On the buckling analysis of functionally graded sandwich beams using a unified beam theory
Document Type : Research Paper
Authors
1 Department of Civil Engineering, Sanjivani College of Engineering, Savitribai Phule Pune University Pune, Kopargaon-423601, M.S., India
2 Department of Applied Mechanics, Government College of Engineering, Karad-415124, Maharashtra, India
Abstract
In this paper, a unified beam theory is developed and applied to study the buckling response of two types of functionally graded sandwich beams. In the first type (Type A), the sandwich beam has a hardcore whereas in the second type (Type B), the sandwich beam has a softcore. In both the type of beams, face sheets are made up of functionally graded material. The material properties of face sheets are varied through the thickness according to the power-law distribution. A unified beam theory developed in the present study uses polynomial and non-polynomial type shape functions in-terms of thickness coordinate to account for the effect of shear deformation. The present theory is built upon classical beam theory and shows a realistic variation of transverse shear stresses through the thickness of the beam. The governing equations are deduced based on the principle of virtual work. Analytical solutions for simply supported sandwich beams subjected to axial force are presented. The critical buckling load factors of two types of FG sandwich beams are investigated. The numerical results are obtained for various power law coefficients and face-core-face thickness ratios. The validity of the present theory is proved by comparing the present results with various available solutions in the literature.
Keywords
- A unified beam theory
- Shear deformation
- FG sandwich beam
- Softcore and hardcore
- Critical buckling load factors
Main Subjects
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[11] J. Bernoulli, Curvatura laminae elasticae Acta Eruditorum Lipsiae, pp. 262–276, 1694.
[12] S. P. Timoshenko, On the correction for shear of the differential equation for transverse vibration of prismatic bars, The Philosophical Magazine Vol. 6, No. 46, pp. 744–746, 1921.
[13] A. S. Sayyad, Y. M. Ghugal, Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures, Vol. 171, pp. 486-504, 2017.
[14] A. S. Sayyad, Y. M. Ghugal, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite Structures, Vol. 129, pp. 177-201, 2015.
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[20] S. M. Ghumare, A. S. Sayyad, A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams, Latin American Journal of Solids and Structures, Vol. 14, pp. 1893-1911, 2017.
[21] L. C. Trinh, T. P. Vo, H.-T. Thai, T.-K. Nguyen, An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads, Composites Part B: Engineering, Vol. 100, pp. 152-163, 2016/09/01/, 2016.
[22] V. Kahya, M. Turan, Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory, Composites Part B: Engineering, Vol. 109, pp. 108-115, 2017/01/15/, 2017.
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On the buckling analysis of functionally graded sandwich beams using a unified beam theory
)
Volume 51, Issue 2
December 2020Pages 443-453
- Receive Date: 16 September 2020
- Revise Date: 01 October 2020
- Accept Date: 02 October 2020