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

When designing structural components using Finite Element Method (FEM), you can choose between surfaces and solids in RFEM. A great advantage of the surfaces is the calculation time as the finite 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 mathematical simplification. Furthermore, surfaces can be meshed more easily than solids (Jacobi matrix).

The 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 methods apply for the thick plate theory (Reissner-Mindlin). In the case of the thin plates, the pure bending effect is dominant. Therefore, the simplified bending theory is also sufficient. As the thickness increases, the component of the transversal shear effect on the load bearing capacity increases. Starting at certain thickness, the error when neglecting this component is so large, that it is absolutely necessary to have a higher theory of the thick plate. Whether a plate is considered as "thin" or "thick" does not depend on the "dimension to thickness" ratio of the individual finite element, but on the conditions in the structural system. The influencing factors include, in addition to the plate thickness, especially span lengths (length, width, radius), a support type, and a 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 "d" value is the thickness of the structural component and "L" is the length of the structural component or the distance between the supports. The d/L ratio indicates when the element is valid for an analysis. If d/L is large, the shear deformation is the governing value and you should prefer to use solids. If d/L is small, the shear deformation has no governing effect and the surface elements are the most effecient choice.

In Figure 02, the calculations were performed using different elements. A top view is displayed so that the deformations can be interpreted in the image plane. For the small d/L ratio of 0.2, the deformations correspond to all three variants very well. If d/L = 0.4, the differences between the thin and the thick plate calculations are already visible. In the extreme case of d/L = 0.7, the difference of the thick plate to the solid can be observed additionally. The loads have been selected in such a way that the same deformation is obtained for all solid elements in order to create a comprehensive expression.