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<p>In complex structural analysis, dealing with uncertainty has become a critical aspect of engineering design and practice. While the finite element method (FEM) remains a fundamental numerical technique for analyzing such structures, deterministic FEM often fails to adequately address the inherent uncertainties in engineering problems. To overcome this limitation, stochastic finite element methods (SFEM) have been developed, integrating random analysis theory into traditional finite element methods. This paper proposes a reliability-based framework that combines finite element analysis, response surface modeling, and Monte Carlo simulation to calibrate structural resistance characteristic values under a predetermined target reliability index. This method provides a transparent and quantitative assessment of the effects of resistance uncertainty, representing an improvement over traditional deterministic or semi-probabilistic approaches. Our findings reveal a crucial aspect: when the coefficient of variation reaches a specific threshold, the variability of resistance characteristics is primarily influenced by material properties. However, beyond this threshold, the influence of material properties diminishes, while factors such as geometric deviations and discrepancies between actual and theoretical fundamental assumptions become more prominent. The insights gained from this study provide valuable guidance for addressing uncertainty in the design and implementation of multi-story steel frame structures in practical applications.</p>

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Bridging Theory and Practice: Managing Uncertainties in Steel Frame Engineering with Stochastic Finite Element Method

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Xin Cao,
  • Yiting Qi,
  • Mingjie Cao,
  • Jing Huang,
  • Ailan Yan,
  • Dong Xu

摘要

In complex structural analysis, dealing with uncertainty has become a critical aspect of engineering design and practice. While the finite element method (FEM) remains a fundamental numerical technique for analyzing such structures, deterministic FEM often fails to adequately address the inherent uncertainties in engineering problems. To overcome this limitation, stochastic finite element methods (SFEM) have been developed, integrating random analysis theory into traditional finite element methods. This paper proposes a reliability-based framework that combines finite element analysis, response surface modeling, and Monte Carlo simulation to calibrate structural resistance characteristic values under a predetermined target reliability index. This method provides a transparent and quantitative assessment of the effects of resistance uncertainty, representing an improvement over traditional deterministic or semi-probabilistic approaches. Our findings reveal a crucial aspect: when the coefficient of variation reaches a specific threshold, the variability of resistance characteristics is primarily influenced by material properties. However, beyond this threshold, the influence of material properties diminishes, while factors such as geometric deviations and discrepancies between actual and theoretical fundamental assumptions become more prominent. The insights gained from this study provide valuable guidance for addressing uncertainty in the design and implementation of multi-story steel frame structures in practical applications.