended approaches have to be assumed for the thick plate theory (Reissner-Mindlin). For thin plates, the pure bending reaction is dominant. Therefore, the simplified bending theory is also sufficient. As the thickness increases, the proportion of the transversal shear influence on the load bearing capacity increases. Starting at a certain thickness, the error due to neglecting this component is so large that it is absolutely necessary to have the higher theory of the thick plate. Considering a slab as being "thin" or "thick" does not depend on the ratio "dimension to thickness" of the single finite element, but on the conditions in the structural system. Influencing factors include, in addition to the plate thickness, especially the span lengths (length, width, radius), the type of support and the load type as well as their distribution. Due to the multitude of influences, it is not possible to specify a mandatory value.

Figure 01 shows a guideline describing the validity of the corresponding elements. The size "d" is the thickness of the structural component and "L" the length of the structural component or the distance between the supports. The ratio d/L gives an indication of when an element is valid for an analysis. If d/L is large, the shear deformation is a critical parameter and the user should prefer to use solids. If d/L is small, the shear deformation has no decisive influence and surface elements are the most effective choice.

Figure 02 performed calculations with the different elements. A top view is shown so that the deformations can be interpreted on the image plane. For a small d/L ratio of 0.2, the deformations very well match for all three variants. If d/L = 0.4, differences between the thin and thick plate calculations are already noticeable. In the extreme case d/L = 0.7, a difference of the thick plate to the solid is additionally observed. The loads have been selected in such a way that the same deformation is achieved for all solid elements to produce a meaningful printout. 