Abstract
This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of positive-definite random elasticity matrices was first used, involving two stochastic parameters: the mean value and a dispersion parameter. In order to compute the nonlinear effects between load and lateral deflection for the buckling problem of the column, a finite element framework combining a Newton-Raphson solver was developed. The finite element tool was validated by comparing the as-obtained critical buckling loads with those from Euler’s formula at zero-fluctuation of the elasticity matrix. Three levels of fluctuations of material uncertainties were then propagated through the validated finite element tool using the probabilistic method as a stochastic solver. Results showed that uncertain material properties considerably influenced the buckling behavior of columns under axial loading. The coefficient of variation of a critical buckling load over 500 realizations were 15.477%, 26.713% and 41.555% when applying dispersion parameters of 0.3, 0.5 and 0.7, respectively. The 95% confidence intervals of column buckling response were finally given. The methodology of modeling presented in this paper is a potential candidate for accounting material uncertainties with some instabilities of structural elements under compression.
Highlights
Various parameters of structural elements are uncertain in nature, for instance, the length of structural components [1]; geometry of the cross-section [2]; boundary conditions [3]; loads [4]; and especially mechanical properties of materials [5,6,7,8,9,10,11,12]
In order to fully characterize the mechanical behavior of structural elements, it is necessary to take into account the uncertainties of material properties in modeling and simulation, as they become relevant
A probabilistic model was introduced in order to quantify the propagation of uncertainties related to the elasticity matrices of materials constituting the structural element under compression in finite displacement
Summary
Various parameters of structural elements are uncertain in nature, for instance, the length of structural components [1]; geometry of the cross-section [2]; boundary conditions [3]; loads [4]; and especially mechanical properties of materials [5,6,7,8,9,10,11,12]. Shi et al [5] found that the ultimate stress of steel circular tubes under axial load was smaller, that is, 0.8–0.9 times, than the corresponding stress calculated by the two standards Eurocode BS EN. 1993-1-12 [16] and ANSI/AISC 360-10 [17] for steel structures. This means instability of steel tubes appears even before estimation that is provided by the two standards mentioned. In order to fully characterize the mechanical behavior of structural elements, it is necessary to take into account the uncertainties of material properties in modeling and simulation, as they become relevant
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