Journal article
Stochastic isogeometric analysis on arbitrary multipatch domains by spline dimensional decomposition
Computer methods in applied mechanics and engineering, Vol.393, 114813
04/01/2022
DOI: 10.1016/j.cma.2022.114813
Abstract
This paper presents a new stochastic method by integrating spline dimensional decomposition (SDD) of a high-dimensional random function and isogeometric analysis (IGA) on arbitrary multipatch geometries to solve stochastic boundary-value problems from linear elasticity. The method, referred to as SDD-mIGA, involves (1) analysis-suitable T-splines with significant approximating power for geometrical modeling, random field discretization, and stress analysis; (2) Bézier extraction operator for isogeometric mesh refinement; and (3) a novel Fourier-like expansion of a high-dimensional output function in terms of measure-consistent orthonormalized splines. The proposed method can handle arbitrary multipatch domains in IGA and uses standard least-squares regression to efficiently estimate the SDD expansion coefficients for uncertainty quantification applications. Analytical formulae have been derived to calculate the second-moment properties of an SDD-mIGA approximation for a general output random variable of interest. Numerical results, including those obtained for a 54-dimensional, industrial-scale problem, demonstrate that a low-order SDD-mIGA is capable of efficiently delivering accurate probabilistic solutions when compared with the benchmark results from crude Monte Carlo simulation.
•A novel fusion between spline dimensional decomposition and isogeometric analysis.•Standard least squares for estimating the SDD coefficients.•T-splines for geometric modeling, random field discretization, and stress analysis.•Low-order, low-variate SDD methods provide efficient and accurate results.•Applications to industrially relevant stochastic problems from linear elasticity.
Details
- Title: Subtitle
- Stochastic isogeometric analysis on arbitrary multipatch domains by spline dimensional decomposition
- Creators
- Ramin JahanbinSharif Rahman
- Resource Type
- Journal article
- Publication Details
- Computer methods in applied mechanics and engineering, Vol.393, 114813
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.cma.2022.114813
- ISSN
- 0045-7825
- eISSN
- 1879-2138
- Grant note
- CMMI-1607398; CMMI-1933114 / U.S. National Science Foundation (http://dx.doi.org/10.13039/100000001)
- Language
- English
- Date published
- 04/01/2022
- Academic Unit
- Mechanical Engineering; Iowa Technology Institute
- Record Identifier
- 9984230622302771
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