The Asymptotic Analysis of the Nonstationary Problem of Variable Shear Loading on the Boundary of an Incompressible Solid

Abstract:

The loading process, in which the shear action on the boundary plane changes both the intensity and direction, is considered by the example of a one-dimensional plane problem for non-linear elastic incompressible half-space. It is shown that the solution in the front region of the shock wave is determined by a nonlinear evolution equations system in the space regions where the nonlinearity of the medium becomes a significant factor. The general solution of the evolution system was obtained. The particular solution of the evolution system for one of the most simple boundary conditions was considered as an example.

• Periodical: Advanced Materials Research (Volume 1040)
• Pages: 646-651
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1040.646
• Online since: September 2014
• Authors: Victoria E. Ragozina, Yulia E. Ivanova*
• Keywords: Evolution Equation for the Shear Direction Change, Evolution Equation for the Shear Intensity Change, Evolution Equations System, Inhomogeneous Medium, Nonlinear Elastic Incompressible Medium, Shear Loading with Variable Directivity, Transverse Shock Waves

References

[1] A.G. Kulikovskii, E.I. Sveshnikova, Nonlinear Waves in Elastic Media, CRC Press, (1995).

[1] V.E. Ragozina, Yu.E. Ivanova, Effect of the medium inhomogeneity on the evolution equation of plane shock waves, Journal of Applied Mechanics and Technical Physics. 54 (2013) 809-818.

DOI: 10.1134/s0021894413050143

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[4] M.D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, (1964).