Abstract
Loading of elastic-plastic rods with account on Prandtl’s scheme is considered in the paper, and nonlinear interactions are taken into account under the law of Coulomb friction. Exact analytical solutions of quasi-stationary problems of interaction of elastic-plastic rod and undeformable media surrounding it are given.
Highlights
In works [1-11], the problem of quasistatic loading of structural elements in the form of an elastic rod interacting with its environment according to the Coulomb dry friction law was formulated and solved
The paper considers the loading of an elastic-plastic rod according to the Prandtl scheme, and nonlinear interactions are taken into account according to the Coulomb dry friction law
The problem of quasistatic loading and unloading of long bar structures in an elastic medium and interacting with it according to the Coulomb dry friction law has been solved
Summary
In works [1-11], the problem of quasistatic loading of structural elements in the form of an elastic rod interacting with its environment according to the Coulomb dry friction law was formulated and solved. It is known that in the problems of longitudinal vibrations of rods interacting with soil media, attention is drawn to the fact that in certain situations, it is possible to neglect the inertial terms in the equations of motion (works [12, 16, 20, 21], etc.) in comparison with the arising shear stresses on the surfaces of interaction between the structure and the environment. In this case, quasistatic formulations of nonlinear problems arise. Rod structures are assumed to be long enough, which are found in deep drilling structures but loaded in the longitudinal direction
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