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2 Computer Assisted Mechanics and Engineering Sciences

2 2008

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Trefftz radial basis functions (TRBF)

Kompiš V., Štiavnicky M., Žmindák M., Murčinková Z.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 3/4

239-249

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 (unction satisfies also the boundary conditions, the more efficient it is. In examples it is shown that a triple dipole (which is a TRBK) 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.

Trefftz functions for 3D stress concentration problems

Murčinková Z., Kompiš V., Štiavnicky M.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 3/4

305-318

The paper deals with solution of 3D problems with stress concentration using the Trefftz functions. The modelled stress concentrators are holes and cavities of spherical and ellipsoidal shapes. Moreover, the random spherical cavity microstructure is modelled. The Method of External Finite Element Approximation (MEFEA) is applied to simulate detailed stress state of mentioned stress concentrators. This boundary-type method was developed to build special approximation fund ions that are associated with surface which causes the stress concentration. The method does not need discretization by classical finite elements, however, instead of elements the domain is divided into Trefftz type subdomains. The displacement and force boundary conditions are met only approximately whereas the governing equations are fulfilled exactly in the volume for linear elasticity, making it possible to assess accuracy in terms of error in boundary conditions.