The Least Squares Stochastic Finite Element Method in Structural Stability Analysis of Steel Skeletal Structures
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Department of Structural Mechanics Faculty of Civil Engineering Architecture and Environmental Engineering Al. Politechniki 6, 90-924 Łódź, POLAND
Online publication date: 2015-05-23
Publication date: 2015-05-01
International Journal of Applied Mechanics and Engineering 2015;20(2):299-318
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.
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