Calculation of the mechanical stresses in a high field magnet by means of a layer model

Abstract

A new model suitable for the calculation of azimuthal stresses σ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</inf> well as the radial stress α <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</inf> in different kind of layers (non current carrying and current carrying) is developed. For the calculation the validity of Hook's law is assumed. The equilibrium condition for a layer volume element leads to a differential equation for the radial component u of the displacement vector. The solution of the differential equation can be used to obtain a system of linear equations for the displacements of the boundaries of the layers. Examples are given where layer models are compared with models averaging the elastic constants of the used materials. In the case of intermediate layers with relatively small E-modul both models give approximately the same results for the stresses in the current carrying layers. In the case of a relatively large E-modul of the intermediate layers the layer model yields more. realistic results for the stresses in both types of layers. Finally the calculations shown for the layer model can be easely extended when additional reinforcing layers are considered.