Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 103051 |
| Fachzeitschrift | Probabilistic Engineering Mechanics |
| Jahrgang | 60 |
| Frühes Online-Datum | 6 Feb. 2020 |
| Publikationsstatus | Veröffentlicht - Apr. 2020 |
Abstract
Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be approximated by the chaos representation by truncating the associated series expansion. Ordinarily, the basis of these series are orthogonal Hermite polynomials which are replaced by B-spline basis functions. Further, the convergence of the B-spline chaos is presented and substantiated by numerical results. Furthermore, it is pointed out, that the B-spline expansion is a generalization of the Legendre multi-element generalized polynomial chaos expansion, which is proven by solving several stochastic differential equations.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Ingenieurwesen (insg.)
- Tief- und Ingenieurbau
- Energie (insg.)
- Kernenergie und Kernkraftwerkstechnik
- Physik und Astronomie (insg.)
- Physik der kondensierten Materie
- Ingenieurwesen (insg.)
- Luft- und Raumfahrttechnik
- Ingenieurwesen (insg.)
- Meerestechnik
- Ingenieurwesen (insg.)
- Maschinenbau
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in: Probabilistic Engineering Mechanics, Jahrgang 60, 103051, 04.2020.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A polynomial chaos method for arbitrary random inputs using B-splines
AU - Eckert, Christoph
AU - Beer, Michael
AU - Spanos, Pol D.
PY - 2020/4
Y1 - 2020/4
N2 - Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be approximated by the chaos representation by truncating the associated series expansion. Ordinarily, the basis of these series are orthogonal Hermite polynomials which are replaced by B-spline basis functions. Further, the convergence of the B-spline chaos is presented and substantiated by numerical results. Furthermore, it is pointed out, that the B-spline expansion is a generalization of the Legendre multi-element generalized polynomial chaos expansion, which is proven by solving several stochastic differential equations.
AB - Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be approximated by the chaos representation by truncating the associated series expansion. Ordinarily, the basis of these series are orthogonal Hermite polynomials which are replaced by B-spline basis functions. Further, the convergence of the B-spline chaos is presented and substantiated by numerical results. Furthermore, it is pointed out, that the B-spline expansion is a generalization of the Legendre multi-element generalized polynomial chaos expansion, which is proven by solving several stochastic differential equations.
KW - Approximation of arbitrary random variables
KW - B-spline chaos
KW - Isogeometric basis
KW - Multi-element generalized polynomial chaos
KW - Stochastic Galerkin
UR - http://www.scopus.com/inward/record.url?scp=85079329995&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2020.103051
DO - 10.1016/j.probengmech.2020.103051
M3 - Article
AN - SCOPUS:85079329995
VL - 60
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
M1 - 103051
ER -