|Journal||Journal of Mechanical Engineering|
|Publisher||A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||2709-2984 (Print), 2709-2992 (Online)|
|Issue||Vol. 24, no. 1, 2021 (March)|
|Cited by||J. of Mech. Eng., 2021, vol. 24, no. 1, pp. 28-35|
This paper describes a technique for analyzing the phenomenon of static buckling of a pre-loaded complex nano-composite shell. Most of the works devoted to the analysis of complex structures consider vibration processes, while the phenomenon of buckling can be an important factor that limits the use of new materials in space-rocket hardware. A nano-composite constant-thickness shell consisting of two spherical covers and a cylindrical body is considered. It is acted upon by internal pressure and an axial compressive force. This shell simulates the fuel tank of a launch vehicle. Conditions under which the shell is deformed non-axisymmetrically, buckling statically, are investigated. A technique is proposed that allows the problem to be divided into the analysis of the pre-loaded state of the shell and the analysis of buckling. Further analysis is performed using a technique based on the high-order shear deformation theory and the Ritz method. The problem is discretized by representing the variables that determine the state of the shell in the form of expansions in basis functions with unknown coefficients. Thus, it is the expansion coefficients that become unknown in the problem. The problem of analyzing the pre-stressed state of a structure is reduced to solving a system of linear algebraic equations with respect to the expansion coefficients. The problem of buckling analysis can be reduced to the problem of eigenvalues. The solution to this problem makes it possible to find the minimum value of the compressive load at which the shell buckles, as well as the forms of buckling. The results of applying the developed technique were compared with those of finite element modeling of a structure made of the simplest nano-composite material. The comparison results indicate a high accuracy of the technique described. At the same time, the use of the finite element method for the analysis of large-scale thin-walled structures made of functionally gradient materials is extremely difficult, in contrast to the methodology proposed in the paper. Comparison of various types of nano-reinforcement showed that a rational choice of the type of reinforcement can significantly increase the critical load. In this case, the internal pressure on the shell also significantly affects the critical load.
Keywords: static buckling, complex shell, nano-composite material, carbon nanotubes, Ritz method.
Full text: Download in PDF
- Allaoui, A., Bai, S, Cheng, H. M., & Bai, J. B. (2002). Mechanical and electrical properties of a MWNT/epoxy composite. Composites Science and Technology, vol. 62, iss. 15, pp. 1993–1998. https://doi.org/10.1016/S0266-3538(02)00129-X.
- Zhou, Z., Ni, Y., Tong, Z., Zhu, S., Sun, J., & Xu, X. (2019). Accurate nonlinear stability analysis of functionally graded multilayer hybrid composite cylindrical shells subjected to combined loads. Materials and Design, vol. 182, 108035. https://doi.org/10.1016/j.matdes.2019.108035.
- Zhou, Z., Ni, Y., Tong, Z., Zhu, S., Sun, J., & Xu, X. (2019). Accurate nonlinear buckling analysis of functionally graded porous graphene platelet reinforced composite cylindrical shells. International Journal of Mechanical Sciences, vol. 151, pp. 537–550. https://doi.org/10.1016/j.ijmecsci.2018.12.012.
- Wang, Y., Feng, C., Zhao, Z., & Yang, J. (2018). Buckling of graphene platelet reinforced composite cylindrical shell with cutout. International Journal of Structural Stability and Dynamics, vol. 18, no. 3, 1850040. https://doi.org/10.1142/S0219455418500402.
- Dong, Y. H., He, L. W., Wang, L., Li, Y. H., & Yang, J. (2018). Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: An analytical study. Aerospace Science and Technology, vol. 82–83, pp. 466–478. https://doi.org/10.1016/j.ast.2018.09.037.
- Shen, H.-S. & Xiang, Y. (2018). Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments. Thin-Walled Structures, vol. 124, pp. 151–160. https://doi.org/10.1016/j.tws.2017.12.005.
- Shen, H.-S. (2011). Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Composite Structures, vol. 93, iss. 8, pp. 2096–2108. https://doi.org/10.1016/j.compstruct.2011.02.011.
- Shen, H.-S. (2011). Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells. Composite Structures, vol. 93, iss. 10, pp. 2496–2503. https://doi.org/10.1016/j.compstruct.2011.04.005.
- Ansari, R. & Torabi, J. (2016). Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading. Composites Part B: Engineering, vol. 95, pp. 196–208. https://doi.org/10.1016/j.compositesb.2016.03.080.
- Ansari, R., Pourashraf, T., Gholami, R., & Shahabodini, A. (2016). Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers. Composites Part B: Engineering, vol. 90, pp. 267–277. https://doi.org/10.1016/j.compositesb.2015.12.012.
- Wang, Y., Feng, C., Zhao, Z., & Yang, J. (2017). Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL), Composite Structures, vol. 202, pp. 38–46. https://doi.org/10.1016/j.compstruct.2017.10.005.
- Liu, D., Kitipornchai, S., Chen, W., & Yang, J. (2018). Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell. Composite Structures, vol. 189, pp. 560–569. https://doi.org/10.1016/j.compstruct.2018.01.106.
- Wang, Y., Feng, C., Zhao, Z., Lu, F., Yang, J. (2018). Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout. Composite Structures, vol. 197, pp. 72–79. https://doi.org/10.1016/j.compstruct.2018.05.056.
- Bagheri, H., Kiani, Y., & Eslami, M. R. (2018). Free vibration of joined conical-cylindrical-conical shells. Acta Mechanica, vol. 229, pp. 2751–2764. https://doi.org/10.1007/s00707-018-2133-3.
- Pang, F., Li, H., Cui, J., Du, Y., & Gao, C. (2019). Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation. European Journal of Mechanics – A/Solids, vol. 74, pp. 381–393. https://doi.org/10.1016/j.euromechsol.2018.12.003.
- Wu, S., Qu, Y., & Hua, H. (2013). Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions. Journal of Mechanical Science and Technology, vol. 27, iss. 5, pp. 1265–1272. https://doi.org/10.1007/s12206-013-0207-7.
- Qu, Y., Chen, Y., Long, X., Hua, H., & Meng, G. (2012). A variational method for free vibration analysis of joined cylindrical-conical shells. Journal of Vibration and Control, vol. 19, iss. 16, pp. 2319–2334. https://doi.org/10.1177/1077546312456227.
- Ma, X., Jin, G., Xiong, Y., & Liu, Z. (2014). Free and forced vibration analysis of coupled conical-cylindrical shells with arbitrary boundary conditions. International Journal of Mechanical Sciences, vol. 88, pp. 122–137. https://doi.org/10.1016/j.ijmecsci.2014.08.002.
- Caresta, M. & Kessissoglou, N. J. (2010). Free vibrational characteristics of isotropic coupled cylindrical-conical shells. Journal of Sound and Vibration, vol. 329, iss. 6, pp. 733–751. https://doi.org/10.1016/j.jsv.2009.10.003.
- Wang, Q., Cui, X., Qin, B., & Liang, Q. (2017). Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions. Composite Structures, vol. 182, pp. 364–379. https://doi.org/10.1016/j.compstruct.2017.09.043.
- Shen, H.-S. (2009). Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, vol. 91, iss. 1, pp. 9–19. https://doi.org/10.1016/j.compstruct.2009.04.026.
- Reddy, J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures, vol. 20, iss. 9–10, pp. 881–896. https://doi.org/10.1016/0020-7683(84)90056-8.
- Amabili, M. & Reddy, J. N. (2010). A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. International Journal of Non-Linear Mechanics, vol. 45, iss. 4, pp. 409–418. https://doi.org/10.1016/j.ijnonlinmec.2009.12.013.
- Sobhaniaragh, B., Nejati, M., & Mansur, W. J. (2017). Buckling modelling of ring and stringer stiffened cylindrical shells aggregated by graded CNTs. Composites Part B: Engineering, vol. 124, pp. 120–133. https://doi.org/10.1016/j.compositesb.2017.05.045.
Received 30 January 2021
Published 30 March 2021