Application of a three-dimensional mixed finite element model to the flexure of sandwich plate

Abstract

The bending analysis of sandwich plates consisting of very stiff face sheets and a comparatively flexible core material offers challenge due to large variation in the magnitude of stress and strain components in the face and in the core regions of the plate. Similarly, the displacement fields do vary in zigzag manner at the layer interface of stiff face sheet and the soft core, thereby making the transverse strains highly discontinuous at such layer interfaces. All these behavioural aspects indicate that only an individual layerwise model can appropriately analyze sandwich plates. A layerwise (three-dimensional), mixed, 18-node finite element (FE) model developed by Ramtekkar et al. [Mech. Adv. Mater. Struct. 9 (2002) 133] has been employed for the accurate evaluation of transverse stresses in sandwich laminates. The FE model consists of six degrees-of-freedom (three displacement components and three transverse stress components τ xz , τ yz , σ z , where z is the thickness direction) per node which ensures the through thickness continuity of transverse stress and displacement fields. Results obtained by using the FE model have shown excellent agreement with the available elasticity solutions for sandwich plates. Additional results on the variation of transverse strains have also been presented to highlight the magnitude of discontinuity in these quantities due to difference in properties of the face and the core materials of sandwich plates.