A Generalized Analytical Modeling of Grid Stiffened Composite Structures

Abstract

With the advancement of manufacturing technology, advanced grid stiffened (AGS) composite structures have been extensively studied recently due to their superior structural performance at a lower cost. Currently, the theoretical analysis involving AGS structures without fillers (empty bay) is dominated by the smeared method and finite element analysis (FEA). Obviously, the smeared method averages the local information and fails to predict structural behavior when the length scale (contact area) of the external load is smaller than the length scale (size) of the unit cell. This is because the actual structural behavior heavily depends on the spatial location of the applied load (at the rib, node, or cell). The limitation of FEA persists in its difficulty in conducting structural optimization. For AGS structures with fillers (filled bay), the interaction between the filler and the grid skeleton offers a higher level of challenge to theoretical modeling. In this study, a generalized analytical model was developed to predict the static structural behavior without smearing. This model was generalized in such a way that it unified the analysis of both empty bay and filled bay and could be reduced to conventional laminated composite or sandwich composite. This model was developed based on the classical lamination theory by treating the bay area as inclusion and the physical discontinuity between the rib and the bay was considered by introducing a stiffness distribution function. Using Hamilton's variational principle, the governing equation and boundary condition were obtained. The variable coefficient differential equation was solved by Fourier series expansion technique. The model was first validated by a numerical result found in the literature. Parametric studies were then conducted to evaluate the effect of various design parameters on the structural behavior subjected to both distributed load and concentrated load.