engleski

Upper Bounds by Stochastic Force Method

The analytical solution for the response variability of stochastic, linearly elastic, statically indeterminate beams is developed for some loading cases by stochastic force method. The flexibility of the beam is taken as a random variable. The randomness of the flexibility is represented in the calculation by its coefficient of variation. The loads are static and deterministic, The response variability is represented by first-order approximation of the response variability function. The upper bounds are estimated for the first-order approximation of the coefficient of the response deflection. The first-order approximation of the response variability function are evaluated by using a different associated statically determinate systems for the same statically indeterminate beam. The response variability is evaluated for fixed-simple beam under the different loading cases. two different associated statically determinate systems are taken for fixed-simple beam, the cantilever beam and the simple beam. The derived examples show that the choose of associated statically determinate systems has no influence on the first-order approximation of the response variability function of the stochastic statically indeterminate beams. The complicated forms for the same problem through the different associated statically determinate systems are annalytically or numerically evaluated to same functions. The upper bounds of the coefficient of variation of the response deflection and associated wave number where the coefficient takes its maximum are obtained graphically from the plotted first-order approximation of the coefficient of variation.

stochastic force method; response variability function; random variable

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