Analytical Solutions for Functionally Graded Sandwich Plates Bonded by Viscoelastic Interlayer Based on Kirchhoff Plate Theory

2020 ◽  
Vol 12 (06) ◽  
pp. 2050062
Author(s):  
Zhiyuan Yang ◽  
Peng Wu ◽  
Weiqing Liu ◽  
Hai Fang
Keyword(s):  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Time Dependent ◽  
Kirchhoff Plate ◽  
Time Step ◽  
Kirchhoff Plate Theory ◽  
Dependent Behavior ◽  
Present Solution ◽  
Viscoelastic Interlayer

In this paper, an analytical solution for functionally graded sandwich plate adhesively bonded by viscoelastic interlayer is proposed to research its time-dependent behavior. The Kirchhoff plate theory is employed to describe the mechanical property of each gradient layer with elastic modulus defined as the arbitrary function through the thickness direction. The standard linear solid model is applied to simulate the viscoelasticity of the interlayer with considering the strain memory effect. By the use of the vibrational method and the Laplace transformation, the solutions of stresses and displacements are solved analytically. The validation study indicates that the present solution is correct and more effective than the finite element solution because of the fine mesh both in the geometric shape and the time step. In addition, the influences of the geometry and material parameters on the time-dependent behavior of the sandwich plate are investigated in detail.

scholarly journals Time-dependent characteristics of two-layer functionally graded plates adhesively bonded by a viscoelastic interlayer based on Kirchhoff plate theory

Mechanika ◽  
2020 ◽  
Vol 26 (6) ◽  
pp. 478-485
Author(s):  
Zhiyuan YANG ◽  
Peng WU ◽  
Weiqing LIU
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Functionally Graded ◽  
Time Dependent ◽  
Functionally Graded Plates ◽  
Time Step ◽  
Fine Mesh ◽  
Present Solution ◽  
Stress And Deformation ◽  
Viscoelastic Interlayer

An analytical solution is proposed to investigate the time-dependent characteristics of two-layer functionally graded plates with a viscoelastic interlayer. The elastic modulus in each graded layer varies through the thickness following an arbitrary function, and its mechanical properties are described based on the Kirchhoff theory. The Maxwell-Wiechert model is applied to simulate the viscoelastic adhesive interlayer with the neglect of memory effect. The energy equation of the system is expressed by the deformation components, which are expanded as the double trigonometric series. By virtue of variational method, the solutions of stress and deformation are determined efficiently. The comparison study indicates that the present solution matches the finite element solution well; however, the finite element method is highly time-consuming because of the fine mesh in the geometric shape and the time step. Finally, the influences of the geometry and material on the time-dependent behavior of the structure are discussed in detail.

scholarly journals On the Time-Dependent Behavior of FGM Plates

2008 ◽  
Vol 399 ◽  
pp. 63-70 ◽  
Author(s):  
Holm Altenbach ◽  
Victor A. Eremeyev
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Material Behavior ◽  
Time Dependent ◽  
Classical Plate Theory ◽  
Graded Materials ◽  
Dependent Behavior ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

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.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

Time-Dependent Behavior and Fracture of Functionally Graded Thermal Barrier Coatings under Thermal Shock

2005 ◽  
Vol 492-493 ◽  
pp. 379-384 ◽  
Author(s):  
Klod Kokini ◽  
Sudarshan V. Rangaraj
Keyword(s):  
Thermal Shock ◽  
Thermal Barrier Coatings ◽  
Functionally Graded ◽  
Yttria Stabilized Zirconia ◽  
Time Dependent ◽  
Thermal Barrier ◽  
Stabilized Zirconia ◽  
Barrier Coatings ◽  
Dependent Behavior ◽  
Bond Coat Alloy

The thermal fracture and its dependence on time-dependent behavior in functionally graded yttria stabilized zirconia - NiCoCrAlY bond coat alloy thermal barrier coatings was studied. The response of three coating architectures of similar thermal resistance to laser thermal shock tests was considered, experimentally and computationally.

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