Global Journal of Researches in Engineering, E: Civil & Structural, Volume 23 Issue 2

Fig. 12: Reinforcement arrangement for the pile cap c) Example 3 – Bridge pier The SESO and VFLSM methods using the MMA as accelerator are applied to a structure representing a column receiving loading from the bridge superstructure, represented by four vertical forces, as shown in Fig. 13. The concrete material properties, rejection ratio (RR), evolutionary ratio (ER) and filter radius are the same as in the previous example. For the numerical simulations, in the SESO method the bridge support is discretized using a fine mesh of 85x55x20 hexahedral elements of eight nodes, with reference side of 1 mm, while in the VFLSM method the mesh used has 85x20x55, totaling 93,500 tetrahedral finite elements. The compliance history and the performance of the methods during the optimization procedure are plotted in Fig. 14. It can be seen in Fig. 14b that the performance index perfectly captures the changes in compliance and increases from unity to a maximum value of 2.3, stabilizing quickly around 2.1, the value at the optimal iteration. The history of the optimization procedure via SESO and VFLSM for the bridge pier are shown in Fig. 1 and Fig. 16. The optimal topologies were achieved at iterations 82 and 100 with final volumes equal to 20% of the initial volume and a computational cost of 4,315.8 sec for SESO while VFLSM showed a computational cost of 5,486.5 sec. Fig. 13: Project domain of the Bridge pier Fig. 14: Performance Index: topological history © 2023 Global Journals Global Journal of Researches in Engineering ( ) E Volume XxXIII Issue II Version I 33 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models