C. Adam, F. Ziegler:

"Oblique flexural vibrations of viscoplastic beams - Monte Carlo simulation";

in: "Computational Stochastic Mechanics - Proc. of the 2nd International Conference on Computational Stochastic Mechanics (CSM'94)", P.D. Spanos (ed.); Balkema, Rotterdam, 1995, ISBN: 9054105275, 277 - 286.

An effective algorithm is developed to determine the stochastic response of biaxially loaded inelastic beams. Constitutive relations of rate-dependent plasticity are considered and the material is deteriorated by ductile damage. The inelastic defects are treated as sources of selfstress in the associated linear elastic beam with time-independent virgin stiffness. Thus, linear methods like those based on Green's functions and Duhamel's integral remain applicable to account for the given as well as for the internal loading. The intensity and the distribution of the internal sources are calculated incrementally in a time-stepping procedure and they are determined by the constitutive law and the evolutionary equation of the damage parameter. In addition to a given static preloading in the vertical direction, a horizontal dynamic load with zero mean value that fluctuates randomly in time is considered. The wide band noise process is generated by the well established procedure of Shinozuka. Such an efficient and stable formulation makes it possible to consider sufficiently large sample sizes resulting in reliable sample averages.

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