Dynamics of the Antiplane Strain of a Nonlinear Elastic Body
B. D. Bondar'
Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: динамика, антиплоская деформация, задача для перемещения, нагрузка, нелинейность, тип уравнения, упругий потенциал, условие совместности, dynamics, antiplane strain, displacement problem, load, nonlinearity, type of the equation, elastic potential, compatibility condition
Abstract
The dynamic antiplane strain of an incompressible cylindrical body is studied in a nonlinear formulation in actual variables. A representation of the velocity and acceleration through the displacement is obtained. The problem of the body deformation with account for geometrical and physical nonlinearities is reduced to an initial boundary-value problem for the displacement. The displacement found is used to determine the pressure and stresses. For a body with a quadratic elastic potential, plane waves and self-similar motion are studied. The linear potential is used to investigate the deformation of a hollow elliptical cylinder for which analytical expressions for displacement and stresses are found and the external load is determined. It is shown that, due to the degeneration of the inner cavity of the body to a plane section, the load on the section remains limited.
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