Buckling of Viscoelastic Thick Plates by Finite Strip Method and Higher Order Shear Deformation Theory

Author

Abstract

Time depended deformation and critical buckling load of viscoelastic thick plates were studied using finite strip method with the trigonometric functions in longitudinal direction and the polynomial functions in transverse direction. The plates were considered to be thick and the third order shear deformation theory was used to consider the effect of shear stresses in thickness. The mechanical properties of the material were considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. Time history of maximum deflection of viscoelastic plates subjected to transverse loading and unloading on plates was calculated using a fully discretized formulation. In addition, the critical in-plane load of plates was calculated by a nonlinear procedure in different times of loading. Moreover, the effect of thickness and the interaction of biaxial in-plane loading on critical load of plate were studied. The results show that the interaction curves of biaxial critical load of viscoelastic plates have the linear behavior for all time of loading.

Keywords

Main Subjects

References

[1] Christensen RM (1982) Theory of viscoelasticity (2nd edn). Academic Press, New York.
[2] Akoz Y, Kadioglu F (1999) The mixed finite element method for the quasi-static and dynamic analysis of viscoelastic Timoshenko beams. Int J Numer Meth Eng 44: 1909-1923.
[3] Chen Q, Chan YW (2000) Integral finite element method for dynamical analysis of elastic-viscoelastic composite structures. Comput Struct 74: 51-64.
[4] Palfalvi A (2008) A comparison of finite element formulations for dynamics of viscoelastic beams. Finite Elem Anal Des 44: 814-818.
[5] Johnson AR, Tessler A, Dambach M (1997) Dynamics of thick viscoelastic beams. J Eng Mater-T ASME 119: 273-278.
[6] Ranzi G, Zona A (2007) A steel–concrete composite beam model with partial interaction including the shear deformability of the steel component. Eng Struct 29: 3026-3014.
[7] Sheng DF, Cheng CJ (2004) Dynamical behavior of nonlinear viscoelastic thick plates with damage. Int J Solids Struct 41: 7287-7308.
[8] Hatami S, Ronagh HR, Azhari M (2008) Exact free vibration analysis of axially moving viscoelastic plates. Comput Struct 86: 1738-1746.
[9] Jin G, Yang C, Liu Z (2016) Vibration and damping analysis of sandwich viscoelastic-core beam using Reddy’s higher-order theory. Compos Struct 140: 390-409.
[10] Ready JN (1985) A simple higher order theory for laminated composite plates. J Appl Mech-T ASME 51: 745-752.
[11] Reddy JN, Phan ND (1985) Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory. J Sound Vib 98(2): 157-170.
[12] Bradford MA, Azhari M (1995) Buckling of plates with different end conditions using the finite strip method. Comput Struct 56: 75-83.
[13] Amoushahi H, Azhari M (2009) Buckling of composite FRP structural plates using the complex finite strip method. Compos Struct 90: 92-99.
[14] Jafari N, Azhari M, Heidarpour A (2011) Local buckling of thin and moderately thick variable thickness viscoelastic composite plates. Struct Eng Mech 40(6): 783-800.
[15] Jafari N, Azhari M, Heidarpour A (2012) Local buckling rectangular viscoelastic composite plates. Accepted in Mech Adv Mater Struc.
[16] Amoushahi H, Azhari M (2013) Static analysis and buckling of viscoelastic plates by a fully discretized nonlinear finite strip method using bubble functions. Compos Struct 100: 205-217.
[17] Amoushahi H, Azhari M (2014) Static and instability analysis of moderately thick viscoelastic plates using a fully discretized nonlinear finite strip formulation. Compos Part B-Eng 56: 222-231.
[18] Amoushahi H, Azhari M, Heidarpour A (2015) A fully discretised nonlinear finite strip formulation for prebuckling and buckling analyses of viscoelastic plates subjected to time-dependent loading. Mech Adv Mater Struc 22(8): 655-669.
[19] Szilard R (2004)  Theories and applications of plate analysis. John Wiley & Sons.
[20] Lai J, Bakker A (1996) 3-D Schapery representation for non-linear viscoelasticity and finite element implementation. Comput Mech 18: 182-191.
[21] Zenkour AM (2004) Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. J Eng Math 50: 75-93.
Journal of Solid and Fluid Mechanics
Volume 6, Issue 4
January and February 2016
Pages 103-124

Files

Share

How to cite

Statistics