Stochastic Dynamic Analysis of Multilayer Saturated Porous Cylindrical Structures Using the Meshless Local Petrov-Galerkin Method

Document Type : Original Article

Authors

1 Ferdowsi University of Mashhad

2 Quchan University of Technology

Abstract

The stochastic meshless local Petrov–Galerkin method is employed for dynamic analysis of multilayer cylinders made of fully saturated porous materials considering uncertainties in the constitutive mechanical properties. The multilayer porous cylinder is assumed to be under shock loading. To approximate the trial functions in the radial point interpolation method  (RPIM), the radial basis functions (RBFs) are utilized. The Monte Carlo simulation is used to generate the random fields for mechanical properties. The results are obtained for various random variables, which are simulated by uniform, normal and lognormal probability density functions with various coefficients of variation (COV), changing from 0 to 20%. The obtained results from the presented stochastic analysis are compared to those obtained from the analysis considering deterministic mechanical properties. The results show that the uncertainty in mechanical properties has a significant effect on the structural responses, especially for big values of COVs.

Keywords

Main Subjects

References

  1. Gingold, R. A., and Monaghan, J. J., “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars”, Monthly Notices of the Royal Astronomical Society, Vol. 181, pp. 375-389, 1977.
  2. Rabczuk, T., Belytschko, T., and Xiao, S. P., “Stable Particle Methods Based on Lagrangian Kernels”, Computer Methods in Applied Mechanics and Engineering, 193, pp. 1035-1063, 2004.
  3. Dilts, G. A., “Moving Least Squares Particle Hydrodynamics: Consistency and Stability”, International Journal for Numerical Methods in Engineering, 44, pp. 1115-1155, 2000.
  4. Liu, W. K., Jun, S., Li, S., Jonathan, A., and Belytschko, T., “Reproducing Kernel Particle Methods for Structural Dynamics”, International Journal for Numerical Methods in Engineering, 38, pp. 1655–1679, 1995.
  5. Liszka, T., and Orkisz, J., “The Finite Difference Method for Arbitrary Meshes”, Computer and Structures, 5, pp. 45–58, 1980.
  6. Strouboulis, T., Copps, K., and Babu, I., “An Example of It’s Implementation and Illustration of It’s Performance”, International Journal for Numerical Methods in Engineering, 47, pp. 1401–1417, 2000.
  7. Onate, E., Idelsohn, S., Zienkiewicz, O. C., and Taylor R. L., “A Finite Point Method in Computational Mechanics, Application to Convective Transport and Fluid Flow”, International Journal for Numerical Methods in Engineering, 39, pp. 3839–3866, 1996.
  8. Onate, E., Idelsohn, S., Zienkiewicz, O. C., Taylor R.L., and Sacco, C., “A Stabilized Finite Point Method for Analysis of Fluid Mechanics Problems”, Computer Methods in Applied Mechanics and Engineering, 139, pp. 315–346, 1996.
  9. Belystchko, T., Liu, Y. Y., and Gu, L., “Element-Free Galerkin Methods”, International Journal for Numerical Methods in Engineering, 37, pp. 229–256, 1994.
  10. Lam, K. Y., Wang, Q. X., and Li, H., “A Novel Meshless Approach – Local Kriging (LoKriging) Method with Two-Dimensional Structural Analysis”, Computational Mechanics, 33, pp. 1475–1480, 2004.
  11. Gu, Y. T., and Liu, G. R., “A Local Point Interpolation Method for Static and Dynamic Analysis of Thin Beams”, Computer Methods in Applied Mechanics and Engineering, 190, pp. 5515–5528, 2001.
  12. Liu, G. R., and Gu, Y. T., “A Local Radial Point Interpolation Method (LRPIM) for Free Vibration Analyses of 2-D Solids”, Journal of Sound and vibration, 246, pp. 29–46, 2001.
  13. Yongchang, C., and Hehua, Z., "A Meshless Local Natural Neighbour Interpolation Method for Stress Analysis of Solids", Engineering Analysis with Boundary Elements, Vol. 28, No. 1, pp. 607-613, 2004.
  14. Atluri, S. N., and Zhu, T., “A New Meshless Local Petrov–Galerkin (MLPG) Approach in Computational Mechanics”, Computational Mechanics, 22, pp. 117–127, 1998.
  15. Atluri, S. N., and Zhu, T., “The Meshless Local Petrov–Galerkin (MLPG) Approach for Solving Problems in Elasto-Statics”, Computational Mechanics, Vol. 25, pp. 169–179, 2000.
  16. Atluri, S. N., and Shen, S., “The Meshless Local Petrov–Galerkin (MLPG) Method: A Simple and Less-Ccostly Alternative to The Finite Element and Boundary Element Methods”, Computer Modeling in Engineering and Sciences, 3, pp. 11–51, 2002.
  17. Lin, H., and Atluri, S. N., “The Meshless Local Petrov-Galerkin (MLPG) Method for Convection-Diffusion Problems”, Computer Modeling in Engineering and Sciences, 21, pp 45-60, 2000.
  18. Kim, H. G., and Atluri, S. N., “Arbitrary Placement of Secondary Nodes, And Error Control, in the Meshless Local Petrov–Galerkin Method”, Computer Modeling in Engineering and Sciences, 3, pp. 11-32, 2000.
  19. Ching, H. K., and Barta, R.C., “Determination of Crack Tip Fields in Linear Elastostatics by Meshless Local Petrov–Galerkin Method”, Computer Modeling in Engineering and Sciences, 2, pp. 273-290, 2001.
  20. Lin, H., and Atluri, S. N., “The Meshless Local Petrov–Galerkin (MLPG) Method for Solving Incompressive Navier-Stokers Equations”, Computer Modeling in Engineering and Sciences, 2, pp. 117-142, 2001.
  21. Cho, J. Y., Kim, H. G., and Atluri, S. N., “Analysis of Shear Flexible Beams, Using the Meshless Local Petrov–Galerkin Method Based on Locking-Free Formulation”, Computational Engineering and Science, 23, pp. 1404–1409, 2001.
  22. Gu, Y. T., and Liu, G. R., “A Meshless Local Petrov–Galerkin (MLPG) Formulation for Static and Free Vibration Analyses of Thin Plates”, Computational Engineering and Science, 4, pp. 463–476, 2001.
  23. Long, S. Y., and Atluri, S.N., “A Meshless Local Petrov-Galerkin Method for Solving the Bending Problem of a Thin Plate”, Computational Engineering and Science, 26, pp. 104–119, 2002.
  24. Sladek, J., Stanak, P., Han, Z. D., Sladek, V., and Atluri, S. N., “Applications of the MLPG Method in Engineering & Sciences: A Review”, Computer Modeling in Engineering & Sciences, 92, pp. 423–475, 2013.
  25. Ferreira, A. J. M., Batra, R. C., Roque, C. M. C., Qian, L. F., and Jorge, R. M. N., “Natural Frequencies of Functionally Graded Plates by a Meshless Method”, Composite Structures, 75, pp. 593–600, 2006.
  26. Zhu, P., and Liew, K. M., “Free Vibration Analysis of Moderately Thick Functionally Graded Plates by Local Kriging Meshless Method”, Composite Structures, 93, pp. 2925–2944, 2011.
  27. Rezaei Mojdehi, A., Darvizeh, A., Basti, A., and Rajabi, H., “Three Dimensional Static and Dynamic Analysis of Thick Functionally Graded Plates by the Meshless Local Petrov-Galerkin (MLPG) Method”, Engineering Analysis with Boundary Elements, 35, pp. 1168–80, 2011.
  28. Zhao, X., and Liew, K., “Free Vibration Analysis of Functionally Graded Conical Shell Panels by a Meshless Method”, Composite Structures, Vol. 93, pp. 649–664, 2011.
  29. Moussavinezhad, S. M., Shahabian, F., and Hosseini, S. M., “Two-dimensional Elastic Wave Propagation Analysis in Finite Length FG Thick Hollow Cylinders with 2D Nonlinear Grading Patterns Using MLPG Method”, Computer Modeling in Engineering & Sciences, 91, pp. 177–204, 2013.
  30. Ghayoumizadeh, H., Shahabian, F., and Hosseini, S. M., “Elastic Wave Propagation in a Functionally Graded Nanocomposite Reinforced by Carbon Nanotubes Employing Meshless Local Integral Equations (LIEs)”, Engineering Analysis with Boundary Elements, 37, pp. 1524–31, 2013.
  31. Selvadurai, A. P., "Mechanics of Poroelastic Media", Springer Science & Business Media, Vol. 35, No. 1, 2013.
  32. Schanz, M., "Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods", Applied Mechanics Reviews, 62, No. 3, pp. 30-83, 2009.
  33. Terzaghi, , “Erdbaumechanik Auf Bodenphysikalischer Grundlage”, Leipzig, Franz Deuticke, 1925.
  34. Biot, A., “General Theory of Three-Dimensional Consolidation”, Journal of Applied Physics, Vol. 12, pp. 155–164, 1941.
  35. Aifantis, E. C., “On the Problem of Diffusion in Solids”, Acta Mechanica, 37, pp. 265–296, 1980.
  36. Vardoulakis, I., and Beskos, D. E., “Dynamic Behavior of Nearly Saturated Porous Media”, Mechanics of Materials, Vol. 5, pp. 87-108,
  37. Schanz, , and Cheng, A. H. D., “Transient Wave Propagation in A One-Dimensional Poroelastic Column”, Acta Mechanica, Vol. 145, pp. 1–18, 2000.
  38. Marek, P., Gustar, M., and Anagnos, T., “Codified Design of Steel Structures Using Monte Carlo Techniques”, Journal of Constructional Steel Research, Vol. 52, pp. 69–82, 1999.
  39. Disciuva, M., and Lomario, D., “A Comparison Between Monte Carlo and FORMs in Calculating The Reliability of A Composite Structure”, Composite Structures, Vol. 59, pp. 155–62, 2003.
  40. Noh, H. C., and Park, T., “Monte Carlo Simulation-Compatible Stochastic Field for Application to Expansion-Based Stochastic Finite Element Method”, Computers and Structures, Vol. 84, pp. 2363–72, 2006.
  41. Hosseini, S. M., and Shahabian, F., “Stochastic Assessment of Thermo-Elastic Wave Propagation in Functionally Graded Materials (FGMs) with Gaussian Uncertainty in Constitutive Mechanical Properties”, Journal of Thermal Stresses, 34, pp. 1071–1099, 2011.
  42. Hosseini, S. M., and Shahabian, F., “Transient Analysis of Thermo-Elastic Waves in Thick Hollow Cylinders Using A Stochastic Hybrid Numerical Method, Considering Gaussian Mechanical Properties”, Applied Mathematical Model, 35, pp. 4697–4714, 2010.
  43. Hosseini, S. M., and Shahabian, F., “Stochastic Dynamic Analysis of a Functionally Graded Thick Hollow Cylinder with Uncertain Material Properties Subjected to Shock Loading”, Materials and Design, 31, pp. 894–910, 2010.
  44. Hosseini, S. M., and Shahabian, F., “Reliability of Stress Field in Al-Al2O3 Functionally Graded Thick Hollow Cylinder Subjected to Sudden Unloading, Considering Uncertian Mechanical Properties”, Materials and Design, 31, pp. 3748-60, 2010.
  45. Sheu, G. Y., “Prediction of Probabilistic Settlements Via Spectral Stochastic Meshless Local Petrov–Galerkin Method” J. Computers and Geotechnics, Vol. 38, pp. 407-415, 2011.
  46. Sladek, J., Sladek, V., and Schanz, M., "A Meshless Method for Axisymmetric Problems in Continuously Nonhomogeneous Saturated Porous Media", Computers and Geotechnics, 62, No. 1, pp. 100-109, 2014.
  47. Sladek, J., Sladek, V., and Schanz, M., "The MLPG Applied to Porous Materials with Variable Stiffness and Permeability", Meccanica, 49, No. 10, pp. 2359-2373, 2014.
  48. Kazemi, H., Shahabian, F., and Hosseini, S. M., “Shock-Induced Stochastic Dynamic Analysis of Cylinders Made of Saturated Porous Materials Using MLPG Method: Considering Uncertainty in Mechanical Properties”, Acta Mechanica, 228, No. 11, pp. 3961-3975, 2017.
  49. Liu, G. R., “Meshfree Methods: Moving Beyond the Finite Element Method”, CRC Press,
  50. Ghadirirad, M. H., Shahabian, F., and Hosseini, S. M., “A Mesh Less Local Petrov–Galerkin Method for Nonlinear Dynamic Analyses of Hyper-Elastic FG Thick Hollow Cylinder With Rayleigh Damping”, Acta Mech, 226, pp. 1497-1513, 2014.
  51. Detournay, E., and Cheng, A. H. D., “Fundamentals of Poroelasticity, Comprehensive Rock Engineering: Principles, Practice and Projects”, Pergamon Press, Vol. 2, No. 5, pp. 113–171, 1993

 

Files

Share

How to cite

Statistics

ارتقاء امنیت وب با وف ایرانی