Theory And Finite Element Analysis For Bending Of Sandwich Plates With Hard Cores

Sandwich plates are constituted by two thin but high-strength face sheets and one thicker butlight-weight core layer. Due to its light weight, high strength and stiffness, good ant-vibration andother excellent mechanical properties, sandwich plates find a wide range of application from aviation,aerospace, marine, wind power, building to packaging industry and become the research focus. Alarge number of domestic and international scholars have conducted in-depth study to it and putforward a variety of theoretical and computational models.Just as linear theory, the common models can be broadly grouped into the following three (1)Reissner’s Theory. Two face sheets are treated as films. Core layer only play the role of shear.(2)Hoff’s Theory. Two face sheets are treated as classic thin plates. Core layer only play the part of shear.(3) Прусаков-Du Qinghua’s Theory. Two face sheets are regarded as classic thin plates. Core layernot only plays the role of shear but also produces lateral elastic deformation. These three models allassume core layer is soft and ignore its bending stiffness and in-plane stress components. In this paperwe treat core layer as hard core and take into account in-plane stress components and bendingstiffness. So core layer play the role of shear and bending at the same time. This paper explores thebending problem of sandwich plates with hard core based on hard core layer assumption.Firstly, based on Reissner’s Theory this paper derives the bending basic equations and boundaryconditions of sandwich plane with hard core layer for the isotropic, orthotropic and different moduliin tension and compression materials, according to principle of minimum potential, respectively. Thenwe decouple the basic equations and work out analytical solution in some common boundaryconditions. Secondly, based on Hoff’s Theory this paper obtains the bending equations and boundaryconditions and boundary conditions according to principle of minimum potential. Finally, the paperpresents the finite element formulations for the bending problem of sandwich plates with hard cores.Four-node and eight-node quadrilateral isoparametric element are constructed and element stiffnessmatrix and equivalent nodal load vector are derived, respectively. The numerical results showthat the finite element solution converges to the analytical solution with sufficient accuracy.