This article is cited in 1 paper

Mechanics of Solids

On the method of orthogonal projections in the theory of elasticity

V. V. Struzhanov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation

Abstract: The method of orthogonal projections applied to the task of determining the stresses in the elastic deformable bodies, which allowed us to relax the requirements to the smoothness of the functions defining external forces and to the components of the tensor of the initial strains, which cause the appearance of balanced self-stresses. Examples of the calculation of quench stresses in a circular cylinder and residual stresses after shrinkage of the binder in composite cylinders made by winding are given.

Keywords: energy Hilbert subspaces, orthogonal spaces, orthonormal system, orthoprojector, residual stresses.

UDC: 539.3

MSC: 74B10

Received: April 12, 2017
Revised: June 9, 2017
Accepted: June 12, 2017
First online: July 10, 2017

DOI: 10.14498/vsgtu1542

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