# Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method

Aplikace matematiky (1983)

- Volume: 28, Issue: 3, page 199-214
- ISSN: 0862-7940

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topNečas, Jindřich, and Hlaváček, Ivan. "Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method." Aplikace matematiky 28.3 (1983): 199-214. <http://eudml.org/doc/15297>.

@article{Nečas1983,

abstract = {A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.},

author = {Nečas, Jindřich, Hlaváček, Ivan},

journal = {Aplikace matematiky},

keywords = {Kachanov’s iterative method; elastostatics; deformation; unilateral contact; elastoplastic body; rigid foundation; neglecting friction; governed by Hencky-von Mises stress strain relations; weak solution; minimum of potential energy; corresponding variational inequality; secant modules; classical Signorini’s problem; convergence; no numerical applications; Kachanov's iterative method; elastostatics; deformation; unilateral contact; elastoplastic body; rigid foundation; neglecting friction; governed by Hencky-von Mises stress strain relations; weak solution; minimum of potential energy; corresponding variational inequality; secant modules; classical Signorini's problem; convergence; no numerical applications},

language = {eng},

number = {3},

pages = {199-214},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method},

url = {http://eudml.org/doc/15297},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Nečas, Jindřich

AU - Hlaváček, Ivan

TI - Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 3

SP - 199

EP - 214

AB - A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

LA - eng

KW - Kachanov’s iterative method; elastostatics; deformation; unilateral contact; elastoplastic body; rigid foundation; neglecting friction; governed by Hencky-von Mises stress strain relations; weak solution; minimum of potential energy; corresponding variational inequality; secant modules; classical Signorini’s problem; convergence; no numerical applications; Kachanov's iterative method; elastostatics; deformation; unilateral contact; elastoplastic body; rigid foundation; neglecting friction; governed by Hencky-von Mises stress strain relations; weak solution; minimum of potential energy; corresponding variational inequality; secant modules; classical Signorini's problem; convergence; no numerical applications

UR - http://eudml.org/doc/15297

ER -

## References

top- J. Nečas I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies, Elsevier, Amsterdam 1981. (1981)
- J. Haslinger I. Hlaváček, Contact between elastic bodies, Apl. mat. 25 (1980), 324-348, 26 (1981), 263-290, 321-344. (1980)
- I. Hlaváček J. Nečas, 10.1007/BF00249518, Arch. Ratl. Mech. Anal., 36 (1970), 305-334. (1970) MR0252844DOI10.1007/BF00249518
- J. Nečas, On regularity of solutions to nonlinear variational inequalities for second-order elliptic systems, Rend. di Matematica 2 (1975), vol. 8, Ser. VL, 481-498. (1975) MR0382827
- L. M. Kačanov, Mechanika plastičeskich sred, Moskva 1948. (1948)
- G. Fichera, Boundary value problems of elasticity with unilateral constraints, In: S. Flüge (ed): Encycl. of Physics, vol. VIa/2, Springer-Verlag, Berlin, 1972. (1972)
- I. Hlaváček J. Lovíšek, A finite element analysis for the Signorini problem in plane elastostatics, Apl. mat. 22, (1977) 215-228, 25 (1980), 273-285. (1977) MR0446014

## Citations in EuDML Documents

top- Ivan Hlaváček, Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
- Jaroslav Haslinger, Raino Mäkinen, Shape optimization of materially non-linear bodies in contact
- Zuzana Dimitrovová, Shape optimization of elasto-plastic bodies
- Miloslav Feistauer, Jan Mandel, Jindřich Nečas, Entropy regularization of the transonic potential flow problem
- S. Drabla, M. Sofonea, B. Teniou, Analysis of a frictionless contact problem for elastic bodies
- Ivan Hlaváček, Oldřich John, Alois Kufner, Josef Málek, Nečasová, Š. , Jana Stará, Vladimír Šverák, In Memoriam Jindřich Nečas

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