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

This paper aimed to extend the application of TO in 3D elasticity to obtain the best solution to STM problems. It brought some processes as innovation, such as the use of the SESO method and the VFLSM employed in conjunction with the OC and MMA methods to accelerate and stabilize the analyses; so that, the first method demonstrated to be more efficient when employed with the SESO, about 2 to 3 times faster in all the examples evaluated. It is highlighted that in these processes the incorporation of the linear solution by the conjugate gradient method with the incomplete Cholesky preconditioner further enhanced the computational cost. In the automated generation of the final designs of the STM, the procedure of obtaining struts and ties computed by the partial derivatives of the stresses of each element was applied highlighting that this novelty is easy to implement and the use of a spatial modal filter in the stress field was enough to completely eliminate the checkerboard. From the automatic generations performed, it was possible to design an example according to the recurring norm in an expeditious manner, in which the required reinforcement areas were evaluated and compared, demonstrating a good similarity. All codes were implemented in the high level language Matlab, which is easily accessible and extensible for future incorporation of other more realistic models, such as a rheological model more suitable for concrete. The study of STM using optimization applied to both materials (steel and concrete), leading to dimensioning and detailing of RC structural elements under the reliability-based topology optimization (RBTO) paradigm, taking advantage of the efficiency and stability of the procedures, are the highlights in the formulations developed in this paper. A cknowledgment The authors acknowledge the Sao Paulo State Research Foundation (FAPESP) under Grant Number 2016/02327-5 for their financial support and CNPq (National Council of Scientific and Technological Development) under Grant Numbers 305093/2018-5 and Federal Institute of Education, Science and Technology of Minas Gerais under Grant Numbers 23792 .001327/2022-49 . R eferences R éférences R eferencias 1. Schlaich, J., Schafer, K., Jennewein, M. Toward a consistent design of structural concrete. PCI- Journal, vol. 32, nr.3, p. 74 – 150, May/June, 1987. 2. Schlaich J, Schäfer K (1991) Design and detailing of structural concrete using strut-and-tie models. Struct Eng 69(6):113–125. 3. Schlaich M, Anagnostou, G (1990) Stress fields for nodes of strut-and-tie models. Struct Eng 116(1):13–23. 4. Marti P (1980) On plastic analysis of reinforced concrete. Institute of Structural Engineers, report no. 104. 5. Marti, P. (1985). "Truss models in detailing." Concr. Int., 7(12), 66-73. 6. 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Generating strut-and-tie patterns for reinforced concrete structures using topology optimization. Computers and Structures, 87:1483- 1495, 2009. 17. Bogomolny, M.; Amir, O. Conceptual design of reinforced concrete structures using topology V. C onclusions © 2023 Global Journals Global Journal of Researches in Engineering ( ) E Volume XxXIII Issue II Version I 39 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models