Dissection Method Applications for Complex Shaped Membranes and Plates

Gabbasov, Radek; Filotov, V.V.; Ovarova, N.B.; Mansour, Alaa E.

doi:10.1016/j.proeng.2016.08.150

Cited by 3 publications

(1 citation statement)

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“…Задачи по определению напряженно-деформированного состояния (НДС) составных балок конечных размеров, загруженных произвольной нагрузкой, с учетом различных краевых условий и отпора упругого основания, могут быть решены с привлечением численных методов. В числе методов, успешно применяемых в расчете конструкций на действие статических и динамических нагрузок на устойчивость, упомянем конечно-разностные методы: метод конечных разностей (МКР) в его классической форме [17][18][19], обобщенные уравнения МКР [20][21][22][23][24], метод последовательных аппроксимаций (МПА) [25][26][27][28][29]. В трудах [17-20, 25, 26, 29] учтена совместная работа конструкции и упругого основания, а в [26] мы уже обращались к вопросам расчета двухслойных составных балок на винклеровском основании, где решение построено с использованием разностной формы МПА [25].…”

Section: Introductionunclassified

The analysis of a free two-layer composite beamon the elastic foundation

2020

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Abstract Introduction. This article offers a methodology for the analysis of a two-layer composite beam on an elastic foundation that represents a one-parameter Winkler model. The behaviour of two-layer beams is described by A.R. Rzhanitsyn in his theory of composite rods that have rigid transverse and elastic-yielding longitudinal connections between layers. The theory of composite rods allows to study the stress-strain state (SSS) of multilayer foundation beams, having a layer featuring low thermal conductivity, and perforated beams. Materials and methods. However, analytical solutions to these problems involve certain difficulties; therefore, they are often inapplicable. We propose to apply a numerical method, a method of successive approximations (MSA), developed by professor R.F. Gabbasov at the Department of structural and theoretical mechanics of the Moscow State University of Civil Engineering. MSA has proven to be an effective and highly accurate method designated for analyzing static/dynamic loads, applied to beams, slabs and shells, and for making stability calculations. The difference-based variation of the MSA method has a number of advantages over difference equations of the “classical” finite difference method (FDM). The proposed methodology allows to take into account various types of boundary conditions without involving contour points. Сoncentrated forces, concentrated moments, and piecewise distributed loads can be taken into account as loading types. The article describes a problem solving algorithm. The system of initial differential equations is solved using difference analogs. Typical difference equations for regular and boundary points are provided. Results. The analysis of a composite free-lying beam on an elastic foundation illustrates the proposed approach. The qua-lity of the analysis results is controlled by performing a numerical study of the solution convergence using several nested meshes. Conclusions. The proposed method can be used in the engineering practice of design organizations and the educational process of higher educational institutions training civil engineering specialists.

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Section: Introductionunclassified

The analysis of a free two-layer composite beamon the elastic foundation

2020

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Behavior analysis of three-layer beams with different stiffness characteristics of layers and seams

Филатов¹,

Hoang²,

Dao³

2023

AIP Conference Proceedings

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Application of generalized equations of finite difference method to computation of bent isotropic stretched and/or compressed plates of variable stiffness under elastic foundation

Youssoufa

Sali

Njifenjou

et al. 2021

Curved and Layered Structures

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The computation of bent isotropic plates, stretched and/or compressed, is a topic widely explored in the literature from both experimental and numerical point of view. We expose in this work an application of the generalized equations of Finite difference method to that topic. The strength of the proposed method is the ability to reconstruct the approximate solution with respect of eventual discontinuities involved in the investigated function as well as its first and second derivatives, including the right-hand side of the equilibrium equation. It is worth mentioning that by opposition to finite element methods our method needs neither fictitious points nor a special condensation of grid. Well-known benchmarks are used in this work to illustrate the efficiency of our numerical and the high accuracy of calculation as well. A comparison of our results with those available in the literature also shows good agreement.

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Dissection Method Applications for Complex Shaped Membranes and Plates

Cited by 3 publications

References 0 publications

The analysis of a free two-layer composite beamon the elastic foundation

The analysis of a free two-layer composite beamon the elastic foundation

Behavior analysis of three-layer beams with different stiffness characteristics of layers and seams

Application of generalized equations of finite difference method to computation of bent isotropic stretched and/or compressed plates of variable stiffness under elastic foundation

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