Computational model using continuous source functions along the fibre axis is presented for simulation of temperature/heat flux in composites reinforced by short fibres with large aspect ratio. The aspect ratio of short fibres reinforcing composite material is often as large as 103？:？1–106？:？1, or even larger. 1D continuous source functions enable simulating the interaction of each fibre with the matrix and also with other fibres. The developed method of continuous source functions is a boundary meshless method reducing the problem considerably comparing to other methods like FEM, BEM, meshless methods, or fast multipole BEM formulation. 1. Introduction Short fibres are widely used as reinforcing materials in most advanced composites [1]. In last decades, fibre-reinforced composites have been widely used in engineering applications due to the superiority of their electrothermomechanical (ETM) properties over the single matrix. Because of these properties very large gradients are localized in all ETM fields along the fibres and in the matrix. Particularly, composite materials reinforced by short fibres/tubes (CRSF) are often defined as materials of future. Understanding the physical behaviour of these fibre-reinforced composites is essential for structural design. Accurate numerical simulation of the fields is important for correct analysis and design of the material behaviour. Among the existing numerical methods, finite element method (FEM) [2, 3], boundary element method (BEM) [4, 5], and meshless methods [6] can be used for simulating the CRSF behaviour. However, these classical numerical methods are suitable for the lowest scale simulation only. All the methods mentioned above require millions or even billions of equations after numerical discretization to obtain a sufficiently accurate solution of this kind of computer simulations. Recently, the fast multipole method (FMM) [7] was developed to increase the efficiency of numerical models. The fast multipole boundary element method (FMBEM) [8], which was used for simulation of these problems, reduces the computational cost for the far field interaction simulations; however, the classical BEM has to be used for simulating the near field interactions and the supercomputers are necessary to solve the problem with good accuracy. The FMBEM is the only numerical method which enables solving representative volume element (RVE) of the matrix containing two to five thousand short fibres (three to eleven million degrees of freedom (d.o.f.)). The problems have been solved on a supercomputers, or on clusters of
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