| The temperature fields of real objects under real conditions of their functioning are stochastic. The stochastic character of the temperatures field depends on the dominating random factors. Often such factors, such as the powers of heat sources, thermal conductivity coefficients, coefficients of heat transfer from the body surface to the medium, ambient temperature, and the width of gap between contacting bodies are random. In those cases when the random character of the temperature field cannot be neglected or high requirements are imposed on the adequacy of the temperature distribution simulation, it is necessary to solve the stochastic heat conduction equation. The most practically important characteristics of the stochastic temperature fields are the fields of its first and second moments, viz. of expectation and dispersion. These are called the solution of the stochastic heat conduction equation.In this paper, the recently developed pseudo excitation method for structural random vibration is extended to the solution of stochastic heat conduction problems, based on the similarity between the random vibration and stochastic heat conduction. Several numerical examples are carried out to verify the proposed method with satisfactory results.The thesis focuses on the law of stochastic heat conduction under random inputs, without regard to the influence of stochastic thermal parameters.The major work of this thesis includes:1. The theory of pseudo excitation method is introduced in detail in the present paper;2. The numerical model of stochastic heat conduction is established;3. The Pseudo Excitation Method is applied in this paper to solve stochastic heat conduction problems with stationary random process inputs;4. The Pseudo Excitation Method is also used in this paper to solve stochastic heat conduction problems with non-stationary random process inputs;5. The inverse stochastic heat conduction problem is studied by the Inverse Pseudo Excitation Method.
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