Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach

• Published in: Computer methods in applied mechanics and engineering Vol. 198; no. 37; pp. 3173 - 3185
• Main Authors: Tootkaboni, M., Graham-Brady, L., Schafer, B.W.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.08.2009; Elsevier
• Subjects: Buckling; Computational techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Geometrically non-linear; Hermite chaos; Koiter’s asymptotic theory; Mathematical methods in physics; Physics; Post-bifurcation regime; Solid mechanics; Stochastic collocation; Stochastic Galerkin; Structural and continuum mechanics; Hermite chaos; Stochastic Galerkin; Stochastic collocation; Geometrically non-linear; Post-bifurcation regime; Koiter’s asymptotic theory; Chaos; Monte Carlo method; Spectral method; Statistical analysis; Probabilistic approach; Hermite interpolation; Spectral properties; Variability; Displacement(deformation); Modeling; Postbuckling; Uncertain system; Galerkin method; Asymptotic approximation; Random medium; Curvature; Buckling; Koiter's asymptotic theory; Structural analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2009.05.014

An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension.