Modeling of the Eigenfield of a Prestressed Hyperelastic Membrane Encapsulating a Liquid
Ivan P. Gavrilyuk, Martin Hermann, Alexander N. Timokha, В. А. Троценко · Computational Methods in Applied Mathematics · 2006
Abstract A spectral boundary problem on the eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circular cylindrical cavity filled with a liquid, is examined. The paper presents an operator formulation of the problem and proposes a new semi-analytical approximate method. The method captures singular behavior of the solution in the pole and at the fastening contour of the membrane.