A novel numerical approach to calculate the time evolution of the three dimensional distribution of the magnetic field and forces in the end winding regions of large turbine generators is presented. The proposed approach is based on an integral formulation for nonlinear magnetostatic problems. Its main advantage is the reduction of the discretization to only the conductors and magnetic materials. In this paper the solution of a coupled magnetostructural problem consisting in the calculation of the mechanical stresses and deformations caused by the electrodynamic forces is presented. The analysis is based on a time stepping simulation where the currents are derived from the integration of a lumped parameter model
The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation) -even in the case of spherical symmetry -at times smaller than the free-fall time trr, provided the initial data of tile Cauchy problem be discontinuous within a sphere of radius < Rc~oud (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical times tot < trr (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.
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