Geodesic
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
Applications of Mathematics, Tome 28 (1983) no. 3, pp. 199-214
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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.
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.
DOI : 10.21136/AM.1983.104027
Classification : 49A29, 49J40, 58E35, 73E99, 73T05, 74A55, 74C99, 74G30, 74H25, 74M15
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 
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Nečas, Jindřich; Hlaváček, Ivan. Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method. Applications of Mathematics, Tome 28 (1983) no. 3, pp. 199-214. doi: 10.21136/AM.1983.104027

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[3] I. Hlaváček J. Nečas: On inequalities of Korn's type. Arch. Ratl. Mech. Anal., 36 (1970), 305-334. | DOI | MR

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[5] L. M. Kačanov: Mechanika plastičeskich sred. Moskva 1948.

[6] G. Fichera: Boundary value problems of elasticity with unilateral constraints. In: S. Flüge (ed): Encycl. of Physics, vol. VIa/2, Springer-Verlag, Berlin, 1972.

[7] 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. | MR

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