Two-Dimensional Geometrically Nonlinear Hyperelastic Wave Propagation Analysis in FG Thick Hollow Cylinders using MLPG Method

Document Type : Research Article

Authors

1 Civil Engineering Department, Quchan University of Technology, Quchan, Iran.

2 Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran.

3 Industrial Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran.

Abstract

The idea of using a meshless method for geometrically nonlinear problems due to its advantage of eliminating mesh distortion has been attracted many researchers. In this paper, the nonlinear wave propagation analysis in two-dimensional functionally graded (2D FG) thick hollow cylinders is studied using the meshless method. For this purpose, the meshless local Petrov-Galerkin (MLPG) method is developed for geometrically nonlinear dynamic analysis based on the total Lagrangian approach. The radial point interpolation, which possesses the delta function property, is used to construct the shape functions. Since the cylinder is assumed to have large deformations, the neo-Hookean hyperelastic model is employed for constitutive modeling of material. The incremental-iterative Newmark/Newton-Raphson technique is applied to iteratively solve the nonlinear equations of motion. The 2D FG cylinder is analyzed under uniform and non-uniform mechanical shock loading. The mechanical properties of the cylinder are assumed to vary nonlinearly through the radial and longitudinal directions which are simulated using two-dimensional volume fractions. Rayleigh damping is utilized to model energy dissipation in analyses. Numerical examples demonstrate the applicability and accuracy of the present approach in tracking the nonlinear wave propagation in two-dimensional FG thick hollow cylinders. The effects of grading patterns on the time history and wave propagation are discussed in detail.

Keywords

Main Subjects

References

  1. Moussavinezhad, F. Shahabian, S.M. Hosseini, Two-dimensional stress-wave propagation in finite-length FG cylinders with two-directional nonlinear grading patterns using the MLPG method, Journal of Engineering Mechanics, 140(3) (2014) 575-592.
  2. Norouzzadeh, R. Ansari, H. Rouhi, An analytical study on wave propagation in functionally graded nano-beams/tubes based on the integral formulation of nonlocal elasticity, Waves in Random and Complex Media, 30(3) (2020) 562-580.
  3. Sur, S. Paul, M. Kanoria, Modeling of memory-dependent derivative in a functionally graded plate, Waves in Random and Complex Media, 31(4) (2021) 618-638.
  4. Aminipour, M. Janghorban, L. Li, Wave dispersion in nonlocal anisotropic macro/nanoplates made of functionally graded materials, Waves in Random and Complex Media, (2020) 1-45.
  5. Khoei, M. Anahid, K. Shahim, An extended arbitrary Lagrangian-Eulerian finite element method for large deformation of solid mechanics, Finite Elements in Analysis and Design, 44(6-7) (2008) 401-416.
  6. Schwarze, S. Reese, A reduced integration solid‐shell finite element based on the EAS and the ANS concept-geometrically linear problems, International Journal for Numerical Methods in Engineering, 80(10) (2009) 1322-1355.
  7. Rezaiee-Pajand, A.R. Masoodi, E. Arabi, Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element, Steel and Composite Structures, 28(3) (2018) 389-401.
  8. C. Guan, C.T. Sun, The isoparametric reproducing kernel particle method for nonlinear deformation of plates, Engineering Analysis with Boundary Elements, 42 (2014) 67-76.
  9. A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the royal astronomical society, 181(3) (1977) 375-389.
  10. Nayroles, G. Touzot, P. Villon, Generalizing the finite element method: diffuse approximation and diffuse elements, Computational Mechanics, 10(5) (1992) 307-318.
  11. K. Liu, S. Jun, S. Li, J. Adee, T. Belytschko, Reproducing kernel particle methods for structural dynamics, International Journal for Numerical Methods in Engineering, 38(10) (1995) 1655-1679.
  12. Belytschko, Y.Y. Lu, L. Gu, Element‐free Galerkin methods, International journal for numerical methods in engineering, 37(2) (1994) 229-256.
  13. Yongchang, Z. Hehua, A meshless local natural neighbor interpolation method for stress analysis of solids, Engineering analysis with boundary elements, 28(6) (2004) 607-613.
  14. N. Atluri, T. Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, 22(2) (1998) 117-127.
  15. N. Atluri, J. Sladek, V. Sladek, T. Zhu, The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity, Computational mechanics, 25(2-3) (2000) 180-198.
  16. Sladek, V. Sladek, C. Zhang, F. Garcia-Sanchez, M. Wunsche, Meshless local Petrov-Galerkin method for plane piezoelectricity, CMC: Computers, Materials & Continua, 4(2) (2006) 109-117.
  17. Hao, W. Zhang, J. Yang, Nonlinear dynamics of an FGM plate with two clamped opposite edges and two free edges, Acta Mechanica Solida Sinica, 27(4) (2014) 394-406.
  18. Sladek, V. Sladek, S. Krahulec, E. Pan, The MLPG analyses of large deflections of magnetoelectroelastic plates, Engineering Analysis with Boundary Elements, 37(4) (2013) 673-682.
  19. Zhang, A. Wittek, G. Joldes, X. Jin, K. Miller, A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue, Engineering Analysis with Boundary Elements, 42 (2014) 60-66.
  20. Zhang, Z. Lei, K. Liew, J. Yu, Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels, Computer Methods in Applied Mechanics and Engineering, 273 (2014) 1-18.
  21. Zhao, Y. Yang, K.M. Liew, Geometrically nonlinear analysis of cylindrical shells using the element-free kp-Ritz method, Engineering Analysis with Boundary Elements, 31(9) (2007) 783-792.
  22. Zhu, L. Zhang, K. Liew, Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation, Composite Structures, 107 (2014) 298-314.
  23. H. Ghadiri Rad, F. Shahabian, S.M. Hosseini, Nonlocal geometrically nonlinear dynamic analysis of nanobeam using a meshless method, Steel and Composite Structures, 32(3) (2019) 293-304.
  24. Mellouli, H. Jrad, M. Wali, F. Dammak, Geometrically nonlinear meshfree analysis of 3D-shell structures based on the double directors shell theory with finite rotations, Steel and Composite Structures, 31(4) (2019) 397-408.
  25. Liu, Y. Gu, A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids, Journal of Sound and Vibration, 246(1) (2001) 29-46.
  26. Gu, Q. Wang, K. Lam, A meshless local Kriging method for large deformation analyses, Computer Methods in Applied Mechanics and Engineering, 196(9-12) (2007) 1673-1684.
  27. M. Hosseini, M. Akhlaghi, M. Shakeri, Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials, Engineering Computations, 24(3) (2007) 288-303.
  28. H.G. Rad, F. Shahabian, S.M. Hosseini, Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method, Engineering Analysis with Boundary Elements, 50 (2015) 83-96.
  29. Vullo, Circular cylinders and pressure vessels. Stress Analysis and Design, Springer: Berlin/Heidelberg, Germany, 2014.
AUT Journal of Civil Engineering
Volume 5, Issue 3
September 2021
Pages 465-480

Files

Share

How to cite

Statistics