Non-Linear Load-Deflection Response of Shape Memory Alloys-Reinforced Composite Cylindrical Shells under Uniform Radial Load

Authors: Behrang Tavousi Tehrani, Mohammad-Zaman Kabir

Abstract:

Shape memory alloys (SMA) are often implemented in smart structures as the active components. Their ability to recover large displacements has been used in many applications, including structural stability/response enhancement and active structural acoustic control. SMA wires or fibers can be embedded with composite cylinders to increase their critical buckling load, improve their load-deflection behavior, and reduce the radial deflections under various thermo-mechanical loadings. This paper presents a semi-analytical investigation on the non-linear load-deflection response of SMA-reinforced composite circular cylindrical shells. The cylinder shells are under uniform external pressure load. Based on first-order shear deformation shell theory (FSDT), the equilibrium equations of the structure are derived. One-dimensional simplified Brinson’s model is used for determining the SMA recovery force due to its simplicity and accuracy. Airy stress function and Galerkin technique are used to obtain non-linear load-deflection curves. The results are verified by comparing them with those in the literature. Several parametric studies are conducted in order to investigate the effect of SMA volume fraction, SMA pre-strain value, and SMA activation temperature on the response of the structure. It is shown that suitable usage of SMA wires results in a considerable enhancement in the load-deflection response of the shell due to the generation of the SMA tensile recovery force.

Keywords: Airy stress function, cylindrical shell, Galerkin technique, load-deflection curve, recovery stress, shape memory alloy.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1317440

References:

[1] J. S. N. Paine, C. A. Rogers, and R. A. Smith, “Adaptive Composite Materials with Shape Memory Alloy Actuators for Cylinders and Pressure Vessels,” Journal of Intelligent Material Systems and Structures, vol. 6, no. 2, pp. 210–219, Mar. 1995.
[2] R. Burgueño, N. Hu, and N. Lajnef, “Controlling the postbuckling response of cylindrical shells under axial compression for applications in smart structures,” ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2013, vol. 2, no. July, 2013.
[3] A. R. Damanpack, W. H. Liao, M. M. Aghdam, M. Shakeri, and M. Bodaghi, “Micro-macro thermo-mechanical analysis of axisymmetric shape memory alloy composite cylinders,” Composite Structures, vol. 131, no. July 2016, pp. 1001–1016, 2015.
[4] S. Nemat-Nasser, J. Yong Choi, J. B. Isaacs, and D. W. Lischer, “Quasi-Static and Dynamic Buckling of Thin Cylindrical Shape-Memory Shells,” Journal of Applied Mechanics, vol. 73, no. 5, p. 825, 2006.
[5] L. G. Sil’chenko, A. A. Movchan, and T. L. Sil’chenko, “Stability of a cylindrical shell made of a shape-memory alloy,” International Applied Mechanics, vol. 50, no. 2, pp. 171–178, 2014.
[6] V. Birman, “Theory and comparison of the effect of composite and shape memory alloy stiffeners on stability of composite shells and plates,” International Journal of Mechanical Sciences, vol. 39, no. 10, pp. 1139–1149, 1997.
[7] H. Asadi, Y. Kiani, M. Aghdam, and M. Shakeri, “Enhanced thermal buckling of laminated composite cylindrical shells with shape memory alloy,” Journal of Composite Materials, vol. 50, no. 2, pp. 243–256, 2016.
[8] H. Asadi, A. H. Akbarzadeh, Z. T. Chen, and M. M. Aghdam, “Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys,” Smart Materials and Structures, vol. 24, no. 4, p. 045022, 2015.
[9] M. R. Amini and S. Nemat-Nasser, “Dynamic buckling and recovery of thin cylindrical shape memory shells,” Proceedings of SPIE - The International Society for Optical Engineering, vol. 5761, pp. 450–453, 2005.
[10] T. Akbari and S. M. R. Khalili, “Experimental investigations on the mechanical properties and buckling behavior of the filament wound composite shells embedded with shape memory alloy wires,” Mechanics of Advanced Materials and Structures, vol. 0, no. 0, pp. 1–7, 2018.
[11] B. Liu and C. Du, “Effects of external pressure on phase transformation of shape memory alloy cylinder,” International Journal of Mechanical Sciences, vol. 88, pp. 8–16, Nov. 2014.
[12] H. Li, H. Li, and H. Tzou, “Frequency Control of Beams and Cylindrical Shells With Light-Activated Shape Memory Polymers,” Journal of Vibration and Acoustics, vol. 137, no. 1, p. 011010, Feb. 2015.
[13] F. Forouzesh and A. A. Jafari, “Radial vibration analysis of pseudoelastic shape memory alloy thin cylindrical shells by the differential quadrature method,” Thin-Walled Structures, vol. 93, pp. 158–168, Aug. 2015.
[14] M. Salim, M. Bodaghi, S. Kamarian, and M. Shakeri, “Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments,” Latin American Journal of Solids and Structures, vol. 15, no. 1, Apr. 2018.
[15] F. Auricchio and E. Sacco, “A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite,” International Journal of Non-Linear Mechanics, vol. 32, no. 6, pp. 1101–1114, 1997.
[16] L. C. Brinson and M. S. Huang, “Simplifications and Comparisons of Shape Memory Alloy Constitutive Models,” Journal of Intelligent Material Systems and Structures, vol. 7, no. 1, pp. 108–114, Jan. 1996.
[17] L. C. Brinson, “One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable,” Journal of Intelligent Material Systems and Structures, vol. 4, no. April, pp. 229–242, 1993.
[18] M.-Z. Kabir and B. Tavousi Tehrani, “Closed-form solution for thermal, mechanical, and thermo-mechanical buckling and post-buckling of SMA composite plates,” Composite Structures, vol. 168, pp. 535–548, May 2017.
[19] C. Liang, “The Constitutive Modeling of Shape Memory Alloys,” Virginia Polytechnic Institute and State University, 1990.
[20] H. J. Lee, J. J. Lee, and J. S. Huh, “A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires,” Composite Structures, vol. 47, no. 1, pp. 463–469, 1999.
[21] J.-H. Roh, I.-K. Oh, S.-M. Yang, J.-H. Han, and I. Lee, “Thermal post-buckling analysis of shape memory alloy hybrid composite shell panels,” Smart Materials and Structures, vol. 13, no. 6, pp. 1337–1344, 2004.
[22] H. Abdollahi, S. E. Esfahani, M. Shakeri, and M. R. Eslami, “Non-Linear Thermal Stability Analysis of SMA Wire-Embedded Hybrid Laminated Composite Timoshenko Beams on Non-Linear Hardening Elastic Foundation,” Journal of Thermal Stresses, vol. 38, no. 3, pp. 277–308, Feb. 2015.
[23] C. C. Chamis, “Simplified Composite Micromechanics Equations of Hygral, Thermal, and Mechanical Properties,” in Thirty-eighth Annual Conference of the Society of the Plastics Industry (SPI) Reinforced Plastics/Composites Institute, 1983.
[24] M. Bohlooly and B. Mirzavand, “Closed form solutions for buckling and postbuckling analysis of imperfect laminated composite plates with piezoelectric actuators,” Composites Part B: Engineering, vol. 72, no. 0, pp. 21–29, 2015.
[25] D. Van Dung and N. T. Nga, “Nonlinear buckling and post-buckling of eccentrically stiffened functionally graded cylindrical shells surrounded by an elastic medium based on the first order shear deformation theory,” Vietnam Journal of Mechanics, vol. 35, no. 4, pp. 285–298, Nov. 2013.
[26] B. Tavousi Tehrani and M.-Z. Kabir, “Non-linear load-deflection response of SMA composite plate resting on winkler-pasternak type elastic foundation under various mechanical and thermal loading,” Thin-Walled Structures, vol. 129, no. C, pp. 391–403, Aug. 2018.