On the Time-Dependent Behavior of FGM Plates

Abstract

Abstract.A non-classical plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. In addition, the material properties are changing in the thickness direction. Solving some problems of the global structural analysis it can be shown that in some cases the results based on the presented theory significantly differ from the results based on the Kirchhofftype theory.

Mechanics of Viscoelastic Plates Made of FGMs

“…For the FGM plate the bounds for K are given in [3]. For the viscoelastic plate both the qualitative and the quantitative influence of the shear stiffness is the same as in [2].…”

“…Analogous to (2.19) the following relation can be established for the shear relaxation function Using experimental data presented in [5] one can assume ν(t) = ν = const. In this case we have the relations [3] A 11 = A 22 1…”

“…For the linear variant of such theory the identification of the elastic stiffness tensors considering changing properties is proposed in [6][7][8], see also [9,10]. Some extensions of the proposed theory of plates to the case of viscoelastic materials are given in [11] and applied to FGMs in [1][2][3].…”

“…Using the correspondence principle (the analogy between (2.12) and the Hooke's law) we can extend the identification procedure presented in [6][7][8] to the Laplace mapping of the effective relaxation or creep functions, see [1,3]. For the orthotropic viscoelastic material the in-plane and the out-of-plane stiffness tensor components are …”

“…Within the proposed theories the elastic, thermoelastic, and magnetoor electroelastic behaviour of the plate material are taken into account. In general, the viscoelastic properties of FGM plates are less considered see [1][2][3] and [18].…”