Effective properties of randomly heterogeneous beams - Pierce-Brown, Jack (2019)
This research is concerned with the application of random fields to model material heterogeneity with implications on the usage of the stochastic finite element method to evaluate structural reliability. In particular, there is extensive consideration of the relationship between the effective modulus of elasticity of randomly heterogeneous timber beams and the underlying lognormal random field of elastic modulus. Under Euler-Bernoulli beam theory, the effective elastic modulus is shown to be a weighted harmonic mean and weighting functions are provided for a number of important loading conditions. Additionally, analytical expressions are derived for the moments of both the displacement and effective elastic modulus of the beam. In the case of multi-dimensional heterogeneity, a generalised weighted mean meta-model is introduced for the effective property of heterogeneous materials and a novel function optimisation algorithm is utilised to optimise the weighting function of this meta-model to the results of both one and two-dimensional finite element models with insights into the sensitivity of the effective property to both spatial weighting and minima of the random field of elastic modulus. Finally, the inference of the parameters of a random field model from effective local and global moduli of elasticity is considered and it is shown that the use of the midpoint approximation results in large epistemic biases which likely leads to underestimation of the variability of heterogeneous materials.