Stochastic buckling analysis of sandwich plates: The importance of higher order modes

The stochastic buckling behaviour of sandwich plates is presented considering uncertain system parameters (material and geometric uncertainty). The higher-order-zigzag theory (HOZT) coupled with stochastic finite element model is employed to evaluate the random first three buckling loads. A cubic in-plane displacement variation is considered for both face sheets and core while quadratic transverse displacement is considered within the core and assumed constant in the faces beyond the core. The global stiffness matrix is stored in a single array by using skyline technique and stochastic buckling equation is solved by simultaneous iteration technique. The individual as well as compound stochastic effect of ply-orientation angle, core thickness, face sheets thickness and material properties (both core and laminate) of sandwich plates are considered in this study. A significant level of computational efficiency is achieved by using artificial neural network (ANN) based surrogate model coupled with the finite element approach. Statistical analyses are carried out to illustrate the results of stochastic buckling behaviour. Normally in case of various engineering applications, the critical buckling load with the least Eigen value is deemed to be useful. However, the results presented in this paper demonstrate the importance of considering higher order buckling modes in case of a realistic stochastic analysis. Besides that, the probabilistic results for global stability behaviour of sandwich structures show that a significant level of variation with respect to the deterministic values could occur due to the presence of inevitable source-uncertainty in the input parameters demonstrating the requirement of an inclusive design paradigm considering stochastic effects.