Variability response functions for stochastic plate bending problems

In this paper, the weighted integral method and the concept of variability response function are successfully extended to plate bending problems where the elastic modulus of the structure is considered to be a two-dimensional, homogeneous stochastic field, overcoming earlier computational problems associated with the large number of terms in the expression for the variability response function. The concept of the variability response function is used to compute spectral-distribution-free upper bounds of the response variability. Such bounds are of paramount importance for the majority of real-life problems where only first and second moments of the stochastic material properties can be estimated with reasonable accuracy. Under the assumption of a prespecified power spectral density function of the stochastic field describing the elastic modulus, it is also possible to compute the response variability (in terms of second moments of response quantities) and the reliability (in terms of the safety index) of the stochastic plate. The use of a variability response function based on the local averaging method reduces the computational effort associated with the weighted integral method, with only a small loss of accuracy in most cases. Numerical examples are provided to demonstrate all of the above capabilities. One of the conclusions is that the coefficient of variation of certain response quantities can become larger than the coefficient of variation of the elastic modulus (the input quantity). (C) 1998 Published by Elsevier Science Ltd. All rights reserved.