3D analytical solution for multilayer functionally graded plates with viscoelastic interlayers

Abstract

In this study, an analytical model is developed to research on the time-varying performance of multilayer functionally graded plates glued by viscoelastic interlayers. In the plate, the elastic modulus in each graded layer is exponentially distributed along the thickness, and its mechanical property is modeled on the basis of the three-dimensional (3D) elasticity theory. The viscoelastic property in the interlayer is described by the standard linear solid model considering hereditary nature of viscoelasticity. By using the series expansion and the Laplace transformation, the solutions of stress and displacement for the multilayer plate are analytically derived out. The comparison analysis indicates that the finite element solution and the present one have a good agreement. The Kirchhoff-Love solution becomes imprecise as the thickness or the gradient index increases, because the transverse shear deformation is ignored. In the parameter analysis, the effects of the time variable, the gradient index and the viscoelastic constants on the time-varying performance of the multilayer functionally graded plate are analyzed in detail. The results show that the stress and displacement distributions of the multilayer functionally graded plate can be optimized by changing the gradient index.

Keywords:

• Multilayer plate
• functionally graded material
• viscoelastic interlayer
• laplace transformation
• series expansion

Additional information

Funding

This research is financially supported by Natural Science Foundation of Jiangsu Province (Grant No. BK20190668), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 19KJB560014) and National Key Research and Development Program of China (Grant No. 2019YFD1101205).