A verified analytical sandwich beam model for soft and hard cores: comparison to existing analytical models and finite element calculations

Abstract

This paper presents a novel approach of modeling of three-layer beam. Such composites are usually known as sandwich structures if the modulus of elasticity of the core is much smaller than those of the faces. In the present approach, the faces are modeled as Bernoulli–Euler beams, the core as a Timoshenko beam. Taking into account the kinematic and dynamic interface conditions, which means that the perfect bonding assumptions hold for the displacement and each layer is subjected to continuous traction stresses across the interface, a sixth-order differential equation is derived for the bending deflection, and a second-order system for the axial displacement. No restrictions are imposed on the elastic properties of the middle layer, and hence the developed theory also yields accurate results for hard cores. The presented refined theory is compared to analytical models from the literature and to finite element calculations for various benchmark examples. Special focus is laid the boundary conditions and the core stiffness. A parametric study varying the Young modulus of the core shows that the present sandwich model agrees very well with the target solutions obtained from finite element calculations under plane stress assumptions, in particular concerning the transverse deflection, the shear stress distribution and the interfacial normal stress.