Robust stability analysis of structures with uncertain parameters using mathematical programming approach

Abstract

SUMMARYThis paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties, geometry of element cross section, and loading conditions, all of which are described by an interval model. The proposed method formulates the two cases of interest, namely, worst and best buckling load calculation, into a pair of mathematical programming problems. Two straightforward advantages are exhibited by such formulations. The first advantage is that the proposed formulation can overcome the interference on the sharpness of bounds of the buckling load due to the interval dependence issue. The second benefit is that the information of uncertain parameters causing the extremities of buckling load can always be retrieved as by‐products of the uncertain stability analysis. Some numerical examples are presented to illustrate the capability of the proposed method on various structures and the sharpness of the bounds of the buckling load factors. The efficiency and effectiveness of the proposed method are also demonstrated through comparison with the classical Monte Carlo simulation method. Copyright © 2014 John Wiley & Sons, Ltd.

A new stochastic residual error based homotopy approach for stability analysis of structures with large fluctuation of random parameters

“…By using symbolic computing software, such as MAPLE, one can generate the explicit expressions of F m and D m through their recursive formulas Equations ( 14) and (15), respectively. Substituting F m and D m into Equation (11), the closed-form solutions of the random buckling eigenvalue F(𝛏) and corresponding buckling eigenvector D(𝛏) can be obtained as…”

“…Considering that the effects of uncertain material properties and geometrical sizes on the buckling load cannot be ignored, 2,3 various methods have been developed to deal with these effects. These methods can be roughly classified as Monte Carlo simulation methods, 4,5 perturbation methods 6–14 and others 15–20 …”

“…These methods can be roughly classified as Monte Carlo simulation methods, 4,5 perturbation methods 6-14 and others. [15][16][17][18][19][20]…”

“…Besides the above methods, some other effective approaches are proposed. Wu et al 15,16 provided an alternative approach to find the best and worst buckling load cases by modeling the uncertain parameters as interval fields, and the fluctuation rangeability of the elasticity modulus does not exceed ±24%. Recently, Li et al 17 emphasized that the lognormal random field is more suitable than the Gaussian field in describing the elastic modulus, and proposed a spectral stochastic isogeometric method for the stability analysis of plates with the COV smaller than 0.1.…”