## 5 Final Discussion and Conclusions  
The robustness of FEM software relies on the fact that a very coarse mesh cannot lead to irrational results. Programs should also include additional options to enhance the obtained solution, such as smoothing the distribution of a given variable during post-processing. There are many ways to verify engineering software, including single-element or patch tests, spectral analysis, or various benchmarks. The paper compares three benchmarks and FEM results obtained for them using two engineering software programs: the Robot Structural Analysis Professional 2023 package [9] (Robot) and the Midas nGen 2023 v.1.3 system [10] (Midas). Both packages are equipped with finite elements, which can ensure objective results. In the case of in-plane bending problems, it is possible to avoid so-called shear-locking. The presence of discrete Kirchhoff-Mindlin elements [13; 14] for plates helps one to prevent so-called transverse shear locking when out-of-plane bending is studied. In the first test, a so-called deep cantilever beam under in-plane bending is considered. The analytical solution is presented. Various types of structures available in the software interfaces are analyzed, which actually influences the selection of FEs for the computations. Different types of membrane elements are provided in both programs. The numerical solu \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Connection** & \(z\)** & **Mesh** & \(M_{y}\) & \(F_{x}\) & \(M_{y}+F_{x}z\) & \(I_{\text{max}}^{\text{a}}\) & \(M_{y}^{\Sigma}\) & \(w_{0}\) \\
**Type** & **[cm]** & & **[kNm]** & **[kN]** & **[kNm]** & **[kNm]** & **[kNm]** & **[kNm]** \\ \hline
1 & 0 & Finer & 2.375 & 0.0 & 2.375 & 2.126 & 4.501 & 0.1707 \\ II-o & 12.5 & Finer & 1.565 & 12.473 & 3.124 & 1.380 & 4.504 & 0.1094 \\ II-m & 12.5 & Finer & 3.190 & 0.0 & 3.190 & 1.310 & 4.500 & 0.1050 \\ III-o & 27.5 & Finer & 0.696 & 11.642 & 3.898 & 0.603 & 4.501 & 0.0477 \\ III-m & 27.5 & Finer & 3.971 & 0.0 & 3.971 & 0.529 & 4.500 & 0.0424 \\ I & 0 & Coarser & 2.415 & 0.0 & 2.415 & 2.084 & 4.499 & 0.1710 \\ II-o & 12.5 & Coarser & 1.586 & 12.430 & 3.140 & 1.364 & 4.504 & 0.1108 \\ II-m & 12.5 & Coarser & 3.217 & 0.0 & 3.217 & 1.283 & 4.500 & 0.1001 \\ III-o & 27.5 & Coarser & 0.714 & 11.502 & 3.877 & 0.636 & 4.513 & 0.0493 \\ III-m & 27.5 & Coarser & 3.982 & 0.0 & 3.982 & 0.518 & 4.500 & 0.0404 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of results from Robot. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Connection** & \(z\)** & **Mesh** & \(M_{y}\) & \(F_{x}\) & \(M_{y}+F_{x}z\) & \(I_{\text{max}}^{\text{a}}\) & \(M_{y}^{\Sigma}\) & \(w_{0}\) \\
**Type** & **[cm]** & & **[kNm]** & **[kNm]** & **[kNm]** & **[kNm]** & **[kNm]** & **[mm]** \\ \hline I & 0 & Finer & 2.364 & 0.0 & 2.364 & 2.137 & 4.501 & 0.1716 \\ II-o & 12.5 & Finer & 1.550 & 12.423 & 3.103 & 1.397 & 4.500 & 0.1107 \\ II-m & 12.5 & Finer & 3.167 & 0.0 & 3.167 & 1.333 & 4.500 & 0.1068 \\ III-o & 27.5 & Finer & 0.685 & 11.592 & 3.873 & 0.627 & 4.500 & 0.0491 \\ III-m & 27.5 & Finer & 3.942 & 0.0 & 3.942 & 0.558 & 4.500 & 0.0448 \\ I & 0 & Coarser & 2.407 & 0.0 & 2.407 & 2.100 & 4.507 & 0.1636 \\ II-o & 12.5 & Coarser & 1.589 & 12.424 & 3.142 & 1.405 & 4.547 & 0.1062 \\ II-m & 12.5 & Coarser & 3.202 & 0.0 & 3.202 & 1.320 & 4.522 & 0.1018 \\ III-o & 27.5 & Coarser & 0.720 & 11.582 & 3.905 & 0.698 & 4.603 & 0.0488 \\ III-m & 27.5 & Coarser & 3.969 & 0.0 & 3.969 & 0.584 & 4.553 & 0.0427 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of results from Midas. tions for increasingly refined meshes converge to the theoretical one first given in [23; 24]. The presence of DOFs called drilling rotations, initially proposed in [15; 29], enhances the result accuracy and accelerates the convergence rate. In this case, the shear locking phenomenon in the membrane state is overcome. However, based on the results obtained at the corner of the fixed edge, the issue of stress concentration arises; see, e.g., [17].