Towards the fast buckling load prediction of composite shells via Bloch wave based numerical vibration correlation technique

The buckling load revealing structural capacity bears significant value for the design of engineering composite shells, especially in the aerospace industry. Non-destructive methods are prevailing for critical buckling load prediction. However, the experimental costs and computational time for the analysis are unaffordable, especially for large-scale and complex shells. Despite the numerical vibration correlation technique (NVCT) and its modifications proposed for faster critical buckling load prediction, the efficiency requires further improvement. For composite shells with rotational periodicity, analyzing one substructure based on the Bloch wave method can be an alternate for the analysis of the entire shell. Since the NVCT comprises the linear buckling analysis and repeated frequency analyses, twofold acceleration can be performed. Thus, the Bloch wave based numerical vibration correlation technique (BW-NVCT) is proposed. Firstly, the formulations for the Bloch wave method and the NVCT are derived. As the curve of Bloch wave numbers and buckling loads is monotonous or principally comprise a single peak, the computations in the Bloch wave method to determine the minimum buckling load are further reduced. Then, the implementation of BW-NVCT is presented wherein the Bloch wave calculations are simplified compared with the Bloch wave buckling analysis method. Secondly, three types of composite shells including the Z33 composite cylindrical shell, the pressure vessel and the nozzle are analyzed by the proposed method. By applying Bloch boundary conditions to the substructure, the linear buckling loads, natural frequencies are in high accuracy with respect to results by finite element analyses directly. In addition, predicted critical buckling loads by the BW-NVCT are in excellent precision and most importantly, remarkable efficiency is achieved compared with both the NVCT and the dynamic explicit analysis. Results show that the proposed method can capture both global and local buckling modes, even when bend-twist coupling exists. It is concluded that the BW-NVCT is widely applicable for composite shells and is substantiated as an effective method for fast buckling load prediction.