A formulation for stochastic finite element analysis of plate structures with uncertain Poissonʹs ratio Original Research Article

Up to now, the Youngʹs modulus is mainly dealt within the analysis of response variability. However, since the Poissonʹs ratio is the other material constant which influences the behavior of structures, the independent evaluation of the effects of this parameter on the response variability is of importance. In this paper, a formulation to determine the response variability in plate structure due to the randomness of Poissonʹs ratio is given. To filter out the independent contributions of randomness in Poissonʹs ratio to the response variability, the constitutive matrix has to be decomposed into several sub-matrices. In order to include the Poissonʹs ratio in the constitutive relation as a non-linear parameter, a polynomial expansion of Poissonʹs ratio is introduced. To demonstrate the validity of the proposed formulation, an example is chosen and the results are compared with those obtained by means of Monte Carlo simulation. Through the formulation proposed in this paper, it becomes possible for the non-statistical weighted integral stochastic approach to deal with all the uncertain material parameters in its application.