Linear Viscoelastic Analysis with Random Material Properties
Analytical studies are presented which extend the elastic-viseoelastie 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.
KeywordsViscoelastic Material Radial Stress Hoop Stress Relaxation Function Probability Density Distribution
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- 1.Eringen, A. C. Stochastic loads. Handbook of Engineering Mechanics McGraw Hill Book Co., 1962, Ch. 18.Google Scholar
- 7.Parkus, H. On the lifetime of viscoelastic structures in a random temperature field. Recent Progress in Applied Mechanics 1967, Wiley, N.Y., 391–397.Google Scholar
- 8.Ziegler, F. Zufallige Temperaturschwankungen und ihr Einfluss auf die Lebensdauer eines Druckstabes aus nichtlinear-viskoelastischem Material. ZAMM 1972, 52, 176–178.Google Scholar
- 11.Parkus, H. and Zeman, J. L. Some stochastic problems of thermoviscoelasticity. IUTAM Symposium on Thermoinelasticity Springer, N.Y., 1970, 226–240.Google Scholar
- 14.Bazant, Z. P. and Xi, Y. Probabilistic prediction of creep and shrinkage in concrete structures: combined sampling and spectral approach. 5th Int. Conf. on Structural Safety and Reliability (ICOSSAR) A. H. S. Ang, and Shinozuka, M. and Schueller, G. I. eds., 1989, 1, 803–808.Google Scholar
- 16.Hilton, H. H. Viscoelastic analysis. Engineering Design for Plastics Reinhold Publ. Corp, New York, 1964, 199–276.Google Scholar
- 17.Hilton, H. H. Thermal stresses in thick walled cylinders exhibiting temperature dependent viscoelastic properties of the Kelvin type. Proc. Second U.S. Nat. Congress on Appl. Mech. 1954, 547-553.Google Scholar
- 24.Hilton, H. H. and Dong, S. B. An analogy for anisotropic, nonhomogeneous linear viscoelasticity including thermal stresses. Proc. Eighth Midwestern Mechanics Conf. 1964, 58-73.Google Scholar
- 26.Hilton, H. H. and Clements, J. R. Formulation and evaluation of approximate analogies for temperature dependent linear viscoelastic media. Proc. Conference on Thermal Loading and Creep Inst. Mech. Eng. London, 1964, 6:17-6:24.Google Scholar
- 29.Beran, M. J. Statistical Continuum Theories. Interscience Publ., 1968.Google Scholar
- 30.Lin, Y. K. Probabilistic Theory of Structural Dynamics, McGraw Hill Book Co., 1967.Google Scholar
- 31.Hilton, H. H., Majerus, J. N. and Tamekuni, M. Analytical formulation of generalized characterization for linear viscoelastic materials from uni-and multi-axial creep and relaxation data. ICRPG Proceedings 1964, 2, 114–128.Google Scholar
- 33.Tricomi, F. G. Integral Equations. Interscience Publishers, 1957.Google Scholar
- 35.Wen, Y. K. Structural Load Modeling and Combination for Performance and Safety Evaluation. Elsevier, 1990, 19-20.Google Scholar