Soft-core sandwich panels with embedded rigid inclusions

The structural response of sandwich panels hosting rigid inclusions (inserts) embedded in a soft core is analytically investigated. Three approaches for the mathematical modeling of the structural behavior of the sandwich panel hosting the rigid inclusion are formulated, examined, and compared. In the first approach, the rigid body displacement field of the inclusion is introduced through a unique constitutive law. The second approach uses a multilayered high-order model in which the rigid insert is modeled using significantly increased but finite mechanical properties. In the third approach, the embedded inclusion is considered infinitely rigid and the compatibility and interaction between the rigid insert and the adjacent structural components are imposed using Lagrange multipliers. In all the cases, the field equations and the boundary condition are derived using variational principles. The continuity conditions that connect between the region hosting the rigid insert and the adjacent ordinary sandwich regions are also derived using the variational principle. The mathematical models resulting from the first and second approaches take the form of a set of coupled differential equations. On the other hand, the third approach, which takes advantage of the rigid body displacement field of the embedded inclusion, yields a reduced order set of coupled differential-integral equations. An analytical procedure for the solution of this set of equations is derived. Numerical results that focus on the deformed shape of the panel under load, the distributions of the internal stress resultants, the shear and vertical normal stresses in the core, and the interaction between the rigid insert and the adjacent components are presented. The numerical results compare between the various modeling approaches, demonstrate their capabilities, and reveal some of the characteristics of such sandwich panels. A summary and conclusions closes the paper.