Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity
- 8 May 2012
- journal article
- Published by ASME International in Journal of Applied Mechanics
- Vol. 79 (4), 041001
- https://doi.org/10.1115/1.4005550
Abstract
A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core/face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout.Keywords
This publication has 14 references indexed in Scilit:
- On wrinkling of a sandwich panel with a compliant core and self-equilibrated loadsJournal of Sandwich Structures & Materials, 2011
- Three-dimensional elasticity solution for sandwich beams/wide plates with orthotropic phases: The negative discriminant caseJournal of Sandwich Structures & Materials, 2011
- Three-Dimensional Closed Form Solutions and ∞3Theories for Orthotropic PlatesMechanics of Advanced Materials and Structures, 2009
- The blast resistance of sandwich composites with stepwise graded coresInternational Journal of Solids and Structures, 2009
- A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich PlatesApplied Mechanics Reviews, 2008
- 2D, Quasi 3D and 3D Exact Solutions for Bending of Thick and Thin Sandwich PlatesJournal of Sandwich Structures & Materials, 2008
- Three-dimensional Elasticity Solution for Uniformly Loaded Cross-ply Laminates and Sandwich PlatesJournal of Sandwich Structures & Materials, 2007
- Dynamic buckling of flat and curved sandwich panels with transversely compressible coreComposite Structures, 2006
- High‐Order Theory for Sandwich‐Beam Behavior with Transversely Flexible CoreJournal of Engineering Mechanics, 1992
- Exact Solutions for Composite Laminates in Cylindrical BendingJournal of Composite Materials, 1969