On a Mathematical Model of Bars with Variable Rectangular Cross‐sections
Identifieur interne : 001866 ( Main/Exploration ); précédent : 001865; suivant : 001867On a Mathematical Model of Bars with Variable Rectangular Cross‐sections
Auteurs : G. V. Jaiani [Géorgie (pays)]Source :
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik [ 0044-2267 ] ; 2001-03.
English descriptors
- Teeft :
- Angew, Approximation, Approximation error, Auxiliary formulas, Boundary conditions, Boundary value problems, Bvps, Const, Cusped, Cusped bars, Differential equations, Dirichlet problem, Displacement vector, Displacement vector components, Double moments, Dynamical, Dynamical case, Dynamical problems, Equilibrium equations, First derivatives, First order, Georgian acad, Hdi2, Hdk2, Hyperbolic equations, Initial conditions, Jaiani, Lateral surfaces, Linear elasticity, Linear theory, Main relations, Math, Mathematical model, Mech, Nondegenerate systems, Numerical solutions, Orthogonal series, Possible solutions, Potential energy, Present paper, Razmadze inst, Rigorous estimation, Static case, Stress tensors, Surface force, Surface forces, Type conditions, Uniqueness theorem, Unknown functions, Variable thickness, Vekua, Volume force, Volume forces, Zamm.
Abstract
Der Vekuasche Ansatz [1] des Aufbaus von Platten‐ und Schalentheorien, bei dem die Felder der Verschiebungen, der Deformationen und der Spannungen des dreidimensionalen Modells der linearen Elastizitätstheorie in Fourier‐Legendresche Reihen nach der Veränderlichen der Dicke entwickelt werden, wird zum Aufbau einer Stabtheorie verallgemeinert. Diese Größen werden hierbei in doppelte Fourier‐Legendresche Reihen nach den Veränderlichen Dicke und Breite entwickelt. Sodann werden alle außer den ersten (N3 + 1) (N2 + 1), N3, N2 = 0, 1, … , Gliedern vernachlässigt. Eine solche Näherung des dreidimensionalen Modells durch ein eindimensionales Modell heißt (N3, N2)‐Approximation. Die Frage der Wohlgestelltheit der Anfangs‐ und Randwertprobleme wird untersucht. Der Fall, in dem der veränderliche Querschnitt zu einem Intervall oder einem Punkt entartet, wird auch betrachtet. Solche Stäbe heißen zugespitzte Stäbe (s. auch [2]).
We generalize an idea of I. Vekua [1] who, in order to construct a theory of plates and shells, expands the fields of displacements, strains, and stresses of the three‐dimensional theory of linear elasticity into orthogonal Fourier‐Legendre series with respect to the variable thickness, to a bar model. In the bar model all above‐mentioned quantities are expanded into orthogonal double Fourier‐Legendre series with respect to the variables thickness and width of the bar, and then all but the first (N3 + 1) (N2 + 1), N3, N2 = 0, 1, …, terms are neglected. This case is called (N3, N2) approximation. The question of well‐posedness of the initial and boundary value problems is investigated. The cases in which a variable cross‐section degenerates to a segment of a straight line or into a point are also considered. Such bars are called cusped bars (see also [2]).
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DOI: 10.1002/1521-4001(200103)81:3<147::AID-ZAMM147>3.0.CO;2-L
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Jaiani</name><affiliation wicri:level="1"><country xml:lang="fr">Géorgie (pays)</country><wicri:regionArea>George Jaiani, Tbilisi State University, Vekua Institute of Applied Mathematics, University st. 2, GE‐380043, Tbilisi, 43</wicri:regionArea><wicri:noRegion>43</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="j" type="main">ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</title><title level="j" type="alt">ZAMM ZEITSCHRIFT FUER ANGEWANDTE MATHEMATIK UND MECHANIK</title><idno type="ISSN">0044-2267</idno><idno type="eISSN">1521-4001</idno><imprint><biblScope unit="vol">81</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="147">147</biblScope><biblScope unit="page" to="173">173</biblScope><biblScope unit="page-count">27</biblScope><publisher>WILEY‐VCH Verlag Berlin GmbH</publisher><pubPlace>Berlin</pubPlace><date type="published" when="2001-03">2001-03</date></imprint><idno type="ISSN">0044-2267</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0044-2267</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Angew</term><term>Approximation</term><term>Approximation error</term><term>Auxiliary formulas</term><term>Boundary conditions</term><term>Boundary value problems</term><term>Bvps</term><term>Const</term><term>Cusped</term><term>Cusped bars</term><term>Differential equations</term><term>Dirichlet problem</term><term>Displacement vector</term><term>Displacement vector components</term><term>Double moments</term><term>Dynamical</term><term>Dynamical case</term><term>Dynamical problems</term><term>Equilibrium equations</term><term>First derivatives</term><term>First order</term><term>Georgian acad</term><term>Hdi2</term><term>Hdk2</term><term>Hyperbolic equations</term><term>Initial conditions</term><term>Jaiani</term><term>Lateral surfaces</term><term>Linear elasticity</term><term>Linear theory</term><term>Main relations</term><term>Math</term><term>Mathematical model</term><term>Mech</term><term>Nondegenerate systems</term><term>Numerical solutions</term><term>Orthogonal series</term><term>Possible solutions</term><term>Potential energy</term><term>Present paper</term><term>Razmadze inst</term><term>Rigorous estimation</term><term>Static case</term><term>Stress tensors</term><term>Surface force</term><term>Surface forces</term><term>Type conditions</term><term>Uniqueness theorem</term><term>Unknown functions</term><term>Variable thickness</term><term>Vekua</term><term>Volume force</term><term>Volume forces</term><term>Zamm</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="de">Der Vekuasche Ansatz [1] des Aufbaus von Platten‐ und Schalentheorien, bei dem die Felder der Verschiebungen, der Deformationen und der Spannungen des dreidimensionalen Modells der linearen Elastizitätstheorie in Fourier‐Legendresche Reihen nach der Veränderlichen der Dicke entwickelt werden, wird zum Aufbau einer Stabtheorie verallgemeinert. Diese Größen werden hierbei in doppelte Fourier‐Legendresche Reihen nach den Veränderlichen Dicke und Breite entwickelt. Sodann werden alle außer den ersten (N3 + 1) (N2 + 1), N3, N2 = 0, 1, … , Gliedern vernachlässigt. Eine solche Näherung des dreidimensionalen Modells durch ein eindimensionales Modell heißt (N3, N2)‐Approximation. Die Frage der Wohlgestelltheit der Anfangs‐ und Randwertprobleme wird untersucht. Der Fall, in dem der veränderliche Querschnitt zu einem Intervall oder einem Punkt entartet, wird auch betrachtet. Solche Stäbe heißen zugespitzte Stäbe (s. auch [2]).</div><div type="abstract" xml:lang="en">We generalize an idea of I. Vekua [1] who, in order to construct a theory of plates and shells, expands the fields of displacements, strains, and stresses of the three‐dimensional theory of linear elasticity into orthogonal Fourier‐Legendre series with respect to the variable thickness, to a bar model. In the bar model all above‐mentioned quantities are expanded into orthogonal double Fourier‐Legendre series with respect to the variables thickness and width of the bar, and then all but the first (N3 + 1) (N2 + 1), N3, N2 = 0, 1, …, terms are neglected. This case is called (N3, N2) approximation. The question of well‐posedness of the initial and boundary value problems is investigated. The cases in which a variable cross‐section degenerates to a segment of a straight line or into a point are also considered. Such bars are called cusped bars (see also [2]).</div></front></TEI><affiliations><list><country><li>Géorgie (pays)</li></country></list><tree><country name="Géorgie (pays)"><noRegion><name sortKey="Jaiani, G V" sort="Jaiani, G V" uniqKey="Jaiani G" first="G. V." last="Jaiani">G. V. Jaiani</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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