Limits of Application for Two-Dimensional Elasticity Solutions in Plates Loaded in Tension and Out-of-Plane Bending

Abstract

Elasticity solutions of plates have been widely researched and used in practice. However, elasticity solutions of plane problems are applicable to structures only under the premise that such structures are very thin. The precise values of thickness for which elasticity solutions are valid have not been studied in detail. It is necessary to clarify the range of appropriate thickness values in order to apply two-dimensional elasticity solutions properly. In this study, we use finite element analyses to study three flat-plate models each containing a U-shaped hole of the same radius, and compared the three-dimensional finite element solutions with two-dimensional elasticity solutions. From the results, the limits of application of two-dimensional elasticity solutions are discussed.