Nonlinear Dynamic Stability Behavior of Sandwich Beams/wide Plates

The static buckling load gives the limit above which a structure can deform in an alternative way associated with a significant deformation and a possible failure mode when the structure is subjected to a quasi-static load. In contrast, when the load is applied dynamically, the stability limit is no longer as significant as in the static case. A dynamic impulsive load with a short load duration may safely exceed the static critical load since the structure has no time to deform to the corresponding to static equilibrium state.  In this research, the dynamic stability analysis of sandwich panels is studied based on the Extended High-order Sandwich Panel Theory (EHSAPT), which successfully analyzed the nonlinear dynamic response of sandwich panels subjected to transverse blast loads. By considering the fact that the faces and core can have very large differences in both material properties and geometry, the EHSAPT employs different displacement fields in the faces and core in order to achieve a balance between computational efficiency and result accuracy. It includes the axial rigidity, transverse compressibility, and high order shear deformation of the core. Thus, the EHSAPT is applicable to sandwich panels made with a wide range of core materials, including very soft ones. The nonlinear dynamic analysis of sandwich panels (Yuan and Kardomateas, Int. J. Sol. Struct. 148-149, pp. 110-121, 2018) has shown that the geometric nonlinearities can have a significant effect on the dynamic response of sandwich panels and, in particular, the nonlinear terms in the core kinematic equations are especially important. In this study, the faces and the core are both considered undergoing large deformations with moderate rotations. In the core, all nonlinear terms of the Green-Lagrange strains are included. In the spatial domain, the sandwich panel is modeled with the EHSAPT-based sandwich finite element  (Yuan, Kardomateas and Frostig, AIAA J., 53, pp. 3006-3015, 2015). The time domain response is obtained by an explicit direct time integration method, the central difference method.  Initial imperfections are considered in order to obtain the possible dynamic stable or unstable response. A simply supported sandwich panel is chosen as the numerical example to discuss the nonlinear dynamic stability behavior of a sandwich panel. Several different types of impulsive loads are considered as the loading profile. The dynamic response and dynamic stability behavior are also compared with the corresponding ones from an earlier study, in which the simplified linear version of EHSAPT was used to model the sandwich panel.

Acknowledgment

The financial support of the Office of Naval Research, Grant N00014-20-1-2605, and the interest and encouragement of the Grant Monitor, Dr. Y.D.S. Rajapakse, is greatefully acknowledged.