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

Fig. 20: Optimization history of bridge pier with openings SESO: (a) initial structure ; (b) topology at iteration 25; (c) optimal topology at iteration 70; (d) final optimal topology Fig. 21: Optimization history of bridge pier with openings VFLSM: (a) initial structure ; (b) topology at iteration 27; (c) optimal topology at iteration 70; (d) optimal topology d) Example 4 – Single Corbel The SESO and VFLSM methods were also experimented with for modeling struts-and-ties in a single corbel attached to a column. A simple structure can eventually result in an intricate STM as the dimensions and load arrangements can be defined. The geometry and dimensions of the structure are shown in Fig. 22. This single corbel is subjected to a concentrated load of 1 kN. The compressive strength of the concrete used in this example is 32 MPa. Young's modulus of the concrete E = 28,567 MPa and the Poisson's ratio = 0.15 were defined in the analysis. A prescribed fraction volume V = 0.22 m 3 and an evolution ratio of ER = 2% was specified in the optimization process. In the SESO method the structure was discretized with a mesh of 44x12x108 unit hexahedral finite elements. The performance of the structure was monitored throughout the optimization procedure and, despite the breaks in the load transfer mechanisms due to element removal, the structure did not present failure modes and the performance index remained higher than 1, stabilizing at 1.6. In the VFLSM method, the same mesh was used, totaling 57,024 tetrahedral elements. Figures 23a, b, c and d show that the optimal topologies obtained by the two models are different and checkerboard patterns were not detected. It is noted in observation made in the deep beam example that both formulations, SESO and VFLSM, define settings differently for elements of strut-and-tie models. Discrete elements are configured on the side faces of the models Global Journal of Researches in Engineering © 2023 Global Journals ( ) E Volume XxXIII Issue II Version I 36 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models