A new model for the eigenvalue buckling analysis with unknown-but-bounded parameters

For the dispersity of material properties, geometry dimensions and other parameters, uncertainty is unavoidable introduced into the solution of structural stability problem. The paper presents a new model for the evaluation of structural buckling loads with unknown-but-bounded parameters. Regarding unknown-but bounded parameters as interval variables, the elastic stiffness matrix, geometric stiffness matrix and eigenvalue with uncertain parameters are divided into deterministic part and perturbation part taking use of perturbation theory. The deterministic part of eigenvalues is calculated by Finite Element method utilizing the deterministic part of elastic stiffness matrix and geometric stiffness matrix. And the interval uncertain part of eigenvalues is derived by interval arithmetic and first order perturbation theory. Eventually, the upper bound and lower bound of structural buckling eigenvalues then can be easily obtained by summing the deterministic part and uncertain part of buckling eigenvalues. Comparing the results with traditional Monte Carlo simulation, two numerical examples are given to demonstrate the accuracy and efficiency of the proposed method for the solution of eigenvalue buckling problems with unknown-but-bounded parameters. The results also present the coincidence of the proposed method with probabilistic method. (C) 2021 Elsevier Masson SAS. All rights reserved.

Automated summary

This paper presents a new model for evaluating structural buckling loads with unknown-but-bounded parameters. By dividing parameters into deterministic and uncertain parts, and combining finite element method with perturbation theory, the deterministic and uncertain parts of buckling eigenvalues can be effectively calculated, resulting in upper and lower bounds for the structural buckling eigenvalues.