Stochastic meshfree method for elastic buckling analysis of columns

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

“…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 …”

“…Altus and Totry 10,11 proposed a functional perturbation method to analytically determine the solution of the buckling load for simple structures with random material properties. Recently, by combining the stochastic element‐free Galerkin method and second‐order perturbation technique, Gupta and Arun 12 studied the elastic buckling of columns with small fluctuation of uncertain parameters. Considering the limitation of low‐order stochastic perturbation, which is only suitable for small fluctuations of random parameters, Kamiński and Świta 13 applied a generalized stochastic finite element method (GSFEM) to solve elastic stability problems, and the up to the 10th‐order stochastic perturbation technique was used to calculate the first several statistics of the critical force or pressure, and the influence of the order of expansion and the COV of the inputs on the probabilistic convergence of GSFEM is discussed in detail in Reference 14.…”

Probabilistic stability analysis of functionally graded graphene reinforced porous beams

“…Rouhi et al [32] studied the buckling behaviours of nanofiber-enhanced cylinder by modelling the random distributed carbon nanofibers in the micromechanical model and Radial Basis Functions or RBFs-based metamodels were introduced to solve the governing equations. The stochastic eigenvalue analysis of isotropic columns was investigated by Gupta and Arun [33] by using perturbation method and compared with Monte Carlo simulation. Pryse and Adhikari [34] studied the stochastic eigenvalue problems by using random eigenfunction expansion method.…”

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

“…To study the uncertainty effect on the natural frequencies of a bridge, the Young's modulus of the bridge is considered having a lognormal distribution (Wan et al, 2017). Other research works on lognormal random inputs can be referred to (Barbato et al, 2013;Gupta and Arun, 2018;Saydam and Frangopol, 2013). Realizations of a Gaussian random field with a large coefficient of variation may include negative outcomes, which are physically meaningless.…”