Sandwich structures are typical found in designs that require high stiffness to weight ratio. Their use has also been demonstrated in the enhancement of acoustic properties, attainment of specific thermal properties, and for mere aesthetics. The classical three-layer sandwich structures have a core that is sandwiched between two face-sheets. The inadequacy of the classical assumptions in light of the growing trend towards flexible-core structures has led to the development of higher-order theories and layer-wise theories.
With regard to sandwich beams, the more prevalent assumptions are that the face-sheets and the core are adequately modelled by Euler-Bernoulli beam theory and Timoshenko beam theory, respectively. This is very limiting, especially in situations where the core is soft. The proposed quasi-two-dimensional finite element formulation expresses the through-thickness dependency of the field variables as polynomials while their span dependency across a finite element is cubically interpolated. The advantage of this formulation is demonstrated via parametric static and dynamic studies that includes the ratio of the modulus of elasticity of the core and face-sheets, and the ratio of their heights.
The fidelity of the formulation in relation to sandwich beams with viscoelastic core is also examined. The viscoelastic damping is represented using fractional derivatives. The Grünwald approximation is adopted and the resulting set of governing equations is integrated using the Newmark time-integration scheme.
The quasi-2D formulation permits the clamping of one end of the beam (i.e. fully cantilevered) or the the clamping of only one end of the face-sheets (i.e. partially cantilevered). The beam transverse displacement, but not the through-the-thickness stresses, is observed to be independent of the boundary condition type.