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An efficient numerical algorithm to solve steady state heat conduction problems with local uncertainty
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DOI：10.1016/j.enganabound.2024.04.002.png)
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Abstract
En 中文
A computational cost-effective algorithm is proposed to solve steady-state heat conduction problems with uncertain thermal conductivity which appears locally at some part of structures. Such local uncertainty is assumed to be induced by a crack or notch, and modelled by probability or interval models. The deterministic steady-state heat conduction problem is formulated by the Scaled Boundary Finite Element Method (SBFEM), facilitating to treat heat flux singularity around the crack conveniently and efficiently, and generate SBFE mesh flexibly, and the uncertain analysis is conducted via the Monte Carlo simulation (MCS). To alleviate the computational burden of repeated updating deterministic solutions in MCS, a Woodbury formula -based tactic is presented, such that the update of inverse heat conduction matrix can be carried out with a small solution scale, and substantial benefit can be achieved in term of computational cost. The proposed algorithm is applicable for the cases with single and multiple local uncertainties. Numerical examples are employed to illustrate the effectiveness and efficiency.
Keywords:
Heat conduction
Local uncertainty
Scaled boundary element finite method
Woodbury formula
Computational efficiency
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