Full Article - Open Access.

Idioma principal


Sotomayor, R. Reyes; Sarmiento, A. F.; García, D. A.; Mantilla, J.M.; Alvarado, D. A. Garzón-; Patiño, E.;

Full Article:

This work presents the initial approach to a novel method for numerical solution of stochastic differential equations, showing the proper formulation for the stochastic term in a Lagrangian method. The mathematical formulation for the uncertainty properties terms of the model is based in the Karhunen –Loeve expansions used in the spectral stochastic finite element method (SSFEM). The particle method used is the Smoothed Particle Hydrodynamics (SPH), which is modified to represent the randomness of the output variables that are affected by the stochastic inlet properties behavior. This method formulation acquires importance for the solution of high deformation problems where there exists an uncertainty on the model properties.

Full Article:

Palavras-chave: Smoothed Particle Hydrodynamics, Stochastic Spectral Methods, Stochastic Differential Equation.,


DOI: 10.5151/meceng-wccm2012-20002

Referências bibliográficas
  • [1] G. Stefanou, “The stochastic finite element method: Past, present and future,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 9–12, pp. 1031-1051, Feb. 2009.
  • [2] S.-K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-based Structural Design. .
  • [3] G. Lin, X. Wan, C.-H. Su, and G. E. Karniadakis, “Stochastic Computational Fluid Mechanics,” pp. 21-29, 2007.
  • [4] V. A. B. Narayanan and N. Zabaras, “A spectral stochastic finite element implementation of probabilistic advective-diffusive transport with stabilization based on multiscale phenomena,” no. May 2003.
  • [5] D. Ghosh and G. Iaccarino, “Applicability of the spectral stochastic finite element method in time-dependent uncertain problems,” vol. 2, pp. 133-141, 2007.
  • [6] H. C. Elman, O. G. Ernst, D. P. Oõleary, and M. Stewart, “Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering,” vol. 194, pp. 1037-1055, 2005.
  • [7] S. Li and W. K. Liu, Meshfree particle methods, vol. 25, no. 2–3. 2000, pp. 99-101.
  • [8] J. J. Monaghan, “Smoothed particle hydrodynamics,” Reports on Progress in Physics, vol. 68, no. 8, pp. 1703-1759, Aug. 2005.
  • [9] G. R. Liu and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. 2003, p. 44
  • [10] R. Capuzzo-Dolcetta, “A criterion for the choice of the interpolation kernel in smoothed particle hydrodynamics,” Applied Numerical Mathematics, vol. 34, no. 4, pp. 363-371, Aug. 2000.
  • [11] S. S. Observatories, “Kernel Estimates as a Basis for General Particle Methods in Hydrodynamics,” vol. 453, pp. 429-453, 1982.
  • [12] B. Sudret and A. Der Kiureghian, “Stochastic Finite Element Methods and Reliability A State-of-the-Art Report,” no. November, 2000.
  • [13] S. K. Sachdeva, P. B. Nair, and A. J. Keane, “Comparative study of projection schemes for stochastic finite element analysis,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 19–22, pp. 2371-2392, Apr. 2006.
  • [14] S. Huang, S. Mahadevan, and R. Rebba, “Collocation-based stochastic finite element analysis for random field problems,” Probabilistic Engineering Mechanics, vol. 22, no. 2, pp. 194-205, Apr. 2007.
  • [15] R. Ghanem, “Polynomial Chaos in Stochastic Finite Elements,” no. 89, 1990.
  • [16] R. Ghanem, “Ingredients for a general purpose stochastic finite elements implementation,” vol. 7825, no. 98, 1999.
  • [17] M. B. Liu and G. R. Liu, “Smoothed Particle Hydrodynamics ( SPH ): an Overview and Recent Developments,” Methods, pp. 25-76, 2010.
  • [18] J. J. Monaghan, “Smoothed Particle Hydrodynamics and Its Diverse Applications,” Annual Review of Fluid Mechanics, vol. 44, no. 1, pp. 323-346, Jan. 2012.
  • [19] P. Cleary, “Conduction Modelling Using Smoothed Particle Hydrodynamics,” Journal of Computational Physics, vol. 148, no. 1, pp. 227-264, Jan. 1999.
  • [20] D. J. Price, “Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH,” no. August 2008.
  • [21] J. J. Monaghan, “On the problem of penetration in particle methods,” Journal of Computational Physics, vol. 82, no. 1, pp. 1-15, May 1989.
Como citar:

Sotomayor, R. Reyes; Sarmiento, A. F.; García, D. A.; Mantilla, J.M.; Alvarado, D. A. Garzón-; Patiño, E.; "PARTICLE METHOD FOR THE SOLUTION OF STOCHASTIC PROBLEMS: FORMULATION", p. 4607-4617 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-20002

últimos 30 dias | último ano | desde a publicação