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

Fig. 4: Flowchart of the STM via TO Fig. 5: Design domain and boundary conditions (measuring in cm) Fig. 6 provides the optimal topologies of the optimization procedures for the SESO (Fig. 6a and Fig. 6b) and VFSLM (Fig. 6c) methods, with a final volume fraction equal to 32%. The optimal configurations have similarity to the classical STM presented by [1] and later by [20]. The computational cost presented by SESO using Optimality Criteria [47] is approximately 40% lower than the SESO and VFLSM methods using the MMA. It can be also noticed in Fig. 6 that the optimal settings obtained by the VFLSM formulation clearly defines distinct elements (strut or tie) near the lateral faces of the deep beam, resulting in a more discrete STM, compared to the optimal settings presented by the SESO method. The classic model, Fig. 7, denotes three diagonal struts starting from the region of load application, one of them external directed to the closest support, another contouring the opening and directed to the support, and a third internal one. The ends of the struts are connected by tie composing the final structure of the STM. Fig. 6: Topology optimal for deep beam: (a) SESO-MMA; (b) SESO – OC and (c) VLSM-MMA © 2023 Global Journals Global Journal of Researches in Engineering ( ) E Volume XxXIII Issue II Version I 29 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models