engleski

Variability Response Function for Stochastic Transient Heat Conduction with Random Conductivity

The concept of variability response function based on the weighted integral method is extended to one-dimensional transient heat conduction. The thermal conductivity of the structure is considered to be two-dimensional (in one-dimensional space-time domain), homogenous, stochastic field. The stochastic element conductivity matrix is decomposed into deterministic part and stochastic part of element conductivity matrix. The stochastic part of element conductivity matrix is expressed as linear function of the random variables (weighted integrals) with zero-mean property. The concept of the variability response function is used to compute the upper bound of the response variability (response temperature). The first and second moment of stochastic thermal conductivity are used as input quantities for the description of the random property. The response temperature is calculated using first-order Taylor expansion approximation of the variability response function. The variability of the response temperature is represented in the terms of the second moment of the response temperature and related coefficient of variation. The k-time-step-randomness method is introduced to reduce the computational effort. The algorithm for calculation with variability of the response temperature from just last k time steps is given. Numerical examples are provided for different values of k. Calculated results with less computational effort are compared with results calculated with complete random history.

transient heat conduction; uncertain conductivity; weighted integral method; response variability

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