Stability analysis of the single-layer dome in probabilistic description by the Monte Carlo method

Abstract

The paper shows the application of the Monte Carlo method to the stability analysis of a single-layer shallow (h/d = 0.04) dome modelled with frame elements. Structures of this type are characterized by strong nonlinearity, consequently, they are extremely susceptible to stability loss resulting from the node snap-through. It is necessary to perform a nonlinear stability analysis that allows determination of limit points related to that mode of stability failure. This paper shows that with the reliability analysis methods, it is possible to trace the failure probability level while moving along the load-displacement path towards the limit point.

The probabilistic model for system reliability analysis of a steel plane and spatial trusses

“…Instead of this fact, as the method is not easy to implement, especially for big structures (with many possible causative elements) its application is limited. Nevertheless, in the last years the system reliability analysis has been successively becomming more popular, especially for steel truss analysis (Mochocki et al, 2018;Park et al, 2004, Zabojszcza andRadoń, 2020).…”

The safety of steel space truss under fire conditions according to the system reliability analysis.

“…The reliability index was introduced because its value is easier for people to compare than the probability of failure, which in the case of civil engineering is very low. There are numerous methods that are used to estimate the reliability index, including approximation methods (FORM, SORM) [2][3][4], simulation methods (Monte Carlo, Subset Simulation) [5][6][7], Stochastic Finite Element Method (SFEM) [8][9][10], Response Surface Method [11][12][13] or Artificial Neural Networks [14][15][16]. The biggest problem with most of mentioned method is that they are appropriate for analysis of individual limit state functions.…”

Optimization of Steel Roof Framing Taking into Account the Random Nature of Design Parameters

“…The role of partial safety factors is to ensure the required level of structural reliability. Probabilistic approximation (FORM [ 2 , 3 , 4 , 5 , 6 ], SORM [ 7 , 8 , 9 ]) or simulation (Monte Carlo, Importance Sampling [ 10 , 11 , 12 , 13 , 14 ]) are an extension of the semi-probabilistic limit state method. The probabilistic approach allows a more accurate and more realistic description of materials, geometric parameters and loads, acting on structures by specifying the type of probability distribution and its parameters.…”