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

Abstract

In the ordinary structural materials, one of the parameters that can be assumed to have spatial uncertainty is PoissonÕs 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 PoissonÕs ratio lie in the fact that the PoissonÕs 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 PoissonÕs 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.

Optimum design of shell structures with random geometric, material and thickness imperfections

“…In the present study, stochastic fields f 2 (x, y) and f 3 (x, y) are assumed uncorrelated. However, since cross-correlation between the aforementioned fields has proven to play an important role on the buckling behavior of shell-type structures leading often to a further reduction of the bearing capacity, with respect to the uncorrelated case (Noh and Kwak, 2006;Noh, 2006;Stefanou and Papadrakakis, 2004), the effect of the above mentioned correlation in the optimum design of shell structures will be specifically addressed in follow-up research. The stochastic stiffness matrix of the shell element is derived using the local average method.…”

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

“…For statically indeterminate structures, exact VRFs have not been derived, yet Taylor expansion techniques were used in [6,7,8,9] for the displacement response of structures whose uncertainty is given by two-dimensional random fields. Also, the fast Monte Carlo methodology proposed in [10] was developed in [11,12] to estimate the VRF efficiently.…”