Exact three-dimensional elasticity analysis for buckling of composite laminated plates resting on viscoelastic foundation

Abstract

This paper aims to present novel exact solutions for the buckling of a laminated plate resting on the viscoelastic foundation with both normal and shear viscoelastic layers. The governing equations of plate buckling are derived using three-dimensional elasticity theory and state-space formulation. The normal and shear layers of the viscoelastic foundations are modeled using the generalized Maxwell model to represent both the elastic and viscose properties of the foundation. To couple the viscoelastic foundation equation with the buckling equation, Boltzmann’s superposition principle along with the Laplace transform is utilized. Then, the effects of geometry, relaxation modulus of normal and shear layers, viscosity, and time are investigated on the buckling load. The results reveal that the higher viscosity coefficient leads to a slower rate of change in the buckling loads. In addition, the viscoelastic properties have a significant impact on the buckling behavior of the plate. In this regard, the results show that instead of the expected second mode at a constant aspect ratio, the plate experiences the first mode as time passes. The computed results also show that there is a critical threshold. When the foundation stiffness exceeds this threshold, the conventional method of reducing the aspect ratio to prevent buckling not only proves ineffective in reducing the probability of buckling but also, in fact, leads to an increase in buckling occurrences. In addition to the analytical investigation, a finite element (FE) analysis is carried out to study the buckling response of the composite plate. The finite element results also show a reasonably good agreement with those of the analytical method.