On the deformation of layered composite arches using exponential shear and normal deformation theory
Valmik M. Mahajan, Amit Sharma
download PDFAbstract. In the present study, the stresses and displacements are analyzed for layered composite arches of various lamination schemes subjected to uniformly loading. The present work is majorly highlighted the effects of transverse normal stress and transverse normal strain using exponential shear and normal deformation theory (ESNDT). Governing equations are derived using Hamilton’s principle with application of Navier’s method subjected to simply supported end conditions. Present theory is free from use of any shear correction factor and it satisfies the zero traction free end boundary condition at the top and bottom surfaces of the layered composite arches. In the present work symmetric and antisymmetric lamination scheme have been studied to obtain the numerical results for four layered composite arches and is validated through results available in prior literature.
Keywords
Deformation, Stresses, Displacements, Layered Composite Arches, ESNDT
Published online 8/10/2023, 11 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Valmik M. Mahajan, Amit Sharma, On the deformation of layered composite arches using exponential shear and normal deformation theory, Materials Research Proceedings, Vol. 31, pp 693-703, 2023
DOI: https://doi.org/10.21741/9781644902592-71
The article was published as article 71 of the book Advanced Topics in Mechanics of Materials, Structures and Construction
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] J. Bernoulli, Curvatura laminae elasticae, Acta Eruditorum Lipsiae. 34 (1694) 262-276.
[2] L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, Apud Marcum-Michaelem Bousquet and Socios. 24 (1744) 1-322. https://doi.org/10.5479/sil.318525.39088000877480.
[3] S.P. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philos. Mag. Series 1. 41 (1921) 744-746. https://doi.org/10.1080/14786442108636264.
[4] J.N. Reddy, A simple higher-order theory for laminated composite plates, J. Appl. Mech. 51(4) (1984) 745-752. https://doi.org/10.1115/1.3167719.
[5] E. Carrera, Transverse normal strain effects on thermal stress analysis of homogeneous and layered plates, AIAA J. 43(10) (2005) 2232-2242. https://doi.org/10.2514/1.11230.
[6] E. Carrera, S. Brischetto and A. Robaldo, Variable kinematic model for the analysis of functionally graded material plates, AIAA J. 46(1) (2008) 194-203. https://doi.org/10.2514/1.32490.
[7] A.M. Zenkour, Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates, J. Sandw. Struct. Mater. 9(3) (2007) 213-238. https://doi.org/10.1177/1099636207065675.
[8] T. Kant and S.M. Shiyekar, Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory, Comput. Struct. 86 (2008) 1594-1603. https://doi.org/10.1016/j.compstruc.2008.01.002.
[9] F. Tornabene, N. Fantuzzi, E. Viola and E. Carrera, Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method, Compos. Struct. 107 (2014) 675-697. https://dx.doi.org/10.1016/j.compstruct.2013.08.038.
[10] F. Tornabene, N. Fantuzzi, E. Viola and R.C. Batra, Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory, Compos. Struct. 119 (2015) 67-89. https://dx.doi.org/10.1016/j.compstruct.2014.08.005.
[11] A.S. Sayyad and Y.M. Ghugal, Cylindrical bending of multilayered composite laminates and sandwiches, Adv. Aircr. Spacecr. Sci. 3(2) (2016) 113-148. https://dx.doi.org/10.12989/aas.2016.3.2.113.
