Abstract
Main goal of the paper is to present an algorithm for stochastic optimization of a steel-reinforced concrete element’s cross section. Firstly, the deterministic problem is introduced and described. The description of uncertainties involved in the process and stochastic reformulation of the problem follows. Afterwards, the algorithm itself is introduced. This algorithm is based on internal cycle of deterministic optimization using reduced gradient method and external cycle of stochastic optimization using regression analysis. From the initialization state, the algorithm assess probabilities that ultimate and serviceability limit states are satisfied. Using regression analysis of these assessed probabilities, the algorithm finds new possible solution. The probabilities are assessed on orthogonal grid via modified bisection method. The paper concludes with presentation of the performed calculations and their results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Chakrabarty, B.K.: A model for optimal design of reinforced concrete beam. J. Struct. Eng. 108, 3238–3242 (1992)
Frangopol, D.M., Kongh, J.S., Ghareibeh, E.S.: Reliability-based life-cycle management of highway bridges. J. Comput. Civil Eng. 15, 27–34 (2001)
Ziemba, W.T., Wallace, S.W.: Applications of stochastic programming. In: SIAM conference (2004)
Cajanek, M., Popela, P.: A two-stage stochastic program with elliptic PDE constraints. In: Proceedings of 16th International Conference on Soft Computing MENDEL 2010, Brno, pp. 447–452 (2010)
Zampachova, E.: Approximations in stochastic optimization and their applications. Ph.D. thesis, Brno University of Technology (2009)
Plsek, J.: Design optimisation of concrete structures. Ph.D. thesis, Brno University of Technology (2011)
Klimes, L., Popela, P.: An implementation of progressive hedging algorithm for engineering problems. Proceedings of 16th International Conference on Soft Computing MENDEL 2010, Brno, pp. 459–464 (2010)
Sklenar, J., Popela, P.: Integer simulation based optimization by local search. Procedia Comput. Sci. 1(1), 1341–1348 (2010)
Sandera, C., Popela, P., Roupec, J.: The worst case analysis by heuristic algorithms. In: Proceedings of 15th International Conference on Soft Computing MENDEL 2009, Brno, pp. 109–114 (2009)
EN 1990:2002+A1—Eurocode: Basis of structural design
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Venclovský, J., Štěpánek, P., Laníková, I. (2021). Stochastic Optimization of a Reinforced Concrete Element with Regard to Ultimate and Serviceability Limit States. In: Matoušek, R., Kůdela, J. (eds) Recent Advances in Soft Computing and Cybernetics. Studies in Fuzziness and Soft Computing, vol 403. Springer, Cham. https://doi.org/10.1007/978-3-030-61659-5_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-61659-5_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61658-8
Online ISBN: 978-3-030-61659-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)