Geodesic
Development of the decomposition method in mechanics of solids
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 54-59

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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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     title = {Development of the decomposition method in mechanics of solids},
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V. A. Lokhov; Yu. I. Nyashin; V. S. Tuktamishev. Development of the decomposition method in mechanics of solids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 54-59. http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a6/