Transient heat conduction analysis of 3D solids with fiber inclusions using the boundary element method

A boundary element formulation is presented in this work for transient heat conduction analysis of three‐dimensional (3D) fiber‐reinforced materials. The cylindrical‐shaped fibers in a 3D matrix are idealized by a system of curvilinear line elements with a prescribed diameter. The variations in the temperature and flux fields in the circumferential direction are represented in terms of a trigonometric shape function together with a linear or quadratic variation in the longitudinal direction. This approach significantly reduces the modeling effort and the computing cost. The storage requirement for the convolution integrals is eliminated by adopting an accurate integration‐based convolution algorithm for the surface of the hole and the fibers as well as a fast convolution algorithm for the outer boundary recently developed by the present authors. Numerical examples are presented to demonstrate the accuracy and applicability of the proposed method of analysis of fiber‐reinforced materials.