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

Fig. 11: Optimal topology: (a) BESO by [26]; (b) SIMP by [16] Although the models result quite similar, when approaching this problem, one must consider the increased computational burden associated with a 3D structure; a solid mesh usually requires that many elements be investigated at an adequate level of detail, with notable consequences on the number of equations and variables. Seeking to minimize this aspect of the processing, the system of equations received the implementation of a sparse approximation preconditioner for the inverse matrix. With this routine active, the computational cost of SESO-3D for this problem was decreased from 8,000 sec to 1,854 sec (4.3 times less) while VFLSM had a decrease from 8,000 sec to 3,851sec (2.1 times less). The dimensioning of the reinforcement of this model is performed, as already presented in [28]; in the calculations of the dimensions of the model elements, namely, inclined compression strut - column-pile and horizontal tension tie - pile-pile, the geometry of the problem presented [26] is used: − 1 = 4,000 4 (29.5) = 2,031 − 1 = 1 cos(29.5) √2 = 1,250 Two evaluations need to be performed, the limits of stresses in the steel bars (CA50) for the tie and stresses in the concrete (C32) of the struts. According to the Brazilian technical standard, we have the following expressions: , = ∗ 1 = 1.4∗1,250 50/1.15 = 40.25 ² (3 layers of 4 . 22) adopting steel bar with diameter = 22 with 12 bars ( , = 45.60 ² ) In the inclined strut, the verification of the compressive stresses is performed according to and the area of the strut required for the design strength of the concrete not to be exceeded: , = ∗ 1 0.8 ∗ = 1.4 ∗ 2,031 0.8 ∗ (3.2/1.4) = 1.555 ² By way of comparison, in [26], the results of this sizing are , = 41.66 2 and , = 1,659 ² . The differences in values (3.5% and 6.3, respectively) are due to different calculation criteria between the technical standards used, but values of the same order of magnitude can be considered. Fig. 12 shows the reinforcement arrangement for the pile cap. Global Journal of Researches in Engineering © 2023 Global Journals ( ) E Volume XxXIII Issue II Version I 32 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models 32 − = 32 = ∗ ∗ 5600 ∗ � = 1.0 ∗ 0.88 ∗ 5600 ∗ √32 = 27,877