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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
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.
[1] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies. Elsevier, Amsterdam 1981.
[2] J. Haslinger I. Hlaváček: Contact between elastic bodies. Apl. mat. 25 (1980), 324-348, 26 (1981), 263-290, 321-344.
[3] I. Hlaváček J. Nečas: On inequalities of Korn's type. Arch. Ratl. Mech. Anal., 36 (1970), 305-334. DOI 10.1007/BF00249518 | MR 0252844
[4] 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. MR 0382827
[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 0446014
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