Large-scale thermal analysis of fiber composites using a line-inclusion model by the fast boundary element method

The fast boundary element method is applied for the three-dimensional large-scale thermal analysis of fiber-reinforced composites based on a line inclusion model. In this approach, fibers are treated as inclusions with temperature assumed constant over the circular cross-section and varying along the length direction. Therefore, fibers can be meshed with line elements, making both the modeling complexity and the number of unknowns significantly reduced. An interface integral boundary element method introduced by Gao in 2009 (Engineering Analysis with Boundary Elements 2009; 33: 539–546) is extended to generate a single-domain boundary integral equation for governing this line-inclusion problem. Thus in principle, fibers with arbitrary length can be modeled. The fast multipole method is employed for the fast analysis of such problems with large-scales. The largest composite model in a personal desktop computer has the number of fibers reaching 20,000. Numerical results clearly demonstrate validity of the proposed model and its potential for large-scale analysis of fiber-reinforced composites.