An adaptive recursive SBFE algorithm for the statistical analysis of stochastic viscoelastic problems

Integrating the advantages of Taylor series expansion and TPAA -SBFEM (temporally adaptive recursive algorithm-scaled boundary finite element method), two efficient algorithms are proposed to solve stochastic viscoelastic problems, in which the constitutive parameters are presented by random variabl...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 395; S. 114878
Hauptverfasser: Wang, Chongshuai, Long, Xiangyun, He, Yiqian, Yang, Haitian, Han, Xu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 15.05.2022
Elsevier BV
Schlagworte:
Accuracy
Adaptive algorithms
Algorithms
Fields (mathematics)
Finite element method
K-L expansion
Monte Carlo simulation
Random fields
Random variables
SBFEM
Series expansion
Statistical analysis
Statistical estimation
Stochastic processes
Stochastic viscoelastic problems
Taylor series
Temporally recursive adaptive computation
Viscoelasticity
K-L expansion
Stochastic viscoelastic problems
Statistical estimation
Random fields
Temporally recursive adaptive computation
SBFEM
ISSN:0045-7825
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Zusammenfassung:Integrating the advantages of Taylor series expansion and TPAA -SBFEM (temporally adaptive recursive algorithm-scaled boundary finite element method), two efficient algorithms are proposed to solve stochastic viscoelastic problems, in which the constitutive parameters are presented by random variables or random fields. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of deterministic problem, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the Taylor series expansion, which is able to provide a stable temporal solution accuracy for different step sizes. For the random variable model, SBFEM appears in BEM form with the unknowns only along the boundary of a super element; for the random field model which is approximated by Karhunen–Loève (K–L) expansion, SBFEM operates as FEM with its own advantages. Numerical tests are conducted to verify the accuracy and efficiency of the proposed approach, in comparison with Monte Carlo simulation, computational cost can significantly be reduced with sufficient accuracy for the stochastic viscoelastic problems with relatively small random dispersity. •Two algorithms are proposed for viscoelastic problems with random variables or fields.•TPAA-SBFE provides a reliable platform to gain the solution of deterministic problems.•The temporal accuracy of solution can be secure via an adaptive computing.•SBFEM appears in FE and BE forms, respectively, flexible for the stochastic analysis.
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ISSN:0045-7825
DOI:10.1016/j.cma.2022.114878