The stress singularity order in a composite wedge of functionally graded materials under antiplane deformation

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dc.citation.epage47
dc.citation.issue1
dc.citation.spage39
dc.contributor.affiliationIнститут прикладних проблем Механiки i математики iм.Я.С. Пiдстригача НАН України
dc.contributor.affiliationЛьвiвський нацiональний аграрний унiверситет
dc.contributor.affiliationЦентр математичного моделювання IППММ iм. Я. С. Пiдстригача
dc.contributor.affiliationPidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
dc.contributor.affiliationLviv National Agrarian University
dc.contributor.affiliationCentre of Mathematical Modelling of IAPMM NASU named after Ya. S. Pidstryhach
dc.contributor.authorМахоркін, М. І.
dc.contributor.authorСкрипочка, Т. А.
dc.contributor.authorТорський, А. Р.
dc.contributor.authorMakhorkin, M. I.
dc.contributor.authorSkrypochka, T. A.
dc.contributor.authorTorskyy, A. R.
dc.date.accessioned2023-03-06T12:28:22Z
dc.date.available2023-03-06T12:28:22Z
dc.date.created2020-01-01
dc.date.issued2020-01-01
dc.description.abstractУ данiй роботi вивчається з’ясування порядку сингулярностi у багатоклинових системах, що мiстять елементи, виконанi з функцiонально градiєнтного матерiалу (ФГМ) з кутовою градiєнтнiстю. Такi елементи запропоновано моделювати за допомогою багатоклинового пакету, де модуль зсуву змiнюється вiд клина до клина згiдно з певною функцiональною залежнiстю (в статтi розглянуто лiнiйну, квадратичну та експоненцiальну залежностi). З’ясовано, що складена з 20 елементiв модельна область забезпечує вiдносну похибку обчислення порядку сингулярностi поля напружень, яка не перевищує 5%. Використовуючи моделювання ФГМ за допомогою багатоклинової системи, вивчено вплив вставки з ФГМ з кутовою градiєнтнiстю на порядок сингулярностi у трикомпонентному композитному клинi. Виявлено низку закономiрност
dc.description.abstractIn this paper, finding the order of singularity in multi-wedge systems containing elements made of functionally gradient material (FGM) with an angular gradient under antiplane deformation is studied. These elements are proposed to be modeled by means of multiwedge composite, where the shear modulus changes from wedge to wedge according to a certain functional dependence (in this article we consider the linear, quadratic, and exponential dependencies). It is found that the model region composed of 20 elements provides a relative error in the calculation of the stress field singularity order, which does not exceed 5%. Using the simulation of FGM by a multi-wedge system, the influence of an insert made of functionally graded material with an angular gradient on the singularity order in a three-component composite wedge has been studied. A number of regularities have been established.
dc.format.extent39-47
dc.format.pages9
dc.identifier.citationMakhorkin M. I. The stress singularity order in a composite wedge of functionally graded materials under antiplane deformation / Makhorkin M. I., Skrypochka T. A., Torskyy A. R. // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 7. — No 1. — P. 39–47.
dc.identifier.citationenMakhorkin M. I., Skrypochka T. A., Torskyy A. R. (2020) The stress singularity order in a composite wedge of functionally graded materials under antiplane deformation. Mathematical Modeling and Computing (Lviv), vol. 7, no 1, pp. 39-47.
dc.identifier.doiDOI: 10.23939/mmc2020.01.039
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/57519
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (7), 2020
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dc.relation.references[4] Paggi M., Carpinteri A., Orta R. A mathematical analogy and a unified asymptotic formulation for singular elastic and electromagnetic fields at multimaterial wedges. Journal of Elasticity. 99 (2), 131–146 (2010).
dc.relation.references[5] Makhorkin M., Makhorkina T. Analytical determination of the order of stress field singularity in some configurations of multiwedge systems for the case of antiplane deformation. Econtechmod. An international quarterly journal. 6 (3), 45–52 (2017).
dc.relation.references[6] Makhorkin M., Sulym H. On determination of the stress-strain state of a multi-wedge system with thin radial defects under antiplane deformation. Civil and environmental engineering reports. 5, 235–251(2010).
dc.relation.references[7] Carpinteri A., Paggi M. On the asymptotic stress field in angularly nonhomogeneous materials. Int. J. Fract. 135 (4), 267–283 (2005).
dc.relation.references[8] Carpinteri A. Paggi M. Singular harmonic problems at a wedge vertex: mathematical analogies between elasticity, diffusion, electromagnetism, and fluid dynamics. Journal of Mechanics of Materials and Structures. 6 (1–4), 113–125 (2011).
dc.relation.references[9] Fedorov A. Yu., Matveenko V. P. Investigation of stress behavior in the vicinity of singular points of elastic bodies made of functionally graded materials. J. Appl. Mech. 85 (6), 061008-1–061008-13 (2018).
dc.relation.references[10] Hu X. F., Yao W. A., Yang S. T. A symplectic analytical singular element for steady-state thermal conduction with singularities in anisotropic material. J. of heat transfer. 140 (9), 091301-1–091301-13 (2018).
dc.relation.references[11] Xiaofei H. Stress singularity analysis of multi-material wedges under antiplane deformation. Acta Mech. Solida Sinica. 26 (2), 151–160 (2013).
dc.relation.references[12] Tranter C. J. The use of the Mellin transform in finding the stress distribution in an infinite wedge. Quarterly Journal of Mechanics and Applied Mathematics. 1, 125–130 (1948).
dc.relation.references[13] Marur P. R., Tippur H. V. Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient. Int. J. Solids Struct. 37, 5353–5370 (2000).
dc.relation.references[14] Linkov A., Rybarska-Rusinek L. Evaluation of stress concentration in multi-wedge systems with functionally graded wedges. International Journal of Engineering Science. 61, 87–93 (2012).
dc.relation.references[15] Linkov A. M., Koshelev V. F. Multi-wedge points and multi-wedge elements in computational mechanics: evaluation of exponents and angular distribution. Int. J. Solids and Structures. 43, 5909–5930 (2006).
dc.relation.references[16] Tikhomirov V. V. Stress singularity in a top of composite wedge with internal functionally graded material. St. Petersburg Polytechnical University J.: Physics and Mathematics. 1 (3), 278–286 (2015).
dc.relation.references[17] Lomakyn V. A. Theory of elasticity of inhomogeneous bodies. Moscow, МGU (1976), (in Russian).
dc.relation.references[18] Parton V., Perlin P. Mathematical methods of the theory of elasticity. Two volumes. Mir (1984).
dc.relation.references[19] Makhorkin M. I., Skrypochka T. A. Stress singularity in a multiwedge system with interconnected elastic characteristics of its elements, under antiplane deformation. Visnyk of Zaporizhzhya National University. Physical and mathematical Sciences. 2, 170–179 (2017), (in Ukrainian).
dc.relation.references[20] Makhorkin M. Effect of a wedge type insert of the functionally graded materialon the stress singularity in a composite wedge structure under antiplane deformation. Applied problems of mechanics and mathematics. Scientific proceeding. 16, 112–118 (2018), (in Ukrainian).
dc.relation.referencesen[1] Wieghardt K. Uber das Spalten und zerreissen elastischer K¨orper. Z. Math. Phys. 55, 60–103 (1907).
dc.relation.referencesen[2] Williams M. L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics. 19 (4), 526–528 (1952).
dc.relation.referencesen[3] Savruk M., Kazberuk A. Stress concentration at notches. Springer International Publishing AG (2016).
dc.relation.referencesen[4] Paggi M., Carpinteri A., Orta R. A mathematical analogy and a unified asymptotic formulation for singular elastic and electromagnetic fields at multimaterial wedges. Journal of Elasticity. 99 (2), 131–146 (2010).
dc.relation.referencesen[5] Makhorkin M., Makhorkina T. Analytical determination of the order of stress field singularity in some configurations of multiwedge systems for the case of antiplane deformation. Econtechmod. An international quarterly journal. 6 (3), 45–52 (2017).
dc.relation.referencesen[6] Makhorkin M., Sulym H. On determination of the stress-strain state of a multi-wedge system with thin radial defects under antiplane deformation. Civil and environmental engineering reports. 5, 235–251(2010).
dc.relation.referencesen[7] Carpinteri A., Paggi M. On the asymptotic stress field in angularly nonhomogeneous materials. Int. J. Fract. 135 (4), 267–283 (2005).
dc.relation.referencesen[8] Carpinteri A. Paggi M. Singular harmonic problems at a wedge vertex: mathematical analogies between elasticity, diffusion, electromagnetism, and fluid dynamics. Journal of Mechanics of Materials and Structures. 6 (1–4), 113–125 (2011).
dc.relation.referencesen[9] Fedorov A. Yu., Matveenko V. P. Investigation of stress behavior in the vicinity of singular points of elastic bodies made of functionally graded materials. J. Appl. Mech. 85 (6), 061008-1–061008-13 (2018).
dc.relation.referencesen[10] Hu X. F., Yao W. A., Yang S. T. A symplectic analytical singular element for steady-state thermal conduction with singularities in anisotropic material. J. of heat transfer. 140 (9), 091301-1–091301-13 (2018).
dc.relation.referencesen[11] Xiaofei H. Stress singularity analysis of multi-material wedges under antiplane deformation. Acta Mech. Solida Sinica. 26 (2), 151–160 (2013).
dc.relation.referencesen[12] Tranter C. J. The use of the Mellin transform in finding the stress distribution in an infinite wedge. Quarterly Journal of Mechanics and Applied Mathematics. 1, 125–130 (1948).
dc.relation.referencesen[13] Marur P. R., Tippur H. V. Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient. Int. J. Solids Struct. 37, 5353–5370 (2000).
dc.relation.referencesen[14] Linkov A., Rybarska-Rusinek L. Evaluation of stress concentration in multi-wedge systems with functionally graded wedges. International Journal of Engineering Science. 61, 87–93 (2012).
dc.relation.referencesen[15] Linkov A. M., Koshelev V. F. Multi-wedge points and multi-wedge elements in computational mechanics: evaluation of exponents and angular distribution. Int. J. Solids and Structures. 43, 5909–5930 (2006).
dc.relation.referencesen[16] Tikhomirov V. V. Stress singularity in a top of composite wedge with internal functionally graded material. St. Petersburg Polytechnical University J., Physics and Mathematics. 1 (3), 278–286 (2015).
dc.relation.referencesen[17] Lomakyn V. A. Theory of elasticity of inhomogeneous bodies. Moscow, MGU (1976), (in Russian).
dc.relation.referencesen[18] Parton V., Perlin P. Mathematical methods of the theory of elasticity. Two volumes. Mir (1984).
dc.relation.referencesen[19] Makhorkin M. I., Skrypochka T. A. Stress singularity in a multiwedge system with interconnected elastic characteristics of its elements, under antiplane deformation. Visnyk of Zaporizhzhya National University. Physical and mathematical Sciences. 2, 170–179 (2017), (in Ukrainian).
dc.relation.referencesen[20] Makhorkin M. Effect of a wedge type insert of the functionally graded materialon the stress singularity in a composite wedge structure under antiplane deformation. Applied problems of mechanics and mathematics. Scientific proceeding. 16, 112–118 (2018), (in Ukrainian).
dc.rights.holder©2020 Lviv Polytechnic National University CMM IAPMM NASU
dc.subjectоска задача
dc.subjectбагатоклинова система
dc.subjectсингулярнiсть напружень
dc.subjectфункцiонально градiєнтний матерiал
dc.subjectкутова градiєнтнiсть
dc.subjectantiplane problem
dc.subjectmulti-wedge system
dc.subjectstress singularity
dc.subjectfunctionally graded material
dc.subjectangular gradient
dc.subject.udc74B05
dc.subject.udc74B99
dc.titleThe stress singularity order in a composite wedge of functionally graded materials under antiplane deformation
dc.title.alternativeПорядок сингулярності напружень у композитному клині з функціонально-градієнтних матеріалів за антиплоскої деформації
dc.typeArticle

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Mathematical Modeling And Computing. – 2020. – Vol. 7, No. 1