# Trefftz radial basis functions (TRBF)

### Abstract

The TRBF's are radial functions satisfying governing equation in the domain. They can be used as interpolation functions of the field variables especially in boundary methods. In present paper discrete dipoles are used to simulate composite material reinforced by stiff particles using with boundary point collocation method which does not require any meshing and any integration. The better the interpolation function satisfies also the boundary conditions, the more efficient it is. In examples it is shown that a triple dipole (which is a TRBF) located into the center of the particle can approximate the inter-domain boundary conditions very good, if the particles are not very close to each other and their size is not very different. In general problem the model can be used as very good start point for international improvements in refined model. Composite reinforced by short fibres with very large aspect ratio continuous TRBF were developed. They enable to reduce problem considerably and to simulate complicated interactions for investigation such composites.

### Keywords

fibre reinforced composites, meshless method, Trefftz Radial Basis Functions, continuous source functions,### References

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**Computer Assisted Methods in Engineering and Science**, [S.l.], v. 15, n. 3-4, p. 239-249, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/732>. Date accessed: 14 sep. 2024.