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

Fig. 15: Optimization history of bridge pier with SESO: (a) initial structure; (b) topology at iteration 25; (c) optimal topology at iteration 82; (d) optimal topology (hexahedral elements) Fig. 16: Optimization history of bridge pier VFLSM: (a) initial structure; (b) topology at iteration 25; (c) optimal topology at iteration 68 (d) optimal topology (tetrahedral elements) The optimal settings with highlights of the distinct regions by colors are presented in Fig. 17 for the two methods proposed in this paper. In these representations, a vertical axial force is expected to balance the symmetric external loads in the region of the base constraint. The applied vertical forces, in fact, are transferred to the column axis by means of two inclined struts and two vertical struts that merge into two in the proximity of the top region of the vertical element, driving the load distribution to the lower region where are the base supports. Note that the SESO method creates a unified region at the base while the VFLSM method sets up two parallel vertical paths. In addition, a horizontal tensile tie is arranged at the top of the body receiving the applied forces, which ensures the "T" geometry of the structure and configures the struts equilibrium in the load application zones. From a numerical point of view, the result obtained is optimal and configures the symmetry defined by the position of the design load. For automatic generation of STM models in the VFLSM method, it was necessary to implement the derivatives of von Mises stresses in the code proposed by [34]. Fig. 17b exhibits an optimal topology of VFLSM with tensile stress flows (blue) in the upper part and compression Global Journal of Researches in Engineering © 2023 Global Journals ( ) E Volume XxXIII Issue II Version I 34 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models