Numerische Ermittlung eines effektiven Elastizitätstensors und der extremalen Spannungen für beliebige Magnetkomposite

For the calculation of mechanical properties of large magnet systems in 3-dimensional space, a very fine subdivision of the magnetstructure is necessary. In the finite element programms, this will lead to unacceptably lang computing times and to the limits of computer-storage capacity. This limitation requires a simplification of the structure model. The objective of this work is to find such simplifications that yield still reliable results by the stress-strain analysis. This problern can be solved by the numerical method, called 11 numerical simulation , by which an effective elasticity tensorwill be obtained for a composite material. The structure can be arbitrarily complicated and may contain voids, e.g. cooling channels, which are weak elements for the structural analysis. The structure has to perform only a homogeneity condition, i.e. it must be possible to define a 11 representative volume element 11 (RVE). With the effective elasticity tensor, which can be found for such RVE, it is possible to calculate the average stress and with the surface displacement method also the extremal stresses in each point of the structure. It is found a good agreement between experimental and theoretical moduli of elasticity.