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IssuesArchive of Issues2004-4pp.61-67

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A. I. Aleksandrovich and P. A. Kuvshinov, "Solution of 3D problem of elastoplasticity for a finite segment of a thick-walled pipe by the local functional method," Mech. Solids. 39 (4), 61-67 (2004)
Year 2004 Volume 39 Number 4 Pages 61-67
Title Solution of 3D problem of elastoplasticity for a finite segment of a thick-walled pipe by the local functional method
Author(s) A. I. Aleksandrovich (Moscow)
P. A. Kuvshinov (Moscow)
Abstract A 3D viscoplasticity problem is solved for a finite segment of a thick-walled pipe with allowance for large strains. The process of loading of the pipe surface is divided into sufficiently small time intervals. For each instant of the passage to the next interval, we calculate the generalized forces reduced to the nodes located at the vertices of the Lagrangian octagonal elements into which the pipe segment is partitioned. At each time instant, the edges of the elements form a frozen-in Lagrangian coordinate mesh. At each transient instant, the coordinates of the internal nodes are refined iteratively by shifting these nodes in the direction opposite to that of the action of the nodal generalized forces, which provides the minimization of these forces. To refine the position of the nodes on the surface, we minimize the discrepancy of the boundary conditions represented in the generalized form in terms of the stress vector and the relationships between the components of this vector for a prescribed friction law. Bilateral kinematic constraints are taken into account by fixing the coordinates of the nodes. Unilateral constraints are taken into account by transferring the nodes onto the constraint surface in case they enter the prohibited region.

The rheological model of the material of the pipe is constructed on the basis of the model of a transversely hardening body modified for the case of large strains. The strain space is utilized as the basis space and the rheological model is represented in the form of integro-differential equations. The solution of this equation by Euler's method is integrated in the algorithm for the numerical analysis of the process of loading of a finite pipe segment. The choice of the strain space as the basis space is accounted for by the numerical technique applied for the analysis.

This numerical technique was applied to the analysis of the process of elastoplastic deformation of thin plates in the axially symmetric case [1, 2] and showed good agreement between the computational results and the experimental data.
References
1.  "Mathematical modeling of the process of axially symmetry forming of an annular plate with a thin rubber-like coating," Problemy Mashinostroeniya i Nadezhnosti Mashin, No. 4, pp. 61-68, 1998.
2.  A. I. Alexandrovich, A. K. Kornouchov, F. Popielas, and A. Weis, Löesung axialsymmetrischer elastisch-plastischer Aufgapen bei der Deformation dünner bleche mit Hilfe der Methode der lokalen Funnktionale, Rechen Zentrum ADW, Moskau, 1999.
Received 26 March 2002
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