Flexural analysis of functionally graded thin walled beams

Keywords: Abaqus; MATLAB; Functionally Graded beam; Flexural response; Thin composite structure; Timoshenko beam theory; Vlasov’s thin walled beam theory.

Abstract

In this paper, an analytical model has been presented for study of flexural response of functionally graded thin walled beam incorporating first order shear deformation theory and Vlasov’s theory for thin walled beam. The material properties are varied along the depth direction according to the power law distribution of volume fraction of mild steel and alumina. Numerical results for functionally graded thin beams under uniformly distributed vertical loading (for various span to depth ratios) have also been presented.

Author Biography

Shamsher Bahadur Singh, Birla Institute of Technology and Science Pilani
Civil Engineering Department

References

[1] Miyamoto, Y., Kaysser, W. A., Rabin, B. H., Kawasaki, A., & Ford, R. G. (Eds.). (2013). Functionally graded materials: design, processing and applications (Vol. 5). Springer Science & Business Media.
[2] Birman, V. (2014). Functionally graded materials and structures. In Encyclopedia of Thermal Stresses (pp. 1858-1865). Springer Netherlands.
[3] Chakraborty, A., Gopalakrishnan, S., & Reddy, J. N. (2003). A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3), 519-539.
[4] Li, X. F. (2008). A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and vibration, 318(4-5), 1210-1229.
[5] Reddy, J. N. (2000). Analysis of functionally graded plates. International Journal for numerical methods in engineering, 47(1-3), 663-684.
[6] Sankar, B. V. (2001). An elasticity solution for functionally graded beams. Composites Science and Technology, 61(5), 689-696.
[7] Aboudi, J., Pindera, M. J., & Arnold, S. M. (1999). Higher-order theory for functionally graded materials. Composites Part B: Engineering, 30(8), 777-832.
[8] Kadoli, R., Akhtar, K., & Ganesan, N. (2008). Static analysis of functionally graded beams using higher order shear deformation theory. Applied Mathematical Modelling, 32(12), 2509-2525.
[9] Zenkour, A. M. (2006). Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling, 30(1), 67-84.
[10] Filippi, M., Carrera, E., & Zenkour, A. M. (2015). Static analyses of FGM beams by various theories and finite elements. Composites Part B: Engineering, 72, 1-9.
[11] Das, S., & Sarangi, S. K. (2016, September). Static Analysis of Functionally Graded Composite Beams. In IOP Conference Series: Materials Science and Engineering (Vol. 149, No. 1, p. 012138). IOP Publishing.
[12] Sina, S. A., Navazi, H. M., & Haddadpour, H. (2009). An analytical method for free vibration analysis of functionally graded beams. Materials & Design, 30(3), 741-747.
[13] Thai, H. T., & Vo, T. P. (2012). Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57-66.
[14] Khan, A. A., Naushad Alam, M., & Wajid, M. (2016). Finite element modelling for static and free vibration response of functionally graded beam. Latin American Journal of Solids and Structures, 13(4), 690-714.
[15] Li, S. R., Cao, D. F., & Wan, Z. Q. (2013). Bending solutions of FGM Timoshenko beams from those of the homogenous Euler–Bernoulli beams. Applied Mathematical Modelling, 37(10-11), 7077-7085.
[16] Chen, D., Yang, J., & Kitipornchai, S. (2015). Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, 54-61.
[17] Nguyen, T. T., Kim, N. I., & Lee, J. (2016). Analysis of thin-walled open-section beams with functionally graded materials. Composite Structures, 138, 75-83.
[18] Mitra, M., Gopalakrishnan, S., & Bhat, M. S. (2004). A new super convergent thin walled composite beam element for analysis of box beam structures. International journal of solids and structures, 41(5-6), 1491-1518.
[19] Lee, J. (2005). Flexural analysis of thin-walled composite beams using shear-deformable beam theory. Composite Structures, 70(2), 212-222.
[20] Lee, J., & Lee, S. H. (2004). Flexural–torsional behaviour of thin-walled composite beams. Thin-Walled Structures, 42(9), 1293-1305.
[21] Pandey, M. D., Kabir, M. Z., & Sherbourne, A. N. (1995). Flexural-torsional stability of thin-walled composite I-section beams. Composites Engineering, 5(3), 321-342.
[22] Shadmehri, F., Haddadpour, H., & Kouchakzadeh, M. A. (2007). Flexural–torsional behaviour of thin-walled composite beams with closed cross-section. Thin-Walled Structures, 45(7-8), 699-705.
[23] Schulz, M., & Filippou, F. C. (1998). Generalized warping torsion formulation. Journal of engineering mechanics, 124(3), 339-347.
[24] Shakourzadeh, H., Guo, Y. Q., & Batoz, J. L. (1995). A torsion bending element for thin-walled beams with open and closed cross sections. Computers & Structures, 55(6), 1045-1054.
[25] Haque, A. (2016). Introduction to Timoshenko Beam Theory. Retrieved April, 2, 2017.
[26] ABAQUS/Standard User's Manual, Version 6.10, Vol. 1 (2010).
[27] MATLAB and Statistics Toolbox Release 2010a, The MathWorks, Inc., Natick, Massachusetts, United States.
Published
2020-01-21
Section
Research Papers