Rigorous solutions of two-dimensional problems of the mechanics of a deformable solid body

1992 ◽  
Vol 28 (10) ◽  
pp. 615-632
Author(s):  
V. B. Pen'kov ◽  
L. A. Tolokonnikov
Keyword(s):  
Solid Body ◽  
Two Dimensional ◽  
Deformable Solid ◽  
Deformable Solid Body

scholarly journals Conditions of equivalence of effects for the solid body from incompressible material

2018 ◽  
Vol 196 ◽  
pp. 01031 ◽  
Author(s):  
Elephan Agakhanov ◽  
Murad Agakhanov ◽  
Lyudmila Sultanova ◽  
Zabiya Hizriyeva
Keyword(s):  
Solid Body ◽  
Design Research ◽  
Rotating Disk ◽  
Experimental Methods ◽  
Incompressible Material ◽  
Engineering Practice ◽  
General View ◽  
Deformable Solid ◽  
Special Cases ◽  
Deformable Solid Body

Polemicizing with the existing opinion that modern numerical methods allow to solve practically any problem of mechanics, it should be noted that analytical and experimental methods still are relevant, and a complex of methods leads to development of mechanics of a deformable solid body. At present one of the most important directions of development of mechanics of a deformable solid body is creation of the approaches that allow to combine organically great computing opportunities of modern supercomputers with experimental methods of the material and design research. In engineering practice at production of designs and products incompressible materials are widely used. Assessment of their durability requires detailed studying of deflected mode caused by action of various loadings and forces. For a solid body from incompressible material, using the resolving equations set of mechanics of a deformable solid body, at action of the compelled deformations of a general view, volume and superficial forces conditions of equivalence are established. It is shown that the known solutions are special cases of the established equivalence conditions. The efficiency of the analytical solution of a three-dimensional task on the rotating disk from incompressible material is shown by the method of equivalence of effects.

Statics of Laminated and Fibrous Composites With Curved Structures

1992 ◽  
Vol 45 (2) ◽  
pp. 17-34 ◽  
Author(s):  
S. D. Akbarov ◽  
A. N. Guz’
Keyword(s):  
Composite Material ◽  
Solid Body ◽  
Three Dimensional ◽  
Local Distribution ◽  
Homogeneous Body ◽  
Deformable Solid ◽  
Body Model ◽  
Curved Structures ◽  
Piecewise Homogeneous Body ◽  
Deformable Solid Body

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.

scholarly journals Displacement: translation and rotation. Differences and Similarities in the Discrete and Continuous Models

2019 ◽  
Vol 4 (1) ◽  
pp. 104-124
Author(s):  
Géza Lámer
Keyword(s):  
Euclidean Space ◽  
Rigid Body ◽  
Solid Body ◽  
Discrete System ◽  
The Body ◽  
Closed Domain ◽  
Discrete Elements ◽  
Deformable Solid ◽  
First Case ◽  
Deformable Solid Body

The motion (displacement) of the Euclidean space can be decomposed into translation and rotation. The two kinds of motion of the Euclidean space based on two structures of the Euclidean space: The first one is the topological structure, the second one is the idea of distance. The motion is such a (topological) map, that the distance of any two points remains the same. The bounded and closed domain of the Euclidean space is taken as a model of the rigid body. The bounded and closed domain of the Euclidean space is also taken as a model of the deformable solid body. The map – i.e. the displacement field – of the deformable solid body is continuous, but is not (necessarily) motion; the size and the shape of body can change. The material has atomic-molecular structure. In compliance with it, the material can be comprehended as a discrete system. In this case the elements of the material, as an atom, molecule, grain, can be comprehended as either material point, or rigid body. In the first case the kinematical freedom is the translation, in the latter case the translation and the rotation. In the paper we analyse how the kinematical behaviour of the discrete and continuous mechanical system can be characterise by translation and rotation. In the discrete system the two motions are independent variable. At the same time they characterise the movement of the body different way. For instance homogeneous local translation gives the global translation, but the homogeneous local rotation does not give the global rotation. To realise global rotation in a discrete system on one hand global rotation of the position of the discrete elements, on the other hand homogeneous local rotations of the discrete elements in harmony with global rotation are required. In the continuous system the two kinds of movement cannot be interpreted: a point cannot rotate, a rotation of surrounding of a point or direction can be interpreted. The kinematical characteristics, as the displacement (practically this is equal to translation) of (neighbourhood of) point, the rotation of surrounding of that point and the rotation of a direction went through that point are not independent variables: the translation of a point determines the rotation of the surrounding of that point as well as the rotation of a direction went through that point. With accordance this statement the displacement (practically translation) (field) as the only kinematical variable can be interpreted in the continuous medium.

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