doi:10.3850/978-981-08-7619-7_P002

ABSTRACT

The variability response function (VRF) is awell established concept in evaluating the response variability of stochastic systems in which material properties are modeled as random field. The VRF approach obviates the need for direct Monte Carlo (MC) simulation of the system response and can therefore deliver dramatic increases in efficiency. In problems in which the material properties fluctuate randomly, it is common to replace the randomly fluctuating properties with a spatially invariant, homogenized, or effective set of properties. Although it is common to treat the resulting homogeneous problem as deterministic, the effective properties are themselves random whenever the volume occupied by the solid body in the problem is finite. Currently, this feature of the homogeneous problem is not well recognized, and no method other than MC simulation exists for evaluating the variability of the effective properties. The concept of a VRF for effective material properties is introduced here, and is derived based on a strain energy based definition of the effective elastic properties of a solid body. This new VRF is shown to exist for statically indeterminate structures and can be calculated exactly or by efficient Fast MC simulation techniques. A key result that is required to show the existence of the VRF for effective properties is that a VRF exists for the covariance of the displacement field along a statically determinate beam. Two numerical examples are used to illustrate the key features of the VRF for effective material properties.

Keywords: Homogenization, Material properties, Uncertainty quantification, Random fields.

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