关键词: 固体介质, 等几何分析, 半离散化, 瞬态热传导, 无网格法, 后向差分格式, Dirichlet边界条件, 鲁棒性

Abstract: To expand application of isogeometric analysis method in transient or dynamics domain, by taking transient heat conduction of solid medium as example, isogeometric analysis method was extended to transient problems. The propoesd problem's space domain was discretized by isogeometric way firstly, and then time domain was discretized with finite difference by semi-discretization method, thus, the backward difference schema of the iteration linear system was obtained. To solve the Dirichlet boundary processing error caused by lack interpolation of Non-Uniform Rational B-Splines(NURBS) basis function, a robust boundary constraint method was proposed by selecting a set of interpolated boundary points. The experiment results demonstrated that isogeometric analysis could achieve better convergence speed than traditional finite element method.

Key words: solid medium, isogeometric analysis, semi-discretization, transient heat conduction, meshless method, backward difference schema, dirichlet boundary conditions, robustness