Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity

Senashov, S. I.; Yakhno, Alexander

doi:10.3842/sigma.2012.071

Cited by 14 publications

(49 citation statements)

References 21 publications

(35 reference statements)

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“…Conservation laws have been successfully used to solve many problems in mathematics and mechanics. Summary of results and solved problems from various fields of mechanics can be found in [1][2][3][5][6][7].…”

Section: Figmentioning

confidence: 99%

On Elastoplastic Torsion of a Rod with Multiply Connected Cross-Section

Kondrin¹,

Senashov²,

Кондрин³

et al. 2015

J. Sib. Fed. Univ., Math. phys.

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The classical problem of torsion of a straight rod with convex contour of the cross-section is considered in the paper. The cross-section is multiply connected domain. It is assumed that the region of plastic deformation occupies the whole outer boundary. To solve the problem the conservation laws are used. In the case when the boundary is piecewise smooth the solution is found in explicit form. Computer programs that allow one to find the elastic-plastic boundary in a rod under torsion with any precision are developed. Examples of calculation of elastic-plastic boundaries from presented analytical formulas are given. The obtained results are in good agreement in comparison with known solutions and experimental data.

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Section: Figmentioning

confidence: 99%

On Elastoplastic Torsion of a Rod with Multiply Connected Cross-Section

Kondrin¹,

Senashov²,

Кондрин³

et al. 2015

J. Sib. Fed. Univ., Math. phys.

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“…Taking into account solutions (19), (21), (22), we can express operator Y 1 in terms of r, ϕ, θ c , σ. Namely, for the higher sing solution tan θ p = η/ξ we have:…”

Section: θ 1 : Quasi-scale Transformationmentioning

confidence: 99%

Some symmetry group aspects of a perfect plane plasticity system

Senashov¹,

Yakhno²

2013

J. Phys. A: Math. Theor.

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In this paper, all the known classical solutions of plane perfect plasticity system under Saint Venant -Tresca -von Mises yield criterion are associated with some group of point symmetries. The equations of slip-line families for all solutions are constructed, which permits to determine explicitly boundaries of plastic areas.It is shown, how one can determine the compatible velocity solution for known stresses, considering symmetries. Some invariant solutions of velocities for Prandtl stresses are constructed. The mechanical sense of obtained velocity fields is discussed.

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“…In [15,16] it was shown that the method of CL permits to avoid the restriction on the Jacobian of hodograph transformation, usually using to solve hyperbolic quasilinear PDEs. The existence of two families of real characteristics has played a significant part and the analogue of Riemann-Green function for quasilinear system has been constructed.…”

Section: Introductionmentioning

confidence: 99%