Calculation of the ribbed plate in the mixed form &amp;#x201C;deflection - function of efforts&amp;#x201D;

Goloskokov, Dmitry P.

doi:10.1109/scp.2015.7342170

Cited by 4 publications

(2 citation statements)

References 2 publications

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“…A comparison of solutions by the superposition method and the method based on the Green function in the form of a trigonometric polynomial for an isotropic pinched plate can be found in Goloskokov and Matrosov [22]. Note that not only a smooth plate was solved using polynomials, but also one supported by rigid edges [23].…”

Section: Introductionmentioning

confidence: 99%

Bending of clamped orthotropic thin plates: polynomial solution

Goloskokov

Matrosov

2022

Mathematics and Mechanics of Solids

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In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.

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Section: Introductionmentioning

confidence: 99%

Bending of clamped orthotropic thin plates: polynomial solution

Goloskokov

Matrosov

2022

Mathematics and Mechanics of Solids

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“…This solution is analytical and presented in the form of two trigonometric series with unknown coefficients, and can be used to satisfy not only force boundary conditions but also kinematic and mixed ones. It should note that analytical approches becomes popular in various scientific [12,13,14,15] and engineering [16,17,18,19,20] domains of investigation due to the wide spread of the systems of analytical calculations (Maple, Mathematica etc.) in modelling processes and structures.…”

Section: Introductionmentioning

confidence: 99%

A superposition method in the analysis of an isotropic rectangle

Goloskokov¹,

Matrosov²

2016

ams

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A superposition method to construct a general solution of the equations of the theory of elasticity as a sum of two solutions obtained by a method of initial functions in the form of trigonometric series is considered. The algorithm to get the main relation of the method of initial functions is introduced. Possibilities of the system of analytical calculations Maple for the implementation of some aspects of this algorithm are shown. The results of analyses of a console rectangle is presented.

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Analysis of elastic systems with discontinuous parameters

Goloskokov

Matrosov

2017

2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov) (CNSA)

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Calculation of the ribbed plate in the mixed form “deflection - function of efforts”

Cited by 4 publications

References 2 publications

Bending of clamped orthotropic thin plates: polynomial solution

Bending of clamped orthotropic thin plates: polynomial solution

A superposition method in the analysis of an isotropic rectangle

Analysis of elastic systems with discontinuous parameters

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