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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Vydáno v:	Finite elements in analysis and design Ročník 200; s. 103648
Hlavní autor:	Kamiński, Marcin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.03.2022 Elsevier BV
Témata:	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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Abstract	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.
AbstractList	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. 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.
ArticleNumber	103648
Author	Kamiński, Marcin
Author_xml	– sequence: 1 givenname: Marcin surname: Kamiński fullname: Kamiński, Marcin email: Marcin.Kaminski@p.lodz.pl organization: Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, Al. Politechniki 6, 90-924, Łódź, Poland
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Cites_doi	10.1109/9.119632 10.1016/j.jeconom.2008.12.014 10.1016/0167-4730(89)90003-9 10.1007/s11012-015-0133-0 10.1007/s004660050300 10.1002/nme.5638 10.1016/j.cma.2014.06.014 10.1016/j.cma.2007.12.011 10.1002/nme.1620231004 10.1098/rspa.1999.0446 10.1007/BF02736747 10.1061/(ASCE)0733-9364(2000)126:1(29) 10.1002/nme.106 10.1016/j.enganabound.2016.06.002 10.1002/nme.4976 10.1016/j.finel.2013.10.003 10.1007/s10955-012-0422-0 10.3846/13926292.2012.664571 10.1016/j.finel.2015.05.001 10.1016/j.cma.2008.11.007 10.1016/j.compstruc.2007.05.041
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Keywords	Stochastic finite element method Triangular probability distribution Uniform probability distribution Iterative stochastic perturbation technique Monte-Carlo simulation Semi-analytical method
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References	Hu, Cui, Feng, Li (bib20) 2016; 70 Sakata, Ashida, Zako (bib15) 2008; 197 Spall (bib6) 1998; 19 Liu, Belytschko, Mani (bib2) 1986; 23 Hinch (bib4) 1995 Kececioglu (bib22) 2002 Jodrá (bib24) 2012; 17 Papadopoulos, Giovanis (bib19) 2017 Xia, Yu, Liu (bib21) 2014; 79 Ostoja-Starzewski (bib26) 2007 Hurtado, Barbat (bib12) 1998; 5 Lucarini (bib33) 2012; 146 Peng, Geng, Liyan, Liu, Lam (bib10) 1998; 21 Yamazki, Shinozuka (bib13) 1998; 114 Roberts, Spanos (bib14) 1990 (bib29) 1998 Gumbel (bib25) 1935; 5 Kamiński (bib8) 2013 Bellman (bib3) 1972 Kamiński (bib32) 2018; 113 Oden, Becker, Carey (bib30) 1981 Kamiński (bib9) 2015; 104 Kamiński, Corigliano (bib28) 2015; 50 Park, Bera (bib36) 2009; 150 Kleiber, Hien (bib1) 1992 Stefanou (bib18) 2009; 198 Spall (bib7) 1992; 37 Settineri, Falsone (bib17) 2014; 278 Ostoja-Starzewski (bib27) 1999; 455 Sakata, Torigoe (bib11) 2015; 102–103 Christensen (bib31) 1979 Moeller, Beer (bib16) 2008; 86 Melchers (bib34) 1989; 6 Back, Boles, Fry (bib23) 2000; 126 Nayfeh (bib5) 1973 Rahman, Rao (bib35) 2001; 50 Gumbel (10.1016/j.finel.2021.103648_bib25) 1935; 5 Nayfeh (10.1016/j.finel.2021.103648_bib5) 1973 Yamazki (10.1016/j.finel.2021.103648_bib13) 1998; 114 Oden (10.1016/j.finel.2021.103648_bib30) 1981 Bellman (10.1016/j.finel.2021.103648_bib3) 1972 Hurtado (10.1016/j.finel.2021.103648_bib12) 1998; 5 Jodrá (10.1016/j.finel.2021.103648_bib24) 2012; 17 Lucarini (10.1016/j.finel.2021.103648_bib33) 2012; 146 Christensen (10.1016/j.finel.2021.103648_bib31) 1979 Peng (10.1016/j.finel.2021.103648_bib10) 1998; 21 Kamiński (10.1016/j.finel.2021.103648_bib9) 2015; 104 Spall (10.1016/j.finel.2021.103648_bib6) 1998; 19 Kececioglu (10.1016/j.finel.2021.103648_bib22) 2002 Kamiński (10.1016/j.finel.2021.103648_bib8) 2013 Spall (10.1016/j.finel.2021.103648_bib7) 1992; 37 Papadopoulos (10.1016/j.finel.2021.103648_bib19) 2017 Settineri (10.1016/j.finel.2021.103648_bib17) 2014; 278 Park (10.1016/j.finel.2021.103648_bib36) 2009; 150 Roberts (10.1016/j.finel.2021.103648_bib14) 1990 Kamiński (10.1016/j.finel.2021.103648_bib28) 2015; 50 Rahman (10.1016/j.finel.2021.103648_bib35) 2001; 50 Liu (10.1016/j.finel.2021.103648_bib2) 1986; 23 Stefanou (10.1016/j.finel.2021.103648_bib18) 2009; 198 Hu (10.1016/j.finel.2021.103648_bib20) 2016; 70 Sakata (10.1016/j.finel.2021.103648_bib11) 2015; 102–103 Hinch (10.1016/j.finel.2021.103648_bib4) 1995 Xia (10.1016/j.finel.2021.103648_bib21) 2014; 79 Moeller (10.1016/j.finel.2021.103648_bib16) 2008; 86 Ostoja-Starzewski (10.1016/j.finel.2021.103648_bib27) 1999; 455 Ostoja-Starzewski (10.1016/j.finel.2021.103648_bib26) 2007 Melchers (10.1016/j.finel.2021.103648_bib34) 1989; 6 Kleiber (10.1016/j.finel.2021.103648_bib1) 1992 Back (10.1016/j.finel.2021.103648_bib23) 2000; 126 (10.1016/j.finel.2021.103648_bib29) 1998 Sakata (10.1016/j.finel.2021.103648_bib15) 2008; 197 Kamiński (10.1016/j.finel.2021.103648_bib32) 2018; 113
References_xml	– volume: 70 start-page: 40 year: 2016 end-page: 55 ident: bib20 article-title: Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method publication-title: Eng. Anal. Bound. Elem. – volume: 102–103 start-page: 74 year: 2015 end-page: 84 ident: bib11 article-title: A successive perturbation-based multiscale stochastic analysis method for composite materials publication-title: Finite Elem. Anal. Des. – year: 1995 ident: bib4 article-title: Perturbation Methods – volume: 6 start-page: 3 year: 1989 end-page: 10 ident: bib34 article-title: Importance sampling in structural systems publication-title: Struct. Saf. – volume: 23 start-page: 1831 year: 1986 end-page: 1845 ident: bib2 article-title: Random field finite elements publication-title: Int. J. Numer. Methods Eng. – volume: 198 start-page: 1031 year: 2009 end-page: 1051 ident: bib18 article-title: The stochastic finite element method: past, present and future publication-title: Comput. Methods Appl. Mech. Eng. – year: 1998 ident: bib29 publication-title: Handbook of Computational Solid Mechanics – volume: 37 start-page: 332 year: 1992 end-page: 341 ident: bib7 article-title: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation publication-title: IEEE Trans. Automat. Contr. – year: 2017 ident: bib19 article-title: Stochastic Finite Element Methods. Introduction – volume: 79 start-page: 9 year: 2014 end-page: 21 ident: bib21 article-title: Transformed perturbation stochastic finite element method for static response analysis of stochastic structures publication-title: Finite Elem. Anal. Des. – year: 1979 ident: bib31 article-title: Mechanics of Composite Materials – volume: 146 start-page: 774 year: 2012 end-page: 786 ident: bib33 article-title: Stochastic perturbations to dynamical systems: a response theory approach publication-title: J. Stat. Phys. – year: 1990 ident: bib14 article-title: Random Vibration and Statistical Linearization – volume: 5 start-page: 3 year: 1998 end-page: 30 ident: bib12 article-title: Monte-Carlo techniques in computational stochastic mechanics publication-title: Arch. Comput. Methods Eng. – volume: 197 start-page: 1953 year: 2008 end-page: 1964 ident: bib15 article-title: Kriging-based approximate stochastic homogenization analysis for composite materials publication-title: Comput. Methods Appl. Mech. Eng. – volume: 17 start-page: 281 year: 2012 end-page: 292 ident: bib24 article-title: Computing the asymptotic expansion of the median of the Erlang distribution publication-title: Math. Model Anal. – volume: 114 year: 1998 ident: bib13 article-title: Neumann expansion for stochastic finite element analysis publication-title: J. Eng. Mech. ASCE – year: 1972 ident: bib3 article-title: Perturbation Techniques in Mathematics, Physics and Engineering – year: 1973 ident: bib5 article-title: Perturbation Methods – volume: 455 start-page: 3189 year: 1999 end-page: 3199 ident: bib27 article-title: Microstructural disorder, mesoscale finite elements and macroscopic response publication-title: Proc. Roy. Soc. Lond. A – volume: 5 start-page: 115 year: 1935 end-page: 158 ident: bib25 article-title: Les valeurs extrêmes des distributions statistiques publication-title: Ann. Inst. Henri Poincaré – volume: 50 start-page: 1841 year: 2015 end-page: 1853 ident: bib28 article-title: Numerical solution of the Duffing equation with random coefficients publication-title: Meccanica – volume: 50 start-page: 1969 year: 2001 end-page: 1991 ident: bib35 article-title: A perturbation method for stochastic meshless analysis in elastostatics publication-title: Int. J. Numer. Methods Eng. – volume: 21 start-page: 253 year: 1998 end-page: 261 ident: bib10 article-title: A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending publication-title: Comput. Mech – volume: 104 start-page: 1038 year: 2015 end-page: 1060 ident: bib9 article-title: On iterative scheme in determination of the probabilistic moments of the structural response in the Stochastic perturbation-based Finite Element Method publication-title: Int. J. Numer. Methods Eng. – volume: 150 start-page: 219 year: 2009 end-page: 230 ident: bib36 article-title: Maximum entropy autoregressive conditional heteroskedasticity model publication-title: J. Econom. – year: 2013 ident: bib8 article-title: The Stochastic Perturbation Method for Computational Mechanics – volume: 19 start-page: 482 year: 1998 end-page: 492 ident: bib6 article-title: An overview of the simultaneous perturbation method for efficient optimization publication-title: Johns Hopkins APL Tech. Dig. – year: 2007 ident: bib26 article-title: Microstructural Randomness and Scaling in Mechanics of Materials – volume: 113 start-page: 834 year: 2018 end-page: 857 ident: bib32 article-title: Tsallis entropy in dual homogenization of random composites using the Stochastic Finite Element Method publication-title: Int. J. Num. Meth. – year: 1992 ident: bib1 article-title: The Stochastic Finite Element Method – volume: 278 start-page: 828 year: 2014 end-page: 852 ident: bib17 article-title: An APDM-based method for the analysis of systems with uncertainties publication-title: Comput. Methods Appl. Mech. Eng. – volume: 86 start-page: 1024 year: 2008 end-page: 1041 ident: bib16 article-title: Engineering computation under uncertainty – capabilities of non-traditional models publication-title: Comput. Struct – year: 1981 ident: bib30 article-title: Finite Elements: an Introduction – volume: 126 start-page: 29 year: 2000 end-page: 37 ident: bib23 article-title: Defining triangular probability distributions from historical cost data publication-title: ASCE J. Constr. Eng. Manag. – year: 2002 ident: bib22 article-title: Reliability Engineering Handbook – year: 1992 ident: 10.1016/j.finel.2021.103648_bib1 – year: 2013 ident: 10.1016/j.finel.2021.103648_bib8 – volume: 37 start-page: 332 year: 1992 ident: 10.1016/j.finel.2021.103648_bib7 article-title: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation publication-title: IEEE Trans. Automat. Contr. doi: 10.1109/9.119632 – volume: 150 start-page: 219 issue: 2 year: 2009 ident: 10.1016/j.finel.2021.103648_bib36 article-title: Maximum entropy autoregressive conditional heteroskedasticity model publication-title: J. Econom. doi: 10.1016/j.jeconom.2008.12.014 – volume: 6 start-page: 3 issue: 1 year: 1989 ident: 10.1016/j.finel.2021.103648_bib34 article-title: Importance sampling in structural systems publication-title: Struct. Saf. doi: 10.1016/0167-4730(89)90003-9 – volume: 50 start-page: 1841 issue: 7 year: 2015 ident: 10.1016/j.finel.2021.103648_bib28 article-title: Numerical solution of the Duffing equation with random coefficients publication-title: Meccanica doi: 10.1007/s11012-015-0133-0 – volume: 21 start-page: 253 issue: 6 year: 1998 ident: 10.1016/j.finel.2021.103648_bib10 article-title: A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending publication-title: Comput. Mech. doi: 10.1007/s004660050300 – year: 1990 ident: 10.1016/j.finel.2021.103648_bib14 – volume: 19 start-page: 482 issue: 4 year: 1998 ident: 10.1016/j.finel.2021.103648_bib6 article-title: An overview of the simultaneous perturbation method for efficient optimization publication-title: Johns Hopkins APL Tech. Dig. – year: 2017 ident: 10.1016/j.finel.2021.103648_bib19 – volume: 113 start-page: 834 issue: 5 year: 2018 ident: 10.1016/j.finel.2021.103648_bib32 article-title: Tsallis entropy in dual homogenization of random composites using the Stochastic Finite Element Method publication-title: Int. J. Num. Meth. doi: 10.1002/nme.5638 – year: 1972 ident: 10.1016/j.finel.2021.103648_bib3 – volume: 278 start-page: 828 year: 2014 ident: 10.1016/j.finel.2021.103648_bib17 article-title: An APDM-based method for the analysis of systems with uncertainties publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.06.014 – year: 1973 ident: 10.1016/j.finel.2021.103648_bib5 – volume: 197 start-page: 1953 issue: 21–24 year: 2008 ident: 10.1016/j.finel.2021.103648_bib15 article-title: Kriging-based approximate stochastic homogenization analysis for composite materials publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2007.12.011 – volume: 5 start-page: 115 issue: 2 year: 1935 ident: 10.1016/j.finel.2021.103648_bib25 article-title: Les valeurs extrêmes des distributions statistiques publication-title: Ann. Inst. Henri Poincaré – volume: 23 start-page: 1831 issue: 10 year: 1986 ident: 10.1016/j.finel.2021.103648_bib2 article-title: Random field finite elements publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620231004 – volume: 455 start-page: 3189 year: 1999 ident: 10.1016/j.finel.2021.103648_bib27 article-title: Microstructural disorder, mesoscale finite elements and macroscopic response publication-title: Proc. Roy. Soc. Lond. A doi: 10.1098/rspa.1999.0446 – volume: 5 start-page: 3 issue: 1 year: 1998 ident: 10.1016/j.finel.2021.103648_bib12 article-title: Monte-Carlo techniques in computational stochastic mechanics publication-title: Arch. Comput. Methods Eng. doi: 10.1007/BF02736747 – volume: 126 start-page: 29 issue: 1 year: 2000 ident: 10.1016/j.finel.2021.103648_bib23 article-title: Defining triangular probability distributions from historical cost data publication-title: ASCE J. Constr. Eng. Manag. doi: 10.1061/(ASCE)0733-9364(2000)126:1(29) – volume: 50 start-page: 1969 year: 2001 ident: 10.1016/j.finel.2021.103648_bib35 article-title: A perturbation method for stochastic meshless analysis in elastostatics publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.106 – volume: 70 start-page: 40 year: 2016 ident: 10.1016/j.finel.2021.103648_bib20 article-title: Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2016.06.002 – year: 1998 ident: 10.1016/j.finel.2021.103648_bib29 – year: 1979 ident: 10.1016/j.finel.2021.103648_bib31 – volume: 104 start-page: 1038 issue: 11 year: 2015 ident: 10.1016/j.finel.2021.103648_bib9 article-title: On iterative scheme in determination of the probabilistic moments of the structural response in the Stochastic perturbation-based Finite Element Method publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.4976 – volume: 79 start-page: 9 year: 2014 ident: 10.1016/j.finel.2021.103648_bib21 article-title: Transformed perturbation stochastic finite element method for static response analysis of stochastic structures publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2013.10.003 – volume: 146 start-page: 774 issue: 4 year: 2012 ident: 10.1016/j.finel.2021.103648_bib33 article-title: Stochastic perturbations to dynamical systems: a response theory approach publication-title: J. Stat. Phys. doi: 10.1007/s10955-012-0422-0 – year: 2007 ident: 10.1016/j.finel.2021.103648_bib26 – year: 1981 ident: 10.1016/j.finel.2021.103648_bib30 – volume: 17 start-page: 281 issue: 2 year: 2012 ident: 10.1016/j.finel.2021.103648_bib24 article-title: Computing the asymptotic expansion of the median of the Erlang distribution publication-title: Math. Model Anal. doi: 10.3846/13926292.2012.664571 – volume: 102–103 start-page: 74 year: 2015 ident: 10.1016/j.finel.2021.103648_bib11 article-title: A successive perturbation-based multiscale stochastic analysis method for composite materials publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2015.05.001 – year: 1995 ident: 10.1016/j.finel.2021.103648_bib4 – year: 2002 ident: 10.1016/j.finel.2021.103648_bib22 – volume: 198 start-page: 1031 issue: 9–12 year: 2009 ident: 10.1016/j.finel.2021.103648_bib18 article-title: The stochastic finite element method: past, present and future publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2008.11.007 – volume: 114 year: 1998 ident: 10.1016/j.finel.2021.103648_bib13 article-title: Neumann expansion for stochastic finite element analysis publication-title: J. Eng. Mech. ASCE – volume: 86 start-page: 1024 year: 2008 ident: 10.1016/j.finel.2021.103648_bib16 article-title: Engineering computation under uncertainty – capabilities of non-traditional models publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2007.05.041
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Snippet	In this paper theoretical formulation and computational implementation of the Stochastic perturbation-based Finite Element Method (SFEM) for uncertainty...
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SubjectTerms	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
Title	Uncertainty analysis in solid mechanics with uniform and triangular distributions using stochastic perturbation-based Finite Element Method
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