The Least Squares Stochastic Finite Element Method in Structural Stability Analysis of Steel Skeletal Structures

Abstract

The main purpose of this work is to verify the influence of the weighting procedure in the Least Squares Method on the probabilistic moments resulting from the stability analysis of steel skeletal structures. We discuss this issue also in the context of the geometrical nonlinearity appearing in the Stochastic Finite Element Method equations for the stability analysis and preservation of the Gaussian probability density function employed to model the Young modulus of a structural steel in this problem. The weighting procedure itself (with both triangular and Dirac-type) shows rather marginal influence on all probabilistic coefficients under consideration. This hybrid stochastic computational technique consisting of the FEM and computer algebra systems (ROBOT and MAPLE packages) may be used for analogous nonlinear analyses in structural reliability assessment.

On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures

“…There are several ways to choose the Δb/b 0 ratio [57,60] as well as this interval's discretization both in terms of uniformity and the number of trial points [29,61]. Here, uniform interval subdivision with n = 11 trial points and the ratio Δb/b 0 = 0.05 was applied (Figure 2) as the most frequently used.…”

Various Response Functions in Lattice Domes Reliability Via Analytical Integration and Finite Element Method

“… . There are several ways to choose the / 0 b b  ratio as well as this interval subdivision both in terms of uniformity and the number of trial points (Kamiński and Szafran, [10]; Kamiński and Świta, [11]; [12]). In the first part of the analysis, an influence of some various configurations (Tab.1) on the final results has been examined.…”

“…[13]; [14]). The Least Squares Method, as well as its weighted version (WLSM), have also been used to obtain commonly applied polynomial responses w(b) (Kamiński and Szafran, [10]; Kamiński and Świta, [11]; [12]). In the latter method, the values computed for the expectation of the Young modulus (210 GPa) have been recognized as crucial.…”

“…In the latter method, the values computed for the expectation of the Young modulus (210 GPa) have been recognized as crucial. Their weights (10) have been assumed as the sum of the rest ten weights of equivalent results (equals 1).…”