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

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.

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

International Journal of Applied Mechanics ◽

10.1142/s1758825120500623 ◽

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.

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Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive

Advances in Polymer Technology ◽

10.1155/2020/7358930 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Ruili Huo ◽

Yichen Liu ◽

Peng Wu ◽

Hai Fang ◽

Weiqing Liu ◽

...

Keyword(s):

Finite Element ◽

Layer Thickness ◽

Radial Direction ◽

Variable Coefficients ◽

Functionally Graded ◽

Fine Mesh ◽

Present Solution ◽

Polar Coordinate ◽

Graded Material ◽

2D Elasticity

In this work, analytical solution of simply supported sandwich arches considering permeation effect of adhesives is presented. The permeation layer is described by the functionally graded material, exponentially graded in the radial direction. The stresses and deformations of each layer are based on the two-dimensional (2D) elasticity theory in the polar coordinate. The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. The solution can be obtained efficiently by means of the recursive matrix method, especially for the arch with many layers. The present solution agrees well with the finite element solution with a fine mesh, while the finite element method is time consuming in mesh division and calculation. The one-dimensional (1D) solution based on the Euler–Bernoulli theory is close to the present one; however, the error increases as the arch becomes thick. The effect of permeation layer thickness on the stresses is studied. It is indicated that the stress distributions tend to be smooth along the radial direction as the permeation layer thickness increases.

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