A complex approach to the solution of problems in mechanics of deformable rigid bodies

Murad Agakhanov,Elifkhan Agakhanov,O Kalinina

doi:10.1051/e3sconf/201911001071

Murad Agakhanov, Elifkhan Agakhanov + Show 1 more

Open Access

https://doi.org/10.1051/e3sconf/201911001071

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Abstract

There exists an opinion that the modern numerical methods allow to solve practically any problem in mechanics. But it should be noted that both analytical and experimental methods, as before, are urgent, and exactly a complex of methods develops the mechanics of deformable rigid bodies. The statement of a problem in displacements for some possible cases of equivalent substitution of loads allows to formulate necessary and sufficient conditions of existence of an analogy presenting the effect of a forced deformation in the form of the sum of surface and volume forces, the effect of volume forces in the form of the sum of surface forces and forced deformations, the effect of surface forces in the form of the sum of forced deformations and volume forces. The substitution of volume forces for surface loads and forced deformations allows to extend the use of experimental methods and often to solve through an experimental-and theoretical approach the problems, which cannot be solved through other methods. The obtained results are a considerable step in the development of one of the approaches combining experimental, analytical and numerical methods of solution of linear problems in mechanics of deformable rigid bodies.

Highlights

The practical construction always enriches itself by new exact experimental-andtheoretical knowledge, and the volume of active information resources with respect to the general volume of accumulated professional knowledge extends much
Arguing against the opinion that the modern numerical methods allow to solve practically any problem in mechanics, we should note that the analytical and experimental methods, as before, are urgent, and exactly a complex of methods develops the mechanics of deformable rigid bodies [1, 2]
One of the most important development trends in mechanics of deformable rigid bodies is the creation of approaches which allow to combine huge computing potentialities of modern super-computers with experimental methods of study of materials and structures

Summary

Introduction

The practical construction always enriches itself by new exact experimental-andtheoretical knowledge, and the volume of active information resources with respect to the general volume of accumulated professional knowledge extends much. In this connection, the solution of problems in mechanics of deformable rigid bodies concerning the total use of the material strength for the purpose of achievement of minimum cost and minimum specific consumption of materials for structural elements of buildings and structures widely use the computer facilities. Some works consider the analogy of the effect of volume and surface forces which exists only under strict constraints [5, 6]

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