Buckling Design of Stochastically Heterogeneous Beam-Columns
Journal of the Mechanical Behavior of Materials
In this paper, a new analytical solution is developed to calculate the probabilistic characters of the critical buckling load for beams with stochastic material properties. The elastic stiffness is modeled as continuous stochastic field described by its mean, variance and autocorrelation function, where the latter is assumed to have an exponential form. The critical buckling load is found by using the principle of minimum potential energy and applying the Functional Perturbation Method (FPM).
... ion Method (FPM). Two examples of simply supported and clamped-free beams demonstrate how the morphology and heterogeneity affect the buckling load. The solution is then used to estimate the design loads for beams with stochastic material properties. It is shown that a common statistical stiffness variance of a few percent may lead to an over conservative design load, which may be more than two times smaller than the ones based on predictions by the FPM, which takes the material morphology into account. An examination of the symmetry breakdown of stochastic beams is also studied.