Response variability due to randomness in Poisson’s ratio for plane-strain and plane-stress states

In the ordinary structural materials, one of the parameters that can be assumed to have spatial uncertainty is Poisson s ratio. Therefore the independent evaluation of the effects of this parameter on the response variability is of importance. The difficulties in obtaining the response variability due to randomness in Poisson s ratio lie in the fact that the Poisson s ratio enters the stiffness matrix as a non-linear parameter. In this paper, a formulation to determine the response variability in plane strain and plane stress states due to the randomness in the Poisson s ratio is given. The formulation is accomplished by means of the stochastic decomposition of the constitutive matrix into several sub-matrices taking into consideration of the polynomial expansion on the coefficients of constitutive relation. To demonstrate the validity of the proposed formulation, some example structures are chosen and the results are compared with those obtained by means of Monte Carlo simulation. Through the formulation proposed in this study, it becomes possible for the weighted integral stochastic finite element analysis to consider all the uncertain material parameters in its application.