Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Lokhov V. A., Nyashin Y. I., Tuktamishev V. S. Development of the Decomposition Method in Mechanics of Solids. Izv. Sarat. Univ. Math. Mech. Inform., 2010, vol. 10, iss. 3, pp. 54-59. DOI: 10.18500/1816-9791-2010-10-3-54-59

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Development of the Decomposition Method in Mechanics of Solids

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

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.

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