Stress and displacement analysis of thick sandwich plates with deformable auxetic cores using an enhanced third order global-local theory

Authors

1 NRI

2 دانشکده مهندسی مکانیک

Abstract

In the present article, a high-order global-local theory with three-dimensional elasticity corrections is employed to trace the local and instantaneous variations of lateral deflections and stress components of sandwich plates with auxetic (negative Poisson ratio) cores under static loads. The governing equations are extracted based on Hamilton’s principle. The main novelties of the present research in comparison to the available literature are the presenting a higher-order global-local plate theory with equilibrium-based 3D-elasticity corrections, incorporation of the transverse flexibility of the core (a fact that is crucial when studying behaviors of thick or soft core sandwich plates) and investigation of the negative Poisson ratio (auxeticity) effects of the core material on the static (stress and displacment) responses. All these items are accomplished here, for the first time. Since the transverse shear stresses are extracted based on the 3D elasticity theory, in contract the traditional constitutive-based theories, the interlaminar continuity condition of the transverse shear stresses is met. The verification results show that the presented finite element formulation leads to highly accurate results, even for thick or soft core sandwich plates. Results reveal that auxeticity of the core material decreases the global and relative stresses and lateral deflections of the face sheets.

Keywords

Main Subjects

References

[1] Kant T, Swaminathan K (2000) Estimation of transverse/interlaminar stresses in laminated composites – a selective review and survey of current developments. Compos Struct 49: 65-75.
[2] Dafedar JB, Desai YM, Mufti AA (2003) Stability of sandwich plates by mixed, higher-order analytical formulation. Int J Solids Struct 40: 4501-17.
[3] Malekzadeh K, Khalili MR, Mittal RK (2005) Local and global damped vibrations of plates with a viscoelastic soft flexible core: An improved high-order approach. J Sandwich Struct Mater 7: 431-456.
[4] Carrera E, Brischetto S (2009) A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl Mech Rev 62: 1-17.
[5] Brischetto S, Carrera E, Demasi L (2009) Improved bending analysis of sandwich plates using a zig-zag function. Compos Struct 89: 408-415.
[6] Botshekanan Dehkordi M, Cinefra M, Khalilia SMR, Carrera E (2013) Mixed LW/ESL models for the analysis of sandwich plates with composite faces. Composite Structures 98: 330-339
[7] Li X, Liu D (1997) Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 40(7): 1197-1212.
[8] Shariyat M (2010) Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global–local plate theory. Compos Struct 92(1): 72-85.
[9] Chakrabarti A, Chalak H, Iqbal MA, Sheikh AH (2011) A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core. Compos Struct 93: 271-279.
[10] Demasi L (2012) Partially zig-zag advanced higher order shear deformation theories based on the generalized unified formulation. Finite Elem Ana Des 56: 20-31.
[11] Rahmani O, Khalili SMR, Thomsen OT (2012) A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads. Compos Struct 94(7): 2129-2142.
[12] Grover N, Maiti DK, Singh BN (2013) A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates. Compos Struct 95: 667-675.
[13] Kapuria S, Nath JK (2013) On the accuracy of recent global–local theories for bending and vibration of laminated plates. Compos Struct 95: 163-172.
[14] Khandelwal RP, Chakrabarti A, Bhargava P  (2013) A new C0 2D FE model based on improved higher order zigzag theory for analysis of soft core sandwich plate. Int J Appl Mech 18(2): 395-423.
[15] Lezgy-Nazargah M (2017) Assessment of refined high-order global–local theory for progressive failure analysis of laminated composite beams. Acta Mechanica 228(5): 1923-1940.
[16] Lezgy-Nazargah M, Shariyat M, Beheshti-Aval SB (2011) A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams. Acta Mechanica 217(3-4): 219-242.
[17] Lezgy-Nazargah M, Beheshti-Aval SB, Shariyat M (2011) A refined mixed global–local finite element model for bending analysis of multi-layered rectangular composite beams with small widths. Thin Wall Struct 49(2): 351-362.
[18] Pandit MK, Sheikhb AH, Singhc BN (2008) An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core. Finite Elem Anal Des 44: 602-610.
Journal of Solid and Fluid Mechanics
Volume 9, Issue 2
June 2019
Pages 109-122

Files

Share

How to cite

Statistics