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

stress flows (green) similar to those of the SESO method, Fig. 17a, highlighting the robustness of both methods for creating strut-and-tie models. With the objective of investigate the effects of D-regions, three holes were inserted in the horizontal element of the bridge pier structure, and the number of finite elements of the mesh was reduced to 88,700, as shown in Fig. 18. The optimal topologies of the SESO and VFLSM models are represented in Fig. 19, where the struts are represented by green color and the ties by blue color. The optimum results obtained demonstrate that the presence of geometric discontinuities produces changes in the stress flows, that seek to contour the discontinuities, describing practically vertical struts in the horizontal body of the bridge pier from the points of load application. These struts bend below the openings to meet at the top of the vertical element, creating points of deviation that need to be equilibrated by tensile ties. In Fig. 19, it can be seen the representations of STM elements created as described. This modification with the presence of the openings affects the STMs models significantly, and the real load transfer mechanism can change with the dimensions of the openings. The optimization histories are shown in Fig. 20 and Fig. 21, by the SESO and VFLSM formulations, respectively. Fig. 17: Bridge Pier: Strut-and-tie models (a) SESO and (b) VFLSM Fig. 18: Bridge pier with three holes as structural discontinuities in horizontal braces Fig. 19: Strut-and-tie model: (a) SESO and (b) VFLSM © 2023 Global Journals Global Journal of Researches in Engineering ( ) E Volume XxXIII Issue II Version I 35 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models