*Visnyk LNAU: Architecture and Farm Building 2018 №19: 5-9*

## REVIEW OF WORKS ON THE APPLICATION OF THE METHOD OF R-FUNCTIONS IN THE MECHANICS OF DEFORMABLE SOLIDS

**Yu. Bodnar**, Candidate of Technical Sciences

Lviv National Agrarian University

https://doi.org/10.31734/architecture2018.19.005

#### Annotation

An analytical review of publications on the application of the theory of R-functions in the problems of the mechanics of a deformable solid is carried out. The plane and axisymmetric problems of the theory of elasticity of isotropic and orthotropic bodies, problems of the theory of thermoelasticity and plasticity theo-ry, dynamic problems of elasticity and thermoelasticity are considered. A brief analysis of methods and algorithms for solving these problems based on theories of R-functions, variational and difference methods is given. The results of solu-tions of specific problems for finite-size bodies have been analyzed, in particular, the effect of changes in the elastic properties, voids and rigid inclusions on the stress-deformed state of isotropic and orthogonal bodies, the interaction of period-ic systems of cracks, holes, cutouts in the strip, dynamic thermoelasticity problems with sudden use of force or temperature loads, eigenvalues and the forms of oscillations of elastic bodies with cavities, etc.

The method of R-functions has become widely developed for the problems of the mechanics of a deformable solid. Structures and algorithms of the solution of plane and axisymmetric problems of the elasticity theory of isotropic and orthotropic bodies, problems of plasticity theory, dynamic problems of elasticity and thermoelasticity are constructed. The considered methods and algorithms can also be used for modeling of the elements of buildings and structures at different loads and influences.

#### Key words

R-functions, elasticity, thermoelasticity, plasticity, isotropic bodies, orthotropic bodies, variational method, difference method, dynamic problems

#### Link

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