In this thesis we analyze the buckling behavior of an infinitely long, thin, uniform, inextensible, elastic plate that has a steady current flowing along its length.
We are concerned with the derivation of the nonlinear equations of motion using nonlinear continuum mechanics, and subsequent analysis of the buckling behavior of the plate under electromagnetic self-forces. In particular, we concentrate on how the body-forces that result from the applied current determine the buckled configurations. We derive both analytical and numerical results, and in the process develop a novel boundary value problem solver for integro-differential equations in addition to a predictor-corrector algorithm to continue solutions with respect to the control parameters.
We take a relatively complex problem in magneto-solid mechanics and elasticity theory and form a realistic model that sheds light on the bifurcation and buckling behavior resulting from the electromagnetic-field- induced self-forces that are derived in their full, exact form using Biot-Savart Law.
