Three-layered plate: Elasticity solution - Foraboschi, Paolo (Composites. Part B, Engineering, 2014)
The subject of this paper is the plate composed of two identical isotropic outer layers and a more compliant inner interlayer, perfectly connected to one another at the interface (three-layered plate). This paper presents a model that describes the behavior of this plate by a system of exact analytical (explicit) equations. An analytical model is preferred over finite element models and simplified formulas if it is fast and easy-to-use. Thus, modeling has been developed within the framework of two-dimensional elasticity, instead of three. In so doing, the model also represents a means for attaining full comprehension of the involved phenomena, something that neither three-dimensional elasticity nor finite element models and simplified formulas can attain. The two-dimensional behavior is governed here by using assumptions that do not impose constraints on the behavior. Starting from these assumptions, the paper illustrates the relationships between displacements and interface stresses. The subsequent sections of the paper describe the model and present some real case applications. The contribution of this paper is to consider both the shear modulus and the elastic modulus of the interlayer. Thus, this model applies to three-layered plates with any interlayer, whether utterly compliant or relatively stiff. Conversely, the previous exact analytical models assumed zero elastic modulus, and hence they applied to utterly compliant interlayers only. Hence, not only does the new model predict the exact behavior of plates that the former analytical models described only approximately, but this model may also be used as a benchmark for finite element models, which cannot assign zero value to the elasticity modulus of the interlayer together with the actual shear modulus.