Computaional modeling of membrane mechanics
Kundomal, Chellaram A.
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In this work we analyze mechanics of thin membranes. After a brief review on the backgrounds and methods, this thesis develops a systematic approach to understanding membrane mechanics. The two essential mathematical tools employed include Principle of Virtual Work and the finite element method. More specifically after defining suitable measures of deformation of an arbitrary body, we describe how one can apply the Principle of Virtual Work for a fully dynamic application. We employ the finite element method to a quasi-static application which results in a system of nonlinear equations. These equations are solved by the Newton-Raphson procedure for systems. The computational methodology discussed in this work was implemented in Maple for two different membrane materials: neo-Hookean and Mooney-Rivlin.