Journal article
Stochastic isogeometric analysis in linear elasticity
Computer methods in applied mechanics and engineering, Vol.364, p.112928
06/01/2020
DOI: 10.1016/j.cma.2020.112928
Abstract
A new stochastic method, integrating spline dimensional decomposition (SDD) and isogeometric analysis (IGA), is proposed for solving stochastic boundary-value problems from linear elasticity. The method, referred to as SDD–IGA, involves Galerkin isogeometric analysis as a deterministic solver for governing partial differential equations and a novel Fourier-like orthogonal spline expansion generated from the analysis-of-variance decomposition of a high-dimensional function. For the stochastic part of the SDD–IGA method, an innovative dimension-reduction integration technique is presented for efficiently calculating the expansion coefficients. Analytical formulae have been derived to calculate the second-moment properties of an SDD–IGA approximation for a general output random variable of interest. Numerical examples demonstrate the capability of a low-order SDD–IGA in efficiently delivering probabilistic solutions with an approximation quality as good as, if not better than, that obtained from a high-order polynomial dimensional decomposition. The proposed SDD–IGA method is most suitable in the presence of locally nonlinear or nonsmooth behavior commonly found in applications.
•A novel fusion between spline dimensional decomposition and isogeometric analysis.•Innovative dimension-reduction integration to estimate the expansion coefficients.•Addresses the curse of dimensionality to the extent possible.•Low-order splines surpass the accuracy of high-order polynomials.•Especially suitable for nonsmooth or highly nonlinear functions.
Details
- Title: Subtitle
- Stochastic isogeometric analysis in linear elasticity
- Creators
- Ramin Jahanbin - University of IowaSharif Rahman - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Computer methods in applied mechanics and engineering, Vol.364, p.112928
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.cma.2020.112928
- ISSN
- 0045-7825
- eISSN
- 1879-2138
- Grant note
- CMMI-1607398 / U.S. National Science Foundation (http://dx.doi.org/10.13039/100000001)
- Language
- English
- Date published
- 06/01/2020
- Academic Unit
- Iowa Technology Institute; Mechanical Engineering
- Record Identifier
- 9984196629902771
Metrics
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