Applications of higher order shear deformation theories on stress distribution in a five layer sandwich plate

Document Type : Research Paper

Authors

Department of Mechanical engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this paper, layerwise theory (LT) along with the first, second and third-order shear deformation theories (FSDT, SSDT and TSDT) are used to determine the stress distribution in a simply supported square sandwich plate subjected to a uniformly distributed load. Two functionally graded (FG) face sheets encapsulate an elastomeric core while two epoxy adhesive layers adhere the core to the face sheets. The sandwich plate is assumed to be symmetric with respect to its core mid-plane. First, second and third-order shear deformation theories are used to model shear distribution in the adhesive layers as well as others. Results obtained from the three theories are compared with those of finite element solution. Results indicate that finite element analysis (FEA) and LT based on the first, second and third-order shear deformation theories give almost the same estimations on planar stresses. Moreover, the out-of-plane shear stresses obtained by FEA, are slightly different from those of LT based on FSDT. The differences are decreased on using LT based on SSDT or TSDT. Additionally, SSDT and TSDT predict almost the same distribution for the two planer stress and out-of-plane shear stress components along the face sheet thickness. Furthermore, third-order shear deformation theory seems to be more appropriate for prediction of out-of-plane shear stress at lower values of a/h ratio.

Keywords

Main Subjects

[1] B. Liu., A. J. M. Ferreira, Y. F. Xing, A. M. A. Neves, Analysis of composite plates using a layerwise theory and a differential quadrature finite element method, Composite Structures Vol. 156, pp. 6, 2016.
[2] M. E. Fares, M. K. H. Elmarghany, M. G. Salem, A layerwise theory for Nth-layer functionally graded plates including thickness stretching effects, Composite Structures, Vol. 133, pp. 12, 2015.
[3] C. H. Thai, A. J. M. Ferreira, E. Carrera, H. N. Xuan, Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory, Composite Structures, Vol. 104, pp. 19, 2013.
[4] A. J. M. Ferreira, G. E. Fasshauer, R. C. Batra, J. D. Rodrigues, Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter, Composite Structures, Vol. 86, pp. 16, 2008.
[5] C. M. C. Roque, J. D. Rodrigues, A. J. M. Ferreira, Static Deformations and Vibration Analysis of Composite and Sandwich Plates Using a Layerwise Theory and a Local Radial Basis Functions-Finite Differences Discretization, Mechanics of Advanced Materials and Structures Vol. 20, pp. 13, 2013.
[6] S. Farahmand, A. A. Atai, Parametric investigation of auto-frettage process in thick spherical vessel made of functionally graded materials, Journal of Computational Applied Mechanics, Vol. 47, No. 1, pp. 9, 2016.
[7] A. Afshin, M. Z. Nejat, K. Dastani, Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 12, 2017.
[8] M. Goodarzi, M. N. Bahrami, V. Tavaf, Refined plate theory for free vibration analysis of FG nanoplates using the nonlocal continuum plate model, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 14, 2017.
[9] M. Gharibi, M. Z. Nejad, A. Hadi, Elastic analysis of functionally graded rotating thich cylindrical pressure vessels with exponentially varying properties using power series method of frobenius, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 10, 2017.
[10] J. L. Mantari, A. S. Oktem, C. G. Soares, Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Composite Structures, Vol. 94, pp. 13, 2011.
[11] H. N. Xuan, C. H. Thai, T. N. Thoi, Isogeometric finite element analysis of composite sandwich plates using a higher-order shear deformation theory, Composites: Part B, Vol. 55, pp. 17, 2013.
[12] M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-mechanical vibration analysis of FG circular and annular nanoplate based on the visco-pasternak foundation, journal of Solid Mechanics, Vol. 8, No. 4, pp. 18, 2016.
[13] M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm based electromechanical sensors via higher order nonlocal strain gradient theory, IET Micro & Nano Letters, Vol. 11, No. 6, pp. 6, 2016.
[14] A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 9, 2014.
[15] A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E, Vol. 44, pp. 9, 2011.
[16] A. Farajpour, M. R. H. Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal Nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 14, 2015.
[17] M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composite: Part B, Vol. 56, pp. 9, 2014.
[18] M. Mohammadi, A. Farajpour, M. Goodarzi, H. S. n. pour, Numerical study of the effect of shear in plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 11, 2014.
[19] M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composite: Part B, Vol. 45, pp. 11, 2013.
[20] A. Farajpour, M. R. Haeri, A. Rastgoo, M. Mohammadi, A higher order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mech, Vol. 227, pp. 19, 2016.
[21] P. Ghabezi, M. Farahani, Composite adhesive bonded joint reinforcement by incorporation of nano-alumina particles, Journal of Computational Applied Mechanics, Vol. 47, No. 2, pp. 9, 2017.
[22] S. J. Lee, H. R. Kim, FE analysis of laminated composite plates using a higher-order shear deformation theory with assumed strains, Latin American Journal of Solids and Structures, Vol. 10, pp. 25, 2013.
[23] M. S. A. Houari, A. Tounsi, A. Beg, Thermoelastic bending analysis of functionally graded sandwich plates using a new higher-order shear and normal deformation theory, International Journal of Mechanical Sciences Vol. 76, pp. 10, 2013.
[24] M. Meunier, R. A. Shenoi, Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory, Composite Structures, Vol. 24, pp. 12, 2001.
[25] M. Shishesaz, M. Kharazi, P. Hosseini, M. Hosseini, Buckling behavior of composite plates with a pre-central circular delamination defect under in plane unaxial compression, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 12, 2017.
[26] C. H. Thai, A. J. M. Ferreira, M. A. Wahab, H. N. Xuan, A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis, Acta Mech, Vol. 227, pp. 26, 2016.
[27] S. Sarangan, B. H. Singh, Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories, Composite Structures, Vol. 138, pp. 13, 2016.
[28] S. Srinivas, A. K. Rao, Bending, Vibration and Buckling of simply supported thick orthotropic rectangular plates and laminates, International Journal of solid structures, Vol. 6, pp. 19, 1970.
[29] H. H. Abdelaziz, H. A. Atmane, I. Mechab, L. Boumia, A. Tounsi, A. B. E. Abbas, Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory, Chinese Journal of Aeronautics, Vol. 24, pp. 15, 2011.
[30] H. Cease, P. F. Derwent, H. T. Diehl, J. Fast, D. Finley, Measurement of mechanical properties of three epoxy adhesives at cryogenic temperatures for CCD construction, Fermilab-TM, 2006.
[31] L. D. Peel, Exploration of high and negative Poisson's ratio elastomer-matrix laminates, Physica status solidi (b), Vol. 244, pp. 16, 2007.
[32] V. Gonca, Definition of poissin’s ratio of elastomers, Engineering for rural development, in 10th International scientific conference Engineering for Rural Development, Jelgava, Latvia, 2011. 
Volume 48, Issue 2
December 2017
Pages 233-252
  • Receive Date: 05 August 2017
  • Revise Date: 25 August 2017
  • Accept Date: 01 September 2017