Exact Solution of the Problem on Elastic Bending of the Segment of a Narrow Multilayer Beam by an Arbitrary Normal Load

Ковальчук, С. Б.

doi:10.1007/s11029-020-09860-y

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…Works [19,20] report trends in the development of the calculation of the stressed state at bending, including attempts to implement generalized approaches to solving applied and general theoretical problems. Paper [19] deals with the problem of bending thick rectangular plates using reciprocity theorems based on Reisner's theory.…”

Section: The Mathematical Model Of Variable Asymmetric Loading Of a Pinched Console As An Applied Problem Of The Theory Of Elasticitymentioning

confidence: 99%

“…Paper [19] deals with the problem of bending thick rectangular plates using reciprocity theorems based on Reisner's theory. Study [20] gives an accurate analytical solution to the problem of flat bending under the action of longitudinal normal loads. In this case, the load is set in the form of a trigonometric series.…”

Section: The Mathematical Model Of Variable Asymmetric Loading Of a Pinched Console As An Applied Problem Of The Theory Of Elasticitymentioning

confidence: 99%

“…Although works [19,20] contain elements of certain generalizations but cannot be used in other areas of continuum mechanics, which limits the possibilities of their application.…”

Section: The Mathematical Model Of Variable Asymmetric Loading Of a Pinched Console As An Applied Problem Of The Theory Of Elasticitymentioning

confidence: 99%

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Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Chigirinsky

Naumenko

2021

EEJET

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Solving the problem of continuum mechanics has revealed the defining generalizations using the function argument method. The aim of this study was to devise new approaches to solving problems of continuum mechanics using defining generalizations in the Cartesian coordinate system. Additional functions, or the argument of the coordinates function of the deformation site, are introduced into consideration. The carriers of the proposed function arguments should be basic dependences that satisfy the boundary or edge conditions, as well as functions that simplify solving the problem in a general form. However, there are unresolved issues related to how not the solutions themselves should be determined but the conditions for their existence. Such generalized approaches make it possible to predict the result for new applied problems, expand the possibilities of solving them in order to meet a variety of boundary and edge conditions. The proposed approach makes it possible to define a series of function arguments, each of which can be a condition of uniqueness for a specific applied problem. Such generalizations concern determining not the specific functions but the conditions of their existence. From these positions, the flat problem was solved in the most detailed way, was tested, and compared with the studies reported by other authors. Based on the result obtained, a mathematical model of the flat applied problem of the theory of elasticity with complex boundary conditions was built. Expressions that are presented in coordinateless form are convenient for analysis while providing a computationally convenient context. The influence of the beam shape factor on the distribution of stresses in transition zones with different intensity of their attenuation has been shown. By bringing the solution to a particular result, the classical solutions have been obtained, which confirms its reliability. The mathematical substantiation of Saint-Venant's principle has been constructed in relation to the bending of a beam under variable asymmetric loading

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Section: The Mathematical Model Of Variable Asymmetric Loading Of a Pinched Console As An Applied Problem Of The Theory Of Elasticitymentioning

confidence: 99%

Section: The Mathematical Model Of Variable Asymmetric Loading Of a Pinched Console As An Applied Problem Of The Theory Of Elasticitymentioning

confidence: 99%

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Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Chigirinsky

Naumenko

2021

EEJET

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Analytical Solution to the Plane Bending Task of the Multilayer Beam with a Circular Axis under Normal Uniform Loading

Ковальчук

2020

Strength Mater

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Exact solutions for anisotropic beams with arbitrary distributed loads

Tang,

Dui,

2025

Applied Mathematical Modelling

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Exact Solution of the Problem on Elastic Bending of the Segment of a Narrow Multilayer Beam by an Arbitrary Normal Load

Cited by 9 publications

References 24 publications

Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Analytical Solution to the Plane Bending Task of the Multilayer Beam with a Circular Axis under Normal Uniform Loading

Exact solutions for anisotropic beams with arbitrary distributed loads

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