Layered plate with discontinuous connection: Exact mathematical model

The subject of this paper is the plate composed of two identical layers connected to each other in a discontinuous way, i.e. via discontinuous elements (connectors). This paper presents a model that describes the mechanical behavior of this plate by a system of exact, analytical (explicit) equations. The discrete distribution of discontinuous connectors is replaced by a fictitious continuous medium (interlayer). Accordingly, the plate is modeled as an equivalent three-layered plate: Two outer layers and a connecting inner interlayer. In order to obtain a fast and easy to use tool, something that is necessary for an analytical model to be chosen over finite elements and empirical formulas, modeling process is developed within the framework of two-dimensional elasticity. In so doing, the model also represents a means for attaining full comprehension of the mechanical phenomena that are involved, something that neither three-dimensional elasticity nor finite elements and empirical formulas can attain. The transition from three to two-dimensional behavior is obtained by relating the normal stress in the direction transverse to the plate to the distortion in the interlayer. The two-dimensional behavior is governed using kinematic and force assumptions that do not impose appreciable constraints on the stress-strain state and structural behavior. Starting from these assumptions, the paper develops the relationships between displacements and interface stresses, for both continuous and discontinuous connection. The latter relationships, which are used in this model, and the former relationships, which were used in a previously presented model, are discussed and compared to each other. The subsequent sections of the paper describe the model and present some real case applications of discontinuously-connected layered plate.