Boundary-value problem of dynamic geometrically nonlinear elasticity
The linear theory of elasticity does not provide the accuracy in a number of important elastic problems, and one of the existing nonlinear theories is used in its place. The nonlinearity of these theories is connected not only with the law that governs the mechanical behavior of the material (physical nonlinearity), but also with the dependence of the strains on the gradients of the displacements (geometric nonlinearity). Here, we examine a two-dimensional dynamic problem in the Novozhilov variant of geometrically nonlinear elasticity. We derive equations in stresses and rotations, represent these quantities in terms of potentials, and construct equations for the potentials. We show that there is an interaction bewteen expansion - compression and shear waves in the material when allowance is made for nonlinearity. We identify a class of solutions to the equations of motion that contains two arbitrary functions and show its application to the solution of the boundary-value problem of the stress distribution in a semi-infinite elastic medium during the motion of a pressure pulse along its surface.
- OSTI ID:
- 105228
- Journal Information:
- Journal of Applied Mechanics and Technical Physics, Journal Name: Journal of Applied Mechanics and Technical Physics Journal Issue: 6 Vol. 35; ISSN JMPYAQ; ISSN 0021-8944
- Country of Publication:
- United States
- Language:
- English
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