Steady heat transfer analysis for anisotropic structures using the coupled IGA-EFG method

Abstract

A numerical model of steady heat transfer analysis for anisotropic structures using coupled isogeometric analysis and element-free Galerkin (IGA-EFG) method was developed. The model uses reproduction conditions to realize the equivalence between moving least squares (MLS) shape function and equal geometric basis function, and realizes adaptive refinement based on temperature gradient. Its advantages include accurate geometric representation, convenient load application and flexible adaptive refinement. The effectiveness of the present model is verified by comparison with those of IGA and EFG models using numerical examples including anisotropic fan blades and airplane wings. The effects of knot vectors of non-uniform rational B-spline (NURBS), orders of NURBS and refinement number of mesh on the computational accuracy of the present model are investigated. The results indicate that the accuracy of coupled IGA-EFG method increases with the uniformity of knot vector distribution and decreases with the order of NURBS. Meanwhile, the higher accuracy is achieved when the orders of NURBS are the same in different directions, while the reasonable range of refinement number of mesh is 1∼2. The influence of thermal conductivity factor and off-angle are explored, and their reasonable ranges for anisotropic airplane wings are 2 ∼ 5 and 15° ∼ 30°, respectively, which can effectively improve the temperature field.