Stress-strain state of a two-layer orthotropic body under plane deformation

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dc.citation.epage412
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та обчислення
dc.citation.spage404
dc.citation.volume11
dc.contributor.affiliationЗапорізький національний університет
dc.contributor.affiliationZaporizhzhia National University
dc.contributor.authorДзундза, Н. С.
dc.contributor.authorЗіновєєв, І. В.
dc.contributor.authorDzundza, N. S.
dc.contributor.authorZinovieiev, I. V.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T08:10:31Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractРозглядається задача про визначення напружень і деформацій двошарового тіла, що складається з ортотропного шару постійної товщини, зчепленого з ортотропним півпростором. На поверхню шару діють відомі зовнішні навантаження, такі що деформація тіла є плоскою. На нескінченності напруження дорівнюють нулю. Напружено-деформований стан тіла визначається за допомогою методу інтегральних перетворень Фур’є. Досліджено особливості розв’язків системи диференціальних рівнянь задачі. Отримано розв’язки конкретних задач та проведено їх аналіз.
dc.description.abstractWe consider the problem of determining the stresses and strains of a two-layer body consisting of an orthotropic layer of constant thickness connected to an orthotropic half-space. The surface of the layer is subjected to known external loads, such that the deformation of the body is plane. At infinity, the stresses are zero. The stress-strain state of the body is determined using the method of integral Fourier transforms. The features of solutions of the system of differential equations of the problem are investigated. The solutions of a particular problems are obtained and analyzed.
dc.format.extent404-412
dc.format.pages9
dc.identifier.citationDzundza N. S. Stress-strain state of a two-layer orthotropic body under plane deformation / N. S. Dzundza, I. V. Zinovieiev // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 404–412.
dc.identifier.citationenDzundza N. S. Stress-strain state of a two-layer orthotropic body under plane deformation / N. S. Dzundza, I. V. Zinovieiev // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 404–412.
dc.identifier.doidoi.org/10.23939/mmc2024.02.404
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113824
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та обчислення, 2 (11), 2024
dc.relation.ispartofMathematical Modeling and Computing, 2 (11), 2024
dc.relation.references[1] Martynenko V. G. Methods of experimental study of viscoelastic properties of orthotropic material. Bulletin of the National Technical University “Kharkiv Polytechnic Institute”. Series: Dynamics and strength of machines. 57, 81–87 (2015), (in Ukrainian).
dc.relation.references[2] Velychko O. V. Planar deformation of an elastic multilayer plate under the action of a periodic system of loads. Bulletin of the Dnipro Univ. Mechanics. 6, 162–170 (2004).
dc.relation.references[3] Antonenko N. M., Velichko I. G. Planar deformation of a multilayer base in the presence of tangential and normal elastic connections between the layers. Bulletin of Zaporizhzhya National University. Physical and Mathematical Sciences. 1, 9–14 (2009).
dc.relation.references[4] Antonenko N. M. Spatial deformation of a multilayer plate with elastic connections between layers. Physical and Chemical Mechanics of Materials. 50 (4), 55–61 (2014), (in Ukrainian).
dc.relation.references[5] Kucher O. G., Khariton V. V. Calculation of the deflected state of a curved multilayer plate by the finite element method with numerical determination of the stiffness matrix. Bulletin of the National Academy of Sciences of Ukraine. 1 (1), 92–97 (2004), (in Ukrainian).
dc.relation.references[6] Grigorenko Y. M., Kryukov M. M. Solution of boundary value problems of the theory of layered orthotropic plates with the use of spline functions. Doklady NAS Ukrainy. 5, 34–37 (2001).
dc.relation.references[7] Kardomateas A. G. Elasticity solutions for sandwich orthotropic cylindrical shells under external/internal pressure or axial force. AIAA Journal. 42 (8), 713–719 (2001).
dc.relation.references[8] Chaudhuri P. K., Subhankar R. Receding contact between an orthotropic layer and an orthotropic half-space. Archives of Mechanics. 50 (4), 743–755 (1998).
dc.relation.references[9] Das S., Patra B., Debnath L. Stress intensity factors for an interfacial crack between an orthotropic half-plane bonded to a dissimilar orthotropic layer with a punch. Computers & Mathematics with Applications. 35 (12), 27–40 (1998).
dc.relation.references[10] Jeong K. M., Beom H. G. Buckling Analysis of an Orthotropic Layer Bonded to a Substrate with an Interface Crack. Journal of Composite Materials. 37 (18), 1613–1628 (2003).
dc.relation.references[11] Hwang S. F. The Buckling of an Orthotropic Layer on a Half-Space. International Journal of Mechanical Sciences. 40 (7), 711–721 (1998).
dc.relation.references[12] Sneddon I. N. Fourier transforms. New York, Dover Publications; 2nd edition (1995).
dc.relation.references[13] Lopushanska H. P., Lopushansky A. O., Miaus O. M. Fourier and Laplace transforms: generalization and application. Study guide. Lviv, Lviv University Press (2014).
dc.relation.references[14] Privarnikov A. K. Two-dimensional boundary problems of the theory of elasticity for multilayered foundations. Zaporozhye, Zaporozhye State University (1990).
dc.relation.references[15] Timoshenko S. P., Winowsky-Krieger S. Theory of Plates and Shells. New York, McGraw-Hill; 2nd edition (1959).
dc.relation.references[16] Timoshenko S. P., Goodier J. N. Theory of Elasticity. New York, McGraw-Hill; 3nd edition (1970).
dc.relation.references[17] Dzundza N. S., Zinovieiev I. V. Algorithm for finding the stress-strain state of an elastic orthotropic layer. Scientific Discussion. 64 (1), 16–20 (2022).
dc.relation.references[18] Dzundza N. S., Zinovieiev I. V. Research of the stress-strain state of the orthotropic half-plane under the planar deformation conditions. Computer Science and Applied Mathematics. 1, 23–30 (2022).
dc.relation.references[19] https://github.com/SeregaGomen/QFEM.
dc.relation.referencesen[1] Martynenko V. G. Methods of experimental study of viscoelastic properties of orthotropic material. Bulletin of the National Technical University "Kharkiv Polytechnic Institute". Series: Dynamics and strength of machines. 57, 81–87 (2015), (in Ukrainian).
dc.relation.referencesen[2] Velychko O. V. Planar deformation of an elastic multilayer plate under the action of a periodic system of loads. Bulletin of the Dnipro Univ. Mechanics. 6, 162–170 (2004).
dc.relation.referencesen[3] Antonenko N. M., Velichko I. G. Planar deformation of a multilayer base in the presence of tangential and normal elastic connections between the layers. Bulletin of Zaporizhzhya National University. Physical and Mathematical Sciences. 1, 9–14 (2009).
dc.relation.referencesen[4] Antonenko N. M. Spatial deformation of a multilayer plate with elastic connections between layers. Physical and Chemical Mechanics of Materials. 50 (4), 55–61 (2014), (in Ukrainian).
dc.relation.referencesen[5] Kucher O. G., Khariton V. V. Calculation of the deflected state of a curved multilayer plate by the finite element method with numerical determination of the stiffness matrix. Bulletin of the National Academy of Sciences of Ukraine. 1 (1), 92–97 (2004), (in Ukrainian).
dc.relation.referencesen[6] Grigorenko Y. M., Kryukov M. M. Solution of boundary value problems of the theory of layered orthotropic plates with the use of spline functions. Doklady NAS Ukrainy. 5, 34–37 (2001).
dc.relation.referencesen[7] Kardomateas A. G. Elasticity solutions for sandwich orthotropic cylindrical shells under external/internal pressure or axial force. AIAA Journal. 42 (8), 713–719 (2001).
dc.relation.referencesen[8] Chaudhuri P. K., Subhankar R. Receding contact between an orthotropic layer and an orthotropic half-space. Archives of Mechanics. 50 (4), 743–755 (1998).
dc.relation.referencesen[9] Das S., Patra B., Debnath L. Stress intensity factors for an interfacial crack between an orthotropic half-plane bonded to a dissimilar orthotropic layer with a punch. Computers & Mathematics with Applications. 35 (12), 27–40 (1998).
dc.relation.referencesen[10] Jeong K. M., Beom H. G. Buckling Analysis of an Orthotropic Layer Bonded to a Substrate with an Interface Crack. Journal of Composite Materials. 37 (18), 1613–1628 (2003).
dc.relation.referencesen[11] Hwang S. F. The Buckling of an Orthotropic Layer on a Half-Space. International Journal of Mechanical Sciences. 40 (7), 711–721 (1998).
dc.relation.referencesen[12] Sneddon I. N. Fourier transforms. New York, Dover Publications; 2nd edition (1995).
dc.relation.referencesen[13] Lopushanska H. P., Lopushansky A. O., Miaus O. M. Fourier and Laplace transforms: generalization and application. Study guide. Lviv, Lviv University Press (2014).
dc.relation.referencesen[14] Privarnikov A. K. Two-dimensional boundary problems of the theory of elasticity for multilayered foundations. Zaporozhye, Zaporozhye State University (1990).
dc.relation.referencesen[15] Timoshenko S. P., Winowsky-Krieger S. Theory of Plates and Shells. New York, McGraw-Hill; 2nd edition (1959).
dc.relation.referencesen[16] Timoshenko S. P., Goodier J. N. Theory of Elasticity. New York, McGraw-Hill; 3nd edition (1970).
dc.relation.referencesen[17] Dzundza N. S., Zinovieiev I. V. Algorithm for finding the stress-strain state of an elastic orthotropic layer. Scientific Discussion. 64 (1), 16–20 (2022).
dc.relation.referencesen[18] Dzundza N. S., Zinovieiev I. V. Research of the stress-strain state of the orthotropic half-plane under the planar deformation conditions. Computer Science and Applied Mathematics. 1, 23–30 (2022).
dc.relation.referencesen[19] https://github.com/SeregaGomen/QFEM.
dc.relation.urihttps://github.com/SeregaGomen/QFEM
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectортотропний шар
dc.subjectортотропна півплощина
dc.subjectплоска деформація
dc.subjectнапружено-деформований стан
dc.subjectфункція напружень
dc.subjectінтегральне перетворення Фур’є
dc.subjectorthotropic layer
dc.subjectorthotropic half-plane
dc.subjectplane deformation
dc.subjectstress-strain state
dc.subjectstress function
dc.subjectintegral Fourier transform
dc.titleStress-strain state of a two-layer orthotropic body under plane deformation
dc.title.alternativeНапружено-деформований стан двошарового ортотропного тіла за умов плоскої деформації
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 2