Uncertainty analysis in solid mechanics with uniform and triangular distributions using stochastic perturbation-based Finite Element Method

In this paper theoretical formulation and computational implementation of the Stochastic perturbation-based Finite Element Method (SFEM) for uncertainty analysis in solid mechanics with symmetric non-Gaussian input parameters are presented. Theoretical foundations of the method are based on the gene...

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Vydané v:Finite elements in analysis and design Ročník 200; s. 103648
Hlavný autor: Kamiński, Marcin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.03.2022
Elsevier BV
Predmet:
Finite element analysis
Finite element method
Iterative stochastic perturbation technique
Least squares method
Mechanical systems
Mechanics
Monte-Carlo simulation
Parameter uncertainty
Perturbation
Polynomials
Probability theory
Semi-analytical method
Solid mechanics
Statistical analysis
Stochastic finite element method
Structural response
Triangular probability distribution
Uncertainty analysis
Uniform probability distribution
Stochastic finite element method
Triangular probability distribution
Uniform probability distribution
Iterative stochastic perturbation technique
Monte-Carlo simulation
Semi-analytical method
ISSN:0168-874X, 1872-6925
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Shrnutí:In this paper theoretical formulation and computational implementation of the Stochastic perturbation-based Finite Element Method (SFEM) for uncertainty analysis in solid mechanics with symmetric non-Gaussian input parameters are presented. Theoretical foundations of the method are based on the general order Taylor expansions of all uncertain input parameters and state functions including even orders only. The first four probabilistic characteristics of the structural responses have been derived for symmetrical triangular and uniform probability distributions of random input including probability distribution truncation effect. The Stochastic Finite Element Method implementation has been completed for the displacement version of the FEM using statistically optimized nodal polynomial response bases, and their coefficients are determined using the Least Squares Method using the weighted and non-weighted schemes. Structural responses of several mechanical systems are analyzed using their basic probabilistic characteristics, which have been validated using the probabilistic semi-analytical approach, and also the crude Monte-Carlo simulation. A relatively good coincidence of three probabilistic numerical techniques confirms the applicability of the Stochastic perturbation-based Finite Element Method to study boundary and initial problems in mechanics with uncertainties having uniform and/or triangular probability distributions. •New formulation of the iterative generalized stochastic perturbation technique.•Implementation of the Stochastic Finite Element Method for the triangular PDF.•Implementation of the Stochastic Finite Element Method for the input uniform PDF.•Comparative numerical analysis with Monte-Carlo simulation.•Comparative numerical analysis with the semi-analytical probabilistic method.
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ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2021.103648