Linear viscoelastic analysis with random material properties

Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic processes caused by random linear viscoelastic material properties. Separation of variable as well as integral transform correspondence principles are formulated and discussed in detail. The statistical differential equation of the moment characteristic functional is derived, but rather than solving the highly complex functional equation, solutions are formulated in terms of first and second order statistical properties. Both Gaussian and beta distributions are considered for the probability density distributions of creep and relaxation functions and their effectiveness is evaluated. In order to illustrate the developed general theory, specific examples of beam bending and pressurized hollow cylinders are solved. The influence of various parameters contributing to the creep and relaxation correlation functions is evaluated and the relationship between deterministic and stochastic bounds is also investigated. It is shown that deterministic bounds based on material data spread are unrealistic in the presence of random viscoelastic properties, since the do not correctly predict the limits of this stochastic process.