3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported

This is the continuation of our previous work on the structural safety of polymer matrix composites, subject to compressive loading and thermal gradient along the out-of-plane direction caused by fire damage [Asaro et al., Technical Report of Department of Structural Engineering, The University of California at San Diego, 1999]. The thermal gradient due to fire induces a gradient of structural properties, reduces the overall stiffness, e.g. degradation, and thus reduces the load carrying capacity. In the previous work, finite element calculation is compared against fire testing data; and based on these numerical and testing results, a methodology to quantify the structural integrity of composites under fire damage was presented. In the current work, an analytical expression for the buckling load is obtained from the theory of functionally graded materials. The rigorous theory of functionally graded materials accounts for the continuous variation of material properties-in this case, the variation of stiffness degradation caused by fire; and gives an exact solution for the buckling loads of structures graded along the thickness direction. The solutions are given in a relatively simple form, which can be used to guide design practice, to verify large finite element calculations, as well as to provide insights in fire testing. Good agreement is observed when comparing the solutions with fire testing data. In the light of fire testing and finite element computations, the implication of the analytical solution for fire safety design is discussed.