The design of a reticulated shell with a small thickness-to-span ratio is generally dominated by structural stability checks under a few load cases (dominant loads). Evaluating and predicting the structural stability is crucial for existing reticulated shells, especially those in corrosive environments. In this paper, a Bayesian modeling approach is proposed to predict the structural stability of an existing reticulated shell by using measured structural displacements induced by scheduled static loadings. The minimum eigenvalue of the tangent stiffness matrix is employed as an indicator of structural stability for a reticulated shell subjected to a given dominant load. The relationship between the minimum eigenvalue and the structural elastic stiffness matrix is established, revealing that the stability indicator can be determined using a few eigenvalues and their corresponding eigenvectors of the elastic stiffness matrix. Using the analytical relationship between the structural displacement and the elastic stiffness matrix, a static loading strategy is then proposed to determine the stability indicator of an existing reticulated shell. An optimization strategy based on the interior-point penalty method is proposed to ensure that all static loads are applied vertically downward. A Bayesian model based on Gaussian process regression is established for the minimum eigenvalue. After the structural displacements under the scheduled static loadings during the service life of a reticulated shell are measured, the corresponding minimum eigenvalues at the observed times can be determined using the proposed method and then employed to optimize the hyperparameters of the Bayesian model using the interior-point penalty method. Thus, the structural stability of an existing reticulated shell can be predicted using the optimized Bayesian model. Two illustrative examples of existing reticulated shells under a given dominant load are created by assigning randomly generated deviations in the member cross-sectional areas of their design models. The structural stability during service life is predicted using the proposed method, and the accuracy and validity of the approach are verified by comparing the results with exact values.
Lyu et al. (Thu,) studied this question.