Prediction of non-linear buckling load of imperfect reticulated shell using modified consistent imperfection and machine learning

A modified method is proposed for the consistent imperfection method, which introduces the shape of the first order linear buckling mode of a spatial structure as the imperfection pattern to estimate the non-linear buckling load of an imperfect structure. By adjusting the magnitudes of the joint deflection component and the member deformation component, the imperfection pattern calculated by the modified method is shown to be more reasonable to represent the construction and fabrication errors in reality. It is also found that the imperfection pattern calculated by the first-order linear buckling mode may not be the most adverse one to the structure, and the non-linear buckling load of the imperfect structure is highly associated with the similarity between the imperfection pattern and the deformation of the structure, which is described by the Euclidean distance between the imperfection pattern and the incremental displacement vectors. Subsequently, a prediction method of the non-linear buckling load of an imperfect structure is proposed using machine learning techniques, including the artificial neural network and the support vector regression (SVR), which avoid the computation cost of multiple non-linear buckling analysis for imperfect structures. Finally, the performance of the prediction method is verified, and a simplified formula is given for the design of reticulated shells based on the SVR with the linear kernel.