Nondeterministic dynamic stability assessment of Euler–Bernoulli beams using Chebyshev surrogate model

• Published in: Applied Mathematical Modelling Vol. 66; p. 1
• Main Authors: Gao, Kang, Gao, Wei, Wu, Binhua, Song, Chongmin
• Format: Journal Article
• Language: English
• Published: New York Elsevier BV 01-02-2019
• Subjects: Boundary conditions; Buckling; Chebyshev approximation; Computer simulation; Cost analysis; Design optimization; Dynamic stability; Euler-Bernoulli beams; Galerkin method; Lower bounds; Modulus of elasticity; Monte Carlo simulation; Nonlinear differential equations; Optimization algorithms; Ordinary differential equations; Particle swarm optimization; Sequences; Stability analysis; Time dependence
• ISSN: 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.09.007

A novel nondeterministic dynamic stability assessment of Euler–Bernoulli beams using Chebyshev surrogate model is proposed to investigate the upper and lower bounds of the dynamic buckling responses in this paper. In the proposed approach, the Galerkin method in conjunction with the force equilibrium is used to obtain the unified implicitly nonlinear ordinary differential equation (ODE) and then this equation can be transformed into a series of ODEs at observation points for each interval variable. Thus, the explicit approximate performance function is constructed with regards to all the interval variables by using Chebyshev surrogate strategy. By combining with the low-discrepancy sequences initialized high-order nonlinear particle swarm optimization (LHNPSO) algorithm, the computational cost is drastically reduced. The comprehensive computational method provides a unified analytical framework to model interval uncertainty for dynamic buckling analysis, which is competent to investigate the extremely upper and lower bounds of structural behaviors. Additionally, the validity, accuracy, as well as the applicability of the proposed computational approach are rigorously investigated by comparing the outputs (i.e., critical buckling load, time of onset of buckling, the corresponding axial shortening displacement and transverse displacement) of the proposed approach with that of Quasi-Monte-Carlo Simulation (QMCS) method for various boundary conditions with interval inputs (i.e., Young's modulus, initial imperfections and loading velocity). The nondeterministic dynamic buckling assessment methodology can help optimization design of beam-type structures under time-dependent loads faster, efficient and flexible.