Optimized strut-and-tie design for double-sided corbels using multi-material topology optimization under multiple load cases
Bibliographic record
Abstract
No abstract is available for this record. The assistant can identify its topic from the title, but cannot infer the study’s results.
Source: Not provided · Quality: missing
Research context
OpenAlex topics: Topology Optimization in Engineering · Composite Structure Analysis and Optimization · Structural Load-Bearing Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. ABNT NBR 6118 (2023) NBR 6118 – Design of concrete structures – Procedure. Associação Brasileira de Normas Técnicas (ABNT): Rio de Janeiro, Brazil. (In Portuguese)
2. ACI Committee 318 (2014) Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary; American Concrete Institute: Indianapolis, IN, USA; Volume 11, p. 6858
3. Abdi M (2015) Evolutionary topology optimization of continuum structures using X-FEM and isovalues of structural performance. PhD thesis, University of Nottingham. https://eprints.nottingham.ac.uk/id/eprint/31226
4. Achtziger, W.: Multiple-load truss topology and sizing optimization: Some properties of minimax compliance. J. Optim. Theory Appl. 98(2), 255–280 (1998). https://doi.org/10.1023/A:102263721610410.1023/A:1022637216104 ↗
5. Ahmad, S., Alghambi, S.: A statistical approach to optimizing concrete mixture design. Sci. World J. 2014, 561539 (2014). https://doi.org/10.1155/2014/56153910.1155/2014/561539 ↗
6. Almeida, V.S., Simonetti, H.L., Neto, L.O.: The strut-and-tie models in reinforced concrete structures analyzed by a numerical technique. IBRACON Struct. Mater. J. 6(1), 139–157 (2013). https://doi.org/10.1590/S1983-4195201300010000810.1590/S1983-41952013000100008 ↗
7. Alvarez, E.G., Stamler, N.L., Mueller, C.T., Norford, L.K.: Shape optimization of chilled concrete ceilings – Reduced embodied carbon and enhanced operational performance. Build. Environ. 221, 109330 (2022). https://doi.org/10.1016/j.buildenv.2022.10933010.1016/j.buildenv.2022.109330 ↗
8. Amaral, R.A., Lamaritni, F.B., Gomes, H.M.: Optimization of reinforced concrete structures using population-based metaheuristic algorithms. Ciência E Natura 45(3), e74927 (2023). https://doi.org/10.5902/2179460X7492710.5902/2179460X74927 ↗
9. Amaral RR, Gomes HM (2021) Multi-material topology optimization with stress constraints. Proceedings of the 26th International Congress of Mechanical Engineering. https://doi.org/10.26678/ABCM.COBEM2021.COB2021-043510.26678/ABCM.COBEM2021.COB2021-0435 ↗
10. Amir, O.: A topology optimization procedure for reinforced concrete structures. Comput. Struct. 114–115, 46–58 (2013). https://doi.org/10.1016/j.compstruc.2012.10.01110.1016/j.compstruc.2012.10.011 ↗
11. Andersen, M.E.M., Poulsen, P.N., Olesen, J.B., Hoang, L.C.: Strength-based material layout optimization of solid reinforced concrete. Comput. Struct. 276, 106941 (2023). https://doi.org/10.1016/j.compstruc.2022.10694110.1016/j.compstruc.2022.106941 ↗
12. Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B., Sigmund, O.: Efficient topology optimization in MATLAB using 88 lines of code. Struct. Multidiscip. Optim. 43, 1–16 (2011). https://doi.org/10.1007/s00158-010-0594-710.1007/s00158-010-0594-7 ↗
13. Banh, T.T., Shin, S., Kang, J., Lee, D.: Frequency-constrained topology optimization in incompressible multi-material systems under design-dependent loads. Thin-Wall. Struct. 196, 111467 (2024). https://doi.org/10.1016/j.tws.2023.11146710.1016/j.tws.2023.111467 ↗
14. Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988). https://doi.org/10.1016/0045-7825(88)90086-210.1016/0045-7825(88)90086-2 ↗
15. Bendsøe, M.P., Sigmund, O.: Topology optimization: theory, methods, and applications. Springer-Verlag, Berlin. (2004). https://doi.org/10.1007/978-3-662-05086-610.1007/978-3-662-05086-6 ↗
16. Bendsøe MP (1995) Optimization of Structural Topology, Shape and Material. Springer-Verlag Berlin Heidelberghttps://doi.org/10.1007/978-3-662-03115-510.1007/978-3-662-03115-5 ↗
17. Borges, J.A., Amaral, R.R., Isoldi, L.A., Casas, W.J.P., Gomes, H.M.: A novel BESO methodology for topology optimization of reinforced concrete structures: A two-loop approach. J. Appl. Comput. Mech. 9, 498–512 (2023). https://doi.org/10.22055/jacm.2022.41708.379910.22055/jacm.2022.41708.3799 ↗
18. CEB-FIP Model Code 1990: Design Code. London; 1993.
19. Cedrim, M.B.M., Lages, E.N., Barboza, A.S.R.: Proposition and analysis of strut and tie models for short corbels from techniques of topology optimization. IBRACON Struct. Mater. J. 14, 14212 (2021). https://doi.org/10.1590/S1983-4195202100020001210.1590/S1983-41952021000200012 ↗
20. Chandrasekhar, A., Suresh, K.: TOuNN: topology optimization using neural networks. Struct. Multidiscip. Optim. 63, 1135–1149 (2020). https://doi.org/10.1007/s00158-020-02748-410.1007/s00158-020-02748-4 ↗
21. Chen, R., Bittencourt, T.N., Della Bella, J.C.: Design of reinforced concrete structures from three-dimensional stress fields. IBRACON Struct. Mater. J. 16(4), e16407 (2023). https://doi.org/10.1590/S1983-4195202300040000710.1590/S1983-41952023000400007 ↗
22. Cornelissen H, Hordijk D, Reinhardt H. Experimental determination of crack softening characteristics of normal weight and lightweight concrete. Heron. 1986; 31(2).
23. Cui, Y., Takahashi, T., Matsumoto, T.: An exact volume constraint method for topology optimization via reaction-diffusion equation. Comput. Struct. 280, 106986 (2023). https://doi.org/10.1016/j.compstruc.2023.10698610.1016/j.compstruc.2023.106986 ↗
24. Da D (2019) Topology optimization design of heterogeneous materials and structures. ISTE Ltd and John Wiley & Sons, Inc.10.1002/9781119687252 ↗
25. Dayaratnam, P., Ranganathan, R.: Statistical analysis of strength of concrete. Build. Environ. 11(2), 145–152 (1976). https://doi.org/10.1016/0360-1323(76)90029-910.1016/0360-1323(76)90029-9 ↗
26. De Marco A (2018) Application of Evolutionary Structural Optimization to Reinforced Concrete Structures. MSc dissertation, TU Delft Civil Engineering and Geosciences; TU Delft Materials- Mechanics- Management & Design. http://resolver.tudelft.nl/uuid:efd1ad24-017f-48ac-8e31-184339a9d148
27. Dey, S., Karthik, M.M.: Modelling four-pile cap behaviour using three-dimensional compatibility strut-and-tie method. Eng. Struct. 198, 109499 (2019). https://doi.org/10.1016/j.engstruct.2019.10949910.1016/j.engstruct.2019.109499 ↗
28. Díaz, A.R., Bendsøe, M.P.: Shape optimization of structures for multiple loading conditions using a homogenization method. Struct. Optim. 4, 17–22 (1992). https://doi.org/10.1007/BF0189407710.1007/BF01894077 ↗
29. Elkady A. ABAQUS_CDP_Generator: A tool for generating concrete damage parameters for ABAQUS. Zenodo, Version v23.04; 2023. https://doi.org/10.5281/zenodo.775592610.5281/zenodo.7755926 ↗
30. Farahmand-Tabar S (2023) Genetic algorithm and accelerating fuzzification for optimum sizing and topology design of real-size tall building systems. Applied Genetic Algorithm and Its Variants, 209–230. https://doi.org/10.1007/978-981-99-3428-7_910.1007/978-981-99-3428-7_9 ↗
31. Foster, S.J., Marti, P., Mojsilović, N.: Design of reinforced concrete solids using stress analysis. ACI Struct. J. 100(6), 758–764 (2003)
32. Golecki, T., Gomez, F., Carrion, J., Spencer, B.F.: Bridge topology optimization considering stochastic moving traffic. Eng. Struct. 292, 116498 (2023). https://doi.org/10.1016/j.engstruct.2023.11649810.1016/j.engstruct.2023.116498 ↗
33. Gomez, F., Spencer, B.F., Carrion, J.: Topology optimization of buildings subjected to stochastic base excitation. Eng. Struct. 223, 111111 (2020). https://doi.org/10.1016/j.engstruct.2020.11111110.1016/j.engstruct.2020.111111 ↗
34. Guan, H., Chen, Y.J., Loo, Y.C., Xie, Y.M., Steven, G.P.: Bridge topology optimisation with stress, displacement and frequency constraints. Comput. Struct. 81(3), 131–145 (2003). https://doi.org/10.1016/S0045-7949(02)00440-610.1016/S0045-7949(02)00440-6 ↗
35. Hinton, E., Sienz, J.: Fully stressed topological design of structures using an evolutionary procedure. Eng. Comput. 12(3), 229–244 (1995). https://doi.org/10.1108/0264440951079957810.1108/02644409510799578 ↗
36. Hong WK (2020) Chapter 3 – The investigation of the structural performance of the hybrid composite precast frames with mechanical joints based on nonlinear finite element analysis. Hybrid Composite Precast Systems – Numerical Investigation to Construction, Woodhead Publishing Series in Civil and Structural Engineering. 89–177. https://doi.org/10.1016/B978-0-08-102721-9.00003-010.1016/B978-0-08-102721-9.00003-0 ↗
37. Huang, X., Xie, Y.M.: Evolutionary topology optimization of continuum structures with an additional displacement constraint. Struct. Multidiscip. Optim. 40, 409–416 (2009). https://doi.org/10.1007/s00158-009-0382-410.1007/s00158-009-0382-4 ↗
38. Huang, X., Xie, Y.M.: Evolutionary topology optimization of continuum structures: methods and applications. Wiley (2010). https://doi.org/10.1002/978047068948610.1002/9780470689486 ↗
39. Huang, X., Zuo, Z.H., Xie, Y.M.: Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput. Struct. 88(5–6), 357–364 (2009). https://doi.org/10.1016/j.compstruc.2009.11.01110.1016/j.compstruc.2009.11.011 ↗
40. Ismail, M.A., Mueler, C.T.: Minimizing embodied energy of reinforced concrete floor systems in developing countries through shape optimization. Eng. Struct. 246, 112955 (2021). https://doi.org/10.1016/j.engstruct.2021.11295510.1016/j.engstruct.2021.112955 ↗
41. Jog, C.S.: Topology design of structures using a dual algorithm and a constraint on the perimeter. Int. J. Numer. Meth. Eng. 54, 1007–1019 (2002). https://doi.org/10.1002/nme.45710.1002/nme.457 ↗
42. Kammoun, Z., Fourati, M., Smaoui, H.: Direct limit analysis based topology optimization of foundations. Soils Found. 59(4), 1063–1072 (2019). https://doi.org/10.1016/j.sandf.2019.05.00310.1016/j.sandf.2019.05.003 ↗
43. Kentli, A.: Topology optimization applications on engineering structures. Truss Frames – Recent Adv New Perspect. (2019). https://doi.org/10.5772/intechopen.9047410.5772/intechopen.90474 ↗
44. Khaiyum, M.Z., Sarker, S., Kabir, G.: Evaluation of carbon emission factors in the cement industry: An emerging economy context. Sustainability 15(21), 15407 (2023). https://doi.org/10.3390/su15211540710.3390/su152115407 ↗
45. Kharmanda, G., Olhoff, N., Mohamed, A., Lemaire, M.: Reliability-based topology optimization. Struct. Multidiscip. Optim. 26, 295–307 (2004). https://doi.org/10.1007/s00158-003-0322-710.1007/s00158-003-0322-7 ↗
46. Kočvara, M.: Topology optimization with displacement constraints: a bilevel programming approach. Struct. Optim. 14, 256–263 (1997). https://doi.org/10.1007/BF0119794810.1007/BF01197948 ↗
47. Kseniia, C., Viktor, C.: Light-weight structures: proposals of resource-saving supporting structures. Truss Frames – Recent Adv. New Perspect. (2019). https://doi.org/10.5772/intechopen.8823710.5772/intechopen.88237 ↗
48. Kundu, R.D., Li, W., Zhang, X.S.: Multimaterial stress-constrained topology optimization with multiple distinct yield criteria. Extreme Mech. Lett. 54, 101716 (2022). https://doi.org/10.1016/j.eml.2022.10171610.1016/j.eml.2022.101716 ↗
49. Lai, S., Serra, M.: Concrete strength prediction by means of neural network. Constr. Build. Mater. 11(2), 93–98 (1997). https://doi.org/10.1016/S0950-0618(97)00007-X10.1016/S0950-0618(97)00007-X ↗
50. Lanes, R.M., Greco, M., Guerra, M.B.B.F.: Strut-and-tie models for linear and nonlinear behavior of concrete based on topological evolutionary structure optimization (ESO). IBRACON Struct. Mater. J. 12, 87–100 (2019). https://doi.org/10.1590/S1983-4195201900010000810.1590/S1983-41952019000100008 ↗
51. Le, C., Norato, J., Bruns, T., Ha, C., Tortorelli, D.: Stress-based topology optimization for continua. Struct. Multidisc. Optim. 41, 605–620 (2010). https://doi.org/10.1007/s00158-009-0440-y10.1007/s00158-009-0440-y ↗
52. Lee, J., Fenves, G.L.: Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124, 892–900 (1998). https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)10.1061/(ASCE)0733-9399(1998)124:8(892) ↗
53. Lee, D.K., Yang, C.J., Starossek, U.: Topology design of optimizing material arrangements of beam-to-column connection frames with maximal stiffness. Scientia Iranica 19, 1025–1032 (2012). https://doi.org/10.1016/j.scient.2012.06.00410.1016/j.scient.2012.06.004 ↗
54. Li, Q., Steven, G.P., Querin, O.M., Xie, Y.M.: Stress-based optimization of torsional shafts using an evolutionary procedure. Int. J. Solids Struct. 38(32–33), 5661–5677 (2001). https://doi.org/10.1016/S0020-7683(00)00365-610.1016/S0020-7683(00)00365-6 ↗
55. Li, Z., Zhou, W.: Optimizing UHPC walls into trusses based on the solid isotropic material with penalization method. Structures 47, 573–585 (2023). https://doi.org/10.1016/j.istruc.2022.11.07610.1016/j.istruc.2022.11.076 ↗
56. Liang, Q.Q., Xie, Y.M., Steven, G.P.: Topology optimization of strut-and-tie models for reinforced concrete structures using an evolutionary procedure. ACI Struct. J. 97, 322–332 (2000). https://doi.org/10.14359/86310.14359/863 ↗
57. Liu, J., Gaynor, A.T., Chen, S., Kang, Z., Suresh, K., Takezawa, A., Wang, C.C.L.: Topology optimization for additive manufacturing: Considerations and directions. Comput. Mater. Sci. 85, 298–307 (2014). https://doi.org/10.1016/j.commatsci.2014.01.02010.1016/j.commatsci.2014.01.020 ↗
58. Liu Y, Jewett JL, Carstensen JV (2020) Experimental Investigation of Topology-Optimized Deep Reinforced Concrete Beams with Reduced Concrete Volume. Second RILEM International Conference on Concrete and Digital Fabrication 601–611, https://hdl.handle.net/1721.1/13842210.1007/978-3-030-49916-7_61 ↗
59. Londoño, O., Paulino, G.H.: PolyStress: a Matlab implementation for local stress-constrained topology optimization using the augmented Lagrangian method. Struct. Multidiscip. Optim. 63, 2065–2097 (2021). https://doi.org/10.1007/s00158-020-02760-810.1007/s00158-020-02760-8 ↗
60. Lubliner, J., Oliver, J., Oller, S., Onãte, E.A.: Plastic damage model for concrete. Int. J. Solids Struct. 25, 299–326 (1989). https://doi.org/10.1016/0020-7683(89)90050-410.1016/0020-7683(89)90050-4 ↗
61. Luo, Y., Wang, M.Y., Zhou, M., Deng, Z.: Optimal topology design of steel–concrete composite structures under stiffness and strength constraints. Comput. Struct. 112–113, 433–444 (2012). https://doi.org/10.1016/j.compstruc.2012.09.00710.1016/j.compstruc.2012.09.007 ↗
62. Malm R. (2006) Shear cracks in concrete structures subjected to in-plane stresses. Doctoral thesis, Royal Institute of Technology.
63. Mihashi, H.: Stochastic approach to study fatigue of concrete. Eng. Fract. Mech. 28, 785–793 (1987). https://doi.org/10.1016/0013-7944(87)90070-110.1016/0013-7944(87)90070-1 ↗
64. Mihashi, H., Izumi, M.: A stochastic theory for concrete fracture. Cem. Concr. Res. 7, 411–421 (1977). https://doi.org/10.1016/0008-8846(77)90069-210.1016/0008-8846(77)90069-2 ↗
65. Nikolov, N.: Concrete: computation and optimization. Build. Technol. Educ. Soc. (2019). https://doi.org/10.7275/qjmj-ny4410.7275/qjmj-ny44 ↗
66. Ottosen, N.S.: A failure criterion for concrete. J. eng. Mech. Div. 103, 527–535 (1977). https://doi.org/10.1061/JMCEA3.000224810.1061/JMCEA3.0002248 ↗
67. Patel P, Mahanta MJ, Bodda SS, Gupta A. (2022) Qualification of Reinforced Concrete Slabs Subjected to Tornado Induced Impact. 26th International Conference on Structural Mechanics in Reactor Technology Berlin/Potsdam.10.1016/j.nucengdes.2021.111512 ↗
68. Querin, O.M., Steven, G.P., Xie, Y.M.: Evolutionary structural optimization (ESO) using a bidirectional algorithm. Eng. Comput. 15, 1031–1048 (1998). https://doi.org/10.1108/0264440981024412910.1108/02644409810244129 ↗
69. Rees DWA (2009) Mechanics of optimal structural design: minimum weight structures John Wiley & Sons, Ltd.https://doi.org/10.1002/978047074978410.1002/9780470749784 ↗
70. Reginato, L., de Sousa, A.M.D., Santos, J.V.C., Debs, M.K.E.: NLFEA of reinforced concrete corbels: proposed framework, sensibility study, and precision level. Buildings 13, 1874 (2023). https://doi.org/10.3390/buildings1307187410.3390/buildings13071874 ↗
71. Rizzian, L., Léger, N., Marchi, M.: Multiobjective sizing optimization of seismic-isolated reinforced concrete structures. Procedia Eng. 199, 372–377 (2017). https://doi.org/10.1016/j.proeng.2017.09.04410.1016/j.proeng.2017.09.044 ↗
72. Rong, X., Zheng, J., Jiang, C.: Topology optimization for structures with bi-modulus material properties considering displacement constraints. Comput. Struct. 276, 106952 (2023). https://doi.org/10.1016/j.compstruc.2022.10695210.1016/j.compstruc.2022.106952 ↗
73. Sethian, J.Á., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 2, 489–528 (2000). https://doi.org/10.1006/jcph.2000.658110.1006/jcph.2000.6581 ↗
74. Sigmund, O., Torquato, S.: Design of materials with extreme thermal expansion using a three-phase topology optimization method. Comput. Mater. Sci. 83, 318–323 (2014). https://doi.org/10.1016/j.commatsci.2013.11.03210.1016/j.commatsci.2013.11.032 ↗
75. Silva, G.A., Cardoso, E.L., Beck, A.T.: Comparison of robust, reliability-based and non-probabilistic topology optimization under uncertain loads and stress constraints. Probab. Eng. Mechan. (2020). https://doi.org/10.1016/j.probengmech.2020.10303910.1016/j.probengmech.2020.103039 ↗
76. Simonetti, H.L., Almeida, V.S., Neto, L.O.: Smooth evolutionary structural optimization procedure applied to plane stress problem. Eng. Struct. 75, 248–258 (2014). https://doi.org/10.1016/j.engstruct.2014.05.04110.1016/j.engstruct.2014.05.041 ↗
77. Simonetti HL, Almeida VS, Del V, Azar SZ, Manuel V (2023) Reliability-based optimization of evolutionary topology and automated generation of strut-and-tie models for 3D structures. Conference: XLIV Ibero-Latin American Congress on Computational Methods in Engineering (CILAMCE 2023).
78. Smith M. ABAQUS/Standard User's Manual, Version 6.9 (2009) Dassault Systèmes Simulia Corp.
79. Srinivas, GL, Mohammad A, Brandstötter, M (2024) Design and Development of Fin-Ray Finger using Topology Optimization with Multiple Load Cases. International Conference on Cognitive Robotics and Intelligent Systems (ICC - ROBINS), Coimbatore, India, 2024, pp. 1–7, https://doi.org/10.1109/ICC-ROBINS60238.2024.10534011.10.1109/ICC-ROBINS60238.2024.10534011 ↗
80. Stoiber, N., Kromoser, B.: Topology optimization in concrete construction: a systematic review on numerical and experimental investigations. Struct. Multidiscip. Optim. 64, 1725–1749 (2021). https://doi.org/10.1007/s00158-021-03019-610.1007/s00158-021-03019-6 ↗
81. Sui Y, Peng X (2018) Modelling, solving and application for topology optimization of continuum structures: ICM method based on step function. Butterworth-Heinemann. https://doi.org/10.1016/C2015-0-04148-X10.1016/C2015-0-04148-X ↗
82. Suksuwan, A., Spence, S.M.J.: Performance-based multi-hazard topology optimization of wind and seismically excited structural systems. Eng. Struct. 172, 573–588 (2018). https://doi.org/10.1016/j.engstruct.2018.06.03910.1016/j.engstruct.2018.06.039 ↗
83. Suresh, K.: A 199-line Matlab code for pareto-optimal tracing in topology optimization. Struct. Multidiscip. Optim. 42, 665–679 (2010). https://doi.org/10.1007/s00158-010-0534-610.1007/s00158-010-0534-6 ↗
84. Tian, X., Liu, G., Deng, W., Xie, Y., Wang, H.: Fatigue-constrained topology optimization for the jacket support structure of offshore wind turbine under the dynamic load. Appl. Ocean Res. 142, 103812 (2024). https://doi.org/10.1016/j.apor.2023.10381210.1016/j.apor.2023.103812 ↗
85. Tomás, A., Martí, P.: Shape and size optimisation of concrete shells. Eng. Struct. 32(6), 1650–1658 (2010). https://doi.org/10.1016/j.engstruct.2010.02.01310.1016/j.engstruct.2010.02.013 ↗
86. Trillet D (2018) Topology optimization in nonlinear vibrations. MSc dissertation, University of Liège: Faculty of Applied Science. http://hdl.handle.net/2268.2/5496
87. Vatanabe, S.L., Lippi, T.N., de Lima, C.R., Paulino, G.H., Silva, E.C.N.: Topology optimization with manufacturing constraints: A unified projection-based approach. Adv. Eng. Softw. 100, 97–112 (2016). https://doi.org/10.1016/j.advengsoft.2016.07.00210.1016/j.advengsoft.2016.07.002 ↗
88. Wang, F., Lazarov, B.S., Sigmund, O.: A comparison of three topology optimization methods for design-dependent loads. Struct. Multidiscip. Optim. 50(1), 207–221 (2014). https://doi.org/10.1007/s00158-014-1114-y10.1007/s00158-014-1114-y ↗
89. Wang, L., Ni, B., Wang, X., Li, Z.: Reliability-based topology optimization for heterogeneous composite structures under interval and convex mixed uncertainties. Appl. Math. Model. 99, 628–652 (2021). https://doi.org/10.1016/j.apm.2021.06.01410.1016/j.apm.2021.06.014 ↗
90. Wang, L., Zhang, H., Zhu, M., Chen, Y.F.: A new Evolutionary structural optimization method and application for aided design to reinforced concrete components. Struct. Multidiscip. Optim. 62, 2599–2613 (2020). https://doi.org/10.1007/s00158-020-02626-z10.1007/s00158-020-02626-z ↗
91. Wilson, H.R., Yousefpour, H., Brown, M.D., Bayrak, O.: Investigation of corbels designed according to strut-and-tie and empirical methods. ACI Struct. J. 115(3), 813–824 (2018). https://doi.org/10.14359/5170191710.14359/51701917 ↗
92. Woju, U.W., Balu, A.S.: Fuzzy uncertainty and its applications in reinforced concrete structures. J. Eng. Design Technol. 18(5), 1175–1191 (2020). https://doi.org/10.1108/JEDT-10-2019-028110.1108/JEDT-10-2019-0281 ↗
93. Xia, L., Da, D., Yvonet, J.: Topology optimization for maximizing the fracture resistance of quasi-brittle composites. Comput. Methods Appl. Mech. Eng. 332, 234–254 (2018). https://doi.org/10.1016/j.cma.2017.12.02110.1016/j.cma.2017.12.021 ↗
94. Xia, Y., Langelaar, M., Hendriks, M.A.N.: Optimization-based three-dimensional strut-and-tie model generation for reinforced concrete. Computer-Aid. Civil Infrastruct. Eng. 36, 526–543 (2020b). https://doi.org/10.1111/mice.1261410.1111/mice.12614 ↗
95. Xia, Y., Langelaar, M., Hendriks, M.A.N.: Optimization-based strut-and-tie model generation for reinforced concrete structures under multiple load conditions. Eng. Struct. 266, 114501 (2022). https://doi.org/10.1016/j.engstruct.2022.11450110.1016/j.engstruct.2022.114501 ↗
96. Xia, Y., Langellar, M., Hendriks, M.A.N.: Automated optimization-based generation and quantitative evaluation of Strut-and-Tie models. Comput. Struct. 238, 106297 (2020a). https://doi.org/10.1016/j.compstruc.2020.10629710.1016/j.compstruc.2020.106297 ↗
97. Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885–896 (1993). https://doi.org/10.1016/0045-7949(93)90035-C10.1016/0045-7949(93)90035-C ↗
98. Yang, X.Y., Xie, Y.M., Steven, G.P., Querin, O.M.: Topology optimization for frequencies using an evolutionary Method. J. Struct. Eng. 125(12), 1432–1438 (1999). https://doi.org/10.1061/(ASCE)0733-9445(1999)125:12(1432)10.1061/(ASCE)0733-9445(1999)125:12(1432) ↗
99. Zhang, H.Z., Luo, P., Yuan, X.X.: Reinforcement layout design for deep beams based on bi-objective topology optimization. Autom. Constr. 158, 105237 (2024). https://doi.org/10.1016/j.autcon.2023.10523710.1016/j.autcon.2023.105237 ↗
100. Zhang, J., Zhang, Z., Chen, C.: Yield criterion in plastic-damage models for concrete. Acta Mech. Solida Sin. 23, 220–230 (2010). https://doi.org/10.1016/S0894-9166(10)60024-910.1016/S0894-9166(10)60024-9 ↗