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Vol. 33 No. 69 (2024)
July-September 2024: Open Science at the Service of Engineering

Papers

Advancing Probabilistic Frame Analysis: A Comprehensive Approach Using Monte Carlo Simulation and Response Surfaces

Published 2024-08-29

Wilson Rodríguez-Calderón
Escuela Superior de Administración Pública image/svg+xml

Myriam-Rocío Pallares-Muñoz
South Colombian University image/svg+xml

Carlos Jurado-Cabañes
Universidad Politécnica de Madrid image/svg+xml

Abstract

An ANSYS-based probabilistic finite element analysis has been created, expanding Haldar and Mahadevan’s canonical frame approach. The model is parameterized with eleven random variables, including applied loads, cross-section properties, member lengths, elastic modulus, and limit horizontal displacement. The sensitivity of these variables is analyzed, and the structure’s failure probability is evaluated using a limit state function for horizontal displacement. Monte Carlo (MC), Monte Carlo with Latin Hypercube sampling (MCLH), and Linear and Quadratic Response Surface (RSM-LIN and RSM-QUAX) methods analyze structural reliability; RSM methods achieved the lowest computational costs. The results are conclusive and future applications involving nonlinearity, dynamic loading, and other extreme scenarios are predicted.

Keywords

design of experiments, finite element, Monte Carlo methods, probabilistic sensitivities, response surface method, structural reliability

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References

  • A. Haldar, S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design. Wiley, 2000.
  • G. A. Fenton, D. V. Griffiths, Risk Assessment in Geotechnical Engineering. 2008.
  • K. K. Phoon, J. Ching, Risk and Reliability in Geotechnical Engineering. CRC Press, 2017.
  • A. T. Beck, R. E. Melchers, Structural reliability analysis and prediction, Third edit. John Wiley & Sons Ltd, 2018.
  • Z. Yang, J. Ching, “A novel simplified geotechnical reliability analysis method,” Appl. Math. Model., vol. 74, pp. 337-349, 2019. https://doi.org/10.1016/j.apm.2019.04.055
  • C. L. B. Yu, B. Ning, “Probabilistic durability assessment of concrete structures in marine environments: Reliability and sensitivity analysis,” China Ocean Eng., vol. 31, no. 1, pp. 63-73, 2017. https://doi.org/10.1007/s13344-017-0008-3
  • C. R. Ávila da Silva Júnior, P. D. Damazio, L. C. Matioli, J. L. Cavichiolo, “A counterexample to FORM and SORM,” Eng. Comput., vol. 37, no. 6, pp. 2127-2135, Jan. 2020. https://doi.org/10.1108/EC-06-2019-0286
  • R. Rackwitz, B. Flessler, “Structural reliability under combined random load sequences,” Comput. Struct., vol. 9, no. 5, e1978. https://doi.org/10.1016/0045-7949(78)90046-9
  • H. M. Gomes, “Técnicas de Avaliação da Confiabilidade em Estruturas de Concreto Armado Structural reliability analysis and prediction,” Doctoral dissertation, Universidade Federal do Rio Grande do Sul, 2001.
  • W. Rodríguez, A. M. Awruch, J. L. Tamayo, H. M. Gomes, “Aplicação da análise da confiabilidade estrutural em treliças usando Ansys e ferramentas desenvolvidas em Matlab e Fortran [Paper presentation],” 2018.
  • W. Rodríguez, “Análise de confiabilidade em problemas de interação solo-estaca incluindo campos estocásticos,” Doctoral dissertation, Universidade Federal do Rio Grande do Sul, 2020.
  • W. Rodríguez, M. R. Pallares, “Comparação do Método Form e Monte Carlo Sequenciais e Paralelizados Numa Análise De Confiabilidade da Função Estado Limite Explícita (Viga em Plastificação) [Paper presentation],” 2021.
  • S. Kaewunruen, C. Ngamkhanong, J. Jiang, “21 - Reliability quantification of the overhead line conductor,” in Rail Infrastructure Resilience, R. Calçada and S. Kaewunruen, Eds. Woodhead Publishing, 2022, pp. 441-462.
  • P. Wang, L. Yang, N. Zhao, L. Li, D. Wang, “A New SORM Method for Structural Reliability with Hybrid Uncertain Variables,” Appl. Sci., vol. 11, no. 1, 2021. https://doi.org/10.3390/app11010346
  • H. A. Jensen, F. Mayorga, C. Papadimitriou, “Reliability sensitivity analysis of stochastic finite element models,” Comput. Methods Appl. Mech. Eng., vol. 296, 2015. https://doi.org/10.1016/j.cma.2015.08.007.
  • A. Haldar, S. Mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis. Wiley, 2000.
  • J. Zhang, “Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey,” Wiley Interdiscip. Rev. Comput. Stat., 2020. https://doi.org/10.1002/wics.1539
  • F. Zhou, Y. Hou, H. Nie, “On High-Dimensional Time-Variant Reliability Analysis with the Maximum Entropy Principle,” Int. J. Aerosp. Eng., vol. 2022, e6612864, 2022. https://doi.org/10.1155/2022/6612864
  • N. Metropolis, S. Ulam, “The Monte Carlo Method,” J. Am. Stat. Assoc., vol. 44, no. 247, pp. 335-341, Sep. 1949. https://doi.org/10.1080/01621459.1949.10483310
  • H. M. Gomes, Apostila e slides da disciplina Confiabilidade em Sistemas Mecânicos. UFRGS, 2004.
  • A. S. Nowak, K. R. Collins, Reliability of Structures, Second Edition. Taylor & Francis, 2012.
  • W. Rodríguez, M. R. Pallares, J. A. Pulecio, “Rheological model of creep and relaxation in asphaltic mixtures using the transformed Carson Laplace, MAXIMA and Maple,” ARPN J. Eng. Appl. Sci., vol. 14, no. 2, 2019.
  • W. Rodríguez, M. R. Pallares, J. A. Pulecio, “Análise de Sensibilidades Probabilísticas e Confiabilidade Estrutural em Treliças de Pontes Usando Ansys [Paper presentation],” 2021.
  • A. Senova, A. Tobisova, R. Rozenberg, “New Approaches to Project Risk Assessment Utilizing the Monte Carlo Method,” Sustainability, vol. 15, no. 2, 2023. https://doi.org/10.3390/su15021006
  • P. L. E. Bruno Tuffin, Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2018, Rennes, France, July 1–6, 1st ed. Springer International Publishing, 2020.
  • Z. Zheng, H. Dai, M. Beer, “Efficient structural reliability analysis via a weak-intrusive stochastic finite element method,” Probabilistic Eng. Mech., vol. 71, 2023. https://doi.org/10.1016/j.probengmech.2023.103414
  • R. L. Iman, W. J. Conover, “Small sample sensitivity analysis techniques for computer models, with an application to risk assessment,” Commun. Stat. - Theory Methods, vol. 9, no. 17, 1980. https://doi.org/10.1080/03610928008827996
  • M. R. Abyani, M. Bahaari, “A Comparative Reliability Study of Corroded Pipelines Based on Monte Carlo Simulation and Latin Hypercube Sampling Methods,” Int. J. Press. Vessel. Pip., e104079, 2020. https://doi.org/10.1016/j.ijpvp.2020.104079
  • Z. Wang, “Comparative Study of Latin Hypercube Sampling and Monte Carlo Method in Structural Reliability Analysis,” Highlights Sci. Eng. Technol., vol. 28, pp. 61-69, 2022. https://doi.org/10.54097/hset.v28i.4061
  • Q. Gu, Y. Liu, Y. Li, C. Lin, “Finite element response sensitivity analysis of three-dimensional soil-foundation-structure interaction (SFSI) systems,” Earthq. Eng. Eng. Vib., vol. 17, no. 3, 2018. https://doi.org/10.1007/s11803-018-0462-9
  • R. Yang, W. Li, Y. Liu, “A novel response surface method for structural reliability,” AIP Adv., vol. 12, no. 1, p. 15205, Jan. 2022. https://doi.org/10.1063/5.0074702
  • B. Sudret, “Meta-models for structural reliability and uncertainty quantification,” arXiv Prepr. arXiv1203.2062, 2012.
  • P. Liu, D. Shang, Q. Liu, Z. Yi, K. Wei, “Kriging Model for Reliability Analysis of the Offshore Steel Trestle Subjected to Wave and Current Loads,” J. Mar. Sci. Eng., vol. 10, no. 1, 2022. https://doi.org/10.3390/jmse10010025
  • J. E. Hurtado, Structural Reliability: Statistical Learning Perspectives. Springer Berlin Heidelberg, 2004.
  • S. Saraygord, F. Enayatollahi, X. Xu, X. Liang, “Machine learning-based methods in structural reliability analysis: A review,” Reliab. Eng. Syst. Saf., vol. 219, e108223, 2022. https://doi.org/10.1016/j.ress.2021.108223
  • S. Reh, J.-D. Beley, S. Mukherjee, E. H. Khor, “Probabilistic finite element analysis using ANSYS,” Struct. Saf., vol. 28, no. 1, pp. 17-43, 2006. https://doi.org/10.1016/j.strusafe.2005.03.010.
  • ANSYS, ANSYS Mechanical APDL Theory Reference. 2015.
  • M. R. Pallares, W. Rodríguez, “Modelación de un sistema oscilante caótico empleando programas libres de Sistemas de Álgebra Computacional [Paper presentation],” 2010. https://www.iiis.org/cds2010/cd2010csc/cisci_2010/paperspdf/ca897gu.pdf
  • Maxima, “Maxima, a Computer Algebra System. Version 5.47.0.”, 2023. https://maxima.sourceforge.io/
  • ANSYS, ANSYS Mechanical APDL Advanced Analysis Guide. 2015.

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