Modeling and simulation of steady heat transfer analysis with material uncertainty: Generalized nth order perturbation isogeometric stochastic method

The contribution herein proposes a novel generalized nth order perturbation isogeometric method (GNP-IGA) for efficient steady heat transfer stochastic analysis with material uncertainty. While various space discretizations may be employed for spatial modeling, first, the isogeometric analysis (IGA) technique is employed and is the selected choice to exactly represent the structural geometry, as well as to provide more accurate results. Secondly, the randomness of thermal conductivity coefficient is considered in the steady heat transfer analysis, and its stochastic field is modeled by a generalized nth order perturbation method. Namely, we derive and expand the IGA based random-input parameters (thermal conductivity coefficient) and all state functions included in the governing equations around their expectations via a generalized nth order Taylor series using a small perturbation parameter ε. More importantly, we can satisfy accuracy requirements of the probabilistic moments of the stochastic solution by expanding Taylor series to nth order. As comparison, the brute force Monte Carlo simulations are conducted in various numerical examples and primarily serve as a benchmark; both, a simple square plate and a real engineering application are demonstrated. The results verify the proposed GNP-IGA is effective and significantly efficient for steady heat transfer stochastic analysis with material uncertainty. In addition, the larger the problem’s scale (DOFs) and/or the number of samples are, the more efficiency the GNP-IGA method will inherit.