Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Lokhov V. A., Nyashin Y. I., Tuktamishev V. S. Development of the Decomposition Method in Mechanics of Solids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 3, pp. 54-59. DOI: 10.18500/1816-9791-2010-10-3-54-59

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.07.2010
Full text:
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Language: 
Russian
Heading: 
Mechanics
UDC: 
539.3
DOI: 
10.18500/1816-9791-2010-10-3-54-59

Development of the Decomposition Method in Mechanics of Solids

Autors: 
Lokhov V. A., Perm State National Research Polytechnical University, Russia
Nyashin Y I, Perm State National Research Polytechnical University, Russia
Tuktamishev V. S., Perm State National Research Polytechnical University, Russia
Abstract: 

The orthogonal projection method for solution of boundary value problem of theory of elasticity with eigenstrain is presented. The main feature of the method is that the orthogonal decomposition is performed in the Hilbert function space of eigenstrains instead of function space of stresses, which is commonly accepted. As a result, the opportunities to create the desired stress field by eigenstrain keeping strain unchanged (strain-free stress control) and vice versa to create the desired strain distribution keeping stress unchanged (stress-free shape control) are shown. The developed approach is applied to control of residual stress in thermoplasticity.

Key words: 
independent stress control
hot rolling
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