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The variability response function (VRF) is generalized to staticallydeterminate Euler Bernoulli beams with arbitrary stress-strain laws followingCauchy elastic behavior. The VRF is a Green's function that maps the spectraldensity function (SDF) of a statistically homogeneous random field describingthe correlation structure of input uncertainty to the variance of a responsequantity. The appeal of such Green's functions is that the variance can bedetermined for any correlation structure by a trivial computation of aconvolution integral. The method introduced in this work derives VRFs in closedform for arbitrary nonlinear Cauchy-elastic constitutive laws and isdemonstrated through three examples. It is shown why and how higher orderspectra of the random field affect the response variance for nonlinearconstitutive laws. In the general sense, the VRF for a statically determinatebeam is found to be a matrix kernel whose inner product by a matrix of higherorder SDFs and statistical moments is integrated to give the response variance.The resulting VRF matrix is unique regardless of the random field's marginalprobability density function (PDF) and SDFs.

Variability response functions for statically determinate beams with arbitrary nonlinear constitutive laws