Treatment of multiple input uncertainties using the scaled boundary finite element method. (English) Zbl 1481.65224
Summary: This paper presents a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry. The types of geometric uncertainties considered include the shape and size of inclusions. The inclusions are implicitly defined, and a robust framework is presented to treat the interfaces, which does not require explicit generation of a conforming mesh or special enrichment techniques. A polynomial chaos expansion is used to represent the input and the output uncertainties. The efficiency and the accuracy of the proposed framework are elucidated in detail with a few problems by comparing the results with the conventional Monte Carlo method. A sensitivity analysis based on Sobol’ indices using the developed framework is presented to identify the critical input parameter that has a higher influence on the output response.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
implicitly defined interfaces; level-set method; non-intrusive stochastic finite element method; scaled boundary finite element methodSoftware:
XFEMReferences:
| [1] | Mo, W., Reliability Calculations with the Stochastic Finite Element (2020), Bentham Science Publishers · Zbl 1508.74001 |
| [2] | Noh, H.-C.; Lee, P.-S., Higher order weighted integral stochastic finite element method and simplified first-order application, Int. J. SolidsStruct., 44, 4120-4144 (2007) · Zbl 1186.74107 |
| [3] | Ghanem, R. G.; D. Spanos, P., Stochastic Finite Elements: A Spectral Approach (2012), Springer: Springer New York |
| [4] | Kaminski, M., The Stochastic Perturbation Methods for Computational Mechanics (2013), Wiley · Zbl 1275.74002 |
| [5] | Johari, A.; Sabzi, A., Reliability analysis of foundation settlement by stochastic response surface and random finite element method, Sci.Iran., 24, 6, 2741-2751 (2017) |
| [6] | Sudret, B.; Kiureghian, A. D., Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report, Technical Report (2000) |
| [7] | Liu, Z.; Lesselier, D.; Sudret, B.; Wiart, J., Surrogate modeling based on resampled polynomial chaos expansions, Reliab. Eng. Syst. Saf., 202, 107008 (2020) |
| [8] | Chen, M.; Guo, T.; Chen, C.; Xu, W., Data-driven arbitrary polynomial chaos expansion on uncertainty quantification for real-time hybrid simulation under stochastic ground motions, Exp. Tech., 1-12 (2020) |
| [9] | Ghanem, R. G.; Spanos, P. D., Spectral stochastic finite-element formulation for reliability analysis, J. Eng. Mech., 117, 10, 2351-2372 (1991) |
| [10] | Eldred, M.; Burkardt, J., Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification, 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 976 (2009) |
| [11] | Gilli, L.; Lathouwers, D.; Kloosterman, J. L.; Van der Hagen, T.; Koning, A.; Rochman, D., Uncertainty quantification for criticality problems using non-intrusive and adaptive polynomial chaos techniques, Ann. Nucl. Energy, 56, 71-80 (2013) |
| [12] | Blatman, G.; Sudret, B., Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys., 230, 6, 2345-2367 (2011) · Zbl 1210.65019 |
| [13] | Khatri, K.; Lal, A., Stochastic XFEM based fracture behavior and crack growth analysis of a plate with a hole emanating cracks under biaxial loading, Theor. Appl. Fract. Mech., 96, 1-22 (2018) |
| [14] | Nouy, A.; Schoefs, F.; Moës, N., X-SFEM, a computational technique based on X-FEM to deal with random shapes, Eur. J. Comput. Mech./Revue Européenne de Mécanique Numérique, 16, 2, 277-293 (2007) · Zbl 1208.74184 |
| [15] | Lang, C.; Makhija, D.; Doostan, A.; Maute, K., A simple and efficient preconditioning scheme for heaviside enriched XFEM, Comput. Mech., 54, 5, 1357-1374 (2014) · Zbl 1311.74124 |
| [16] | Song, C.; Wolf, J., Consistent infinitesimal finite-element cell method: three-dimensional vector wave equation, Int. J. Numer. MethodsEng., 39, 2189-2208 (1996) · Zbl 0885.73089 |
| [17] | Long, X.; Jiang, C.; Yang, C.; Han, X.; Gao, W.; Liu, J., A stochastic scaled boundary finite element method, Comput. Methods Appl. Mech.Eng., 308, 23-46 (2016) · Zbl 1439.74445 |
| [18] | Chowdhury, M. S.; Song, C.; Gao, W., Shape sensitivity analysis of stress intensity factors by the scaled boundary finite element method, Eng. Fract. Mech., 116, 13-30 (2014) |
| [19] | Long, X.; Jiang, C.; Han, X.; Gao, W., Stochastic response analysis of the scaled boundary finite element method and application to probabilistic fracture mechanics, Comput. Struct., 153, 185-200 (2015) |
| [20] | Do, D. M.; Gao, W.; Saputra, A. A.; Song, C.; Leong, C. H., The stochastic Galerkin scaled boundary finite element method on random domain, Int. J. Numer. MethodsEng., 110, 3, 248-278 (2017) · Zbl 1365.65252 |
| [21] | Long, X.; Jiang, C.; Han, X.; Gao, W.; Zhang, D., Stochastic fracture analysis of cracked structures with random field property using the scaled boundary finite element method, Int. J. Fract., 195, 1, 1-14 (2015) |
| [22] | Long, X.; Liu, K.; Jiang, C.; Han, X., Probabilistic fracture mechanics analysis of three-dimensional cracked structures considering random field fracture property, Eng. Fract. Mech., 218, 106586 (2019) |
| [23] | Mathew, T. V.; Pramod, A.; Ooi, E. T.; Natarajan, S., An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method, Comput. Methods Appl. Mech.Eng., 367, 112994 (2020) · Zbl 1442.74233 |
| [24] | Johari, A.; Heydari, A., Reliability analysis of seepage using an applicable procedure based on stochastic scaled boundary finite element method, Eng. Anal. Boundary Elem., 94, 44-59 (2018) · Zbl 1403.76081 |
| [25] | Ooi, E. T.; Song, C.; Tin-Loi, F.; Yang, Z., Polygon scaled boundary finite elements for crack propagation modelling, Int. J. Numer. MethodsEng., 91, 3, 319-342 (2012) · Zbl 1246.74062 |
| [26] | Wang, F.; Zhang, D.; Yu, J.; Xu, H., Numerical integration technique in computation of extended finite element method, Advanced Materials Research, vol. 446, 3557-3560 (2012), Trans Tech Publ |
| [27] | Natarajan, S.; Mahapatra, D. R.; Bordas, S. P., Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework, Int. J. Numer. Methods Eng., 83, 3, 269-294 (2010) · Zbl 1193.74153 |
| [28] | Huynh, H. D.; Nguyen, M. N.; Cusatis, G.; Tanaka, S.; Bui, T. Q., A polygonal XFEM with new numerical integration for linear elastic fracture mechanics, Eng. Fract. Mech., 213, 241-263 (2019) |
| [29] | Song, C.; Wolf, J. P., The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-for elastodynamics, Comput. Methods Appl. Mech.Eng., 147, 3-4, 329-355 (1997) · Zbl 0897.73069 |
| [30] | Song, C., The scaled boundary finite element method in structural dynamics, Int. J. Numer. MethodsEng., 77, 8, 1139-1171 (2009) · Zbl 1156.74387 |
| [31] | Wolf, J. P.; Song, C., The scaled boundary finite-element method-a primer: derivations, Comput. Struct., 78, 1-3, 191-210 (2000) |
| [32] | Sukumar, N.; Chopp, D.; Moës, N.; Belytschko, T., Modeling holes and inclusions by level sets in the extended finite-element method, Comput. Methods Appl. Mech.Eng., 190, 46, 6183-6200 (2001) · Zbl 1029.74049 |
| [33] | Kabir, M.; Khazaka, R.; Talukder, M. A.; Ahadi, M.; Chobanyan, E.; Smull, A.; Roy, S.; Notaros, B. M., Non-intrusive pseudo spectral approach for stochastic macromodeling of em systems using deterministic full-wave solvers, 2014 IEEE 23rd Conference on Electrical Performance of Electronic Packaging and Systems, 235-238 (2014), IEEE |
| [34] | Hosder, S.; Walters, R. W.; Balch, M., Point-collocation nonintrusive polynomial chaos method for stochastic computational fluid dynamics, AIAA J., 48, 12, 2721-2730 (2010) |
| [35] | Sheng, H.; Wang, X., Probabilistic power flow calculation using non-intrusive low-rank approximation method, IEEE Trans. Power Syst., 34, 4, 3014-3025 (2019) |
| [36] | Kieslich, C. A.; Boukouvala, F.; Floudas, C. A., Optimization of black-box problems using Smolyak grids and polynomial approximations, J. Global Optim., 71, 4, 845-869 (2018) · Zbl 1405.90107 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
