http://www.ce.jhu.edu/cfs/cfslibrary/jcsr_47_3_schafer_and_pekoz%20comp%20modeling.pdf

Computational modeling of cold-formed steel: characterizing geometric imperfections and residual stresses

The probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non-linear continua.

The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem and a two-dimensional plane-stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Random field finite elements

Keywords: aeroelasticite ; structure : dynamique Reference Record created on 2005-11-18, modified on 2016-08-08

/pdf/introduction-to-structural-dynamics-and-aeroelasticity-43ce9fxz1b.pdf

Introduction to Structural Dynamics and Aeroelasticity

https://hal-upec-upem.archives-ouvertes.fr/hal-00686293/document

A nonparametric model of random uncertainties for reduced matrix models in structural dynamics

A random vibration method is developed for the response analysis of hysteretic structural systems under stochastic two-dimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of the effects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.

Yu-Kweng Michael Lin

Papers

Probabilistic Theory of Structural Dynamics