Geometric nonlinearity effects on the behavior of sandwich structures
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The Extended High-order Sandwich Panel Theory (EHSAPT) accounts for the axial rigidity, the transverse compressibility, and the shear effect of the core. Thus, it is suitable for sandwich composites made of a wide range of core materials, including soft cores and stiff cores. However, its analytical solution is only available to particular cases, i.e., sandwich panels with simply supported edges and subjected to sinusoidally distributed transverse loads. To obtain its solutions under general boundary conditions and loadings, a special finite element is first proposed to implement the EHSAPT with the finite element method. The proposed method extends the application of the EHSAPT and can easily handle arbitrary combinations of boundary conditions and loadings. Small deformation and infinitesimal strain were considered in the EHSAPT. In this dissertation, the EHSAPT is further developed to include geometric nonlinearities. Both faces and core are considered undergoing large deformation and moderate rotation. The weak form nonlinear governing equations of static behavior are derived from the principle of minimum total potential energy, and the equations of motion for dynamic response are derived from Hamilton's principle. The geometric nonlinearity effects on both static behavior and dynamic response of sandwich structures are investigated. In the literature, there are various simplifying assumptions adopted in the kinematic relations of the faces and the core when considering the geometric nonlinearities in sandwich structures. It is common that only one nonlinear term that appears in faces is included, and the core nonlinearities are neglected. A critical assessment of these assumptions, as well as the effects of including the other nonlinear terms in the faces and the core is made. It shows that the geometric nonlinearities of the core have significant effects on the behavior of sandwich structures. The stability behavior is very important to sandwich structures. The compressive strength of the thin faces and the overall behavior of sandwich structure can be realized only if it is stabilized against buckling. As a compound structure, a sandwich structure has more complicated stability behavior than an ordinary beam. The compressibility of the core significantly affects the stability response and contributes to the local instability phenomenon. Therefore, despite the global buckling (Euler buckling), very common in ordinary beams and plates, wrinkling, characterized as short-wave buckling, may also occur in sandwich structures. The stability investigation of sandwich structures is carried out based on the derived weak form nonlinear governing equations. The buckling analysis, which determines the buckling mode shape and critical buckling load at a convenient manner, and the nonlinear post-buckling analysis, which evaluates the post-buckling response of sandwich structures, are both presented. Both wrinkling and global buckling are observed. It is shown that although the axial rigidity of the core usually is hundreds times smaller than that of the faces, which is often negligible in the static analysis, it has significant influence on the stability response.