DEFORMATION OF ANNULAR ORTHOTROPIC PLATES OF MEDIUM THICKNESS MADE OF MATERIALS SENSITIVE TO THE TYPE OF STRESS STATE
https://doi.org/10.33979/2073-7416-2022-101-3-60-74
Abstract
Discusses a model of a three-layer annular plate of medium thickness. It is assumed that the load on the plate is assumed to be uniformly distributed. The universal relations constructed in the normalized tensor stress space associated with the main axes of the anisotropy of the material are taken as the determining relations. The load was taken in such a way that the deflections of the middle surface of the plate were considered small in comparison with its thickness. The fixing of the plate is rigid along the external and internal contours.
Since some orthotropic materials with different resistance exhibit a nonlinear dependence of deformations on stresses, the material characteristics are taken as functions of stress intensity. As a result of the formulation of the boundary value problem, a mathematical model was developed for the analyzed class of problems, implemented as a numerical algorithm integrated into the Mathcad software package.
To solve the system of resolving differential equations of bending of annular orthotropic plates, the method of variable elasticity parameters with a finite-difference approximation of the second order of accuracy was used.
About the Authors
A. A. TRESHCHEV
Tula State Univercity
Russian Federation
Russian Federation
Treshchev Alexandr An., corresponding member of RAACN, doctor of technical sciences, professor, head of the department of Construction, Building Materials and Structures
Tula
Y. A. ZAVYALOVA
Tula State Univercity
Russian Federation
Russian Federation
Zavyalova Yuliya An., graduate student of the department of Construction, Building Materials and Structures
Tula
References
1. Schmueser D.W. Nonlinear Stress-Strain and Strength Response of Axisymmetric Bimodulus Composite Material Shells / D.W.Schmueser // AIAA Journal. 1983. Vol. 21. No.12. рр. 1742-1747.
2. Reddy L.N. On the Behavior of Plates Laminated of Bimodulus Composite Materials / L.N.Reddy, C.W.Bert // ZAMM. 1982. Vol. 62. No.6. Рр. 213–219.
3. Jones R.M. A Nonsymmetric Compliance Matrix Approach to Nonlinear MultimodulusOrtotropic Materials / R.M.Jones // AIAA Journal. 1977. Vol. 15. No.10. Рр. 1436–1443.
4. Jones R.M. Modeling Nonlinear Deformation of Carbon-Carbon Composite Material / R.M.Jones // AIAA Journal. 1980. Vol. 18. No.8. Рр. 995–1001.
5. Jones R.M. Bucling of Stiffened Multilayered Circular Shells with Different Ortotropic Moduli in Tension and Compression / R.M.Jones // AIAA Journal. 1971. Vol. 9. No.5. Рр. 917–923.
6. Kregers A.F. Nelineynaya polzuchest’ tkanevogo stekloplastika pri nekotorih vidah slojnogo napryajonnogo sostoyaniya [Nonlinear creep of fiberglass fabric in some types of complex stress state] / A.F.Kregers, R.D.Maksimov, R.P.Turcinysh // Mechanics of polymers. 1973. No. 2. Рp. 212–218. (rus)
7. Amelina E.V. O nelineynom deformirovanii ugleplastikov: eksperiment, model’, raschot [On nonlinear deformation of carbon fiber plastics: experiment, model, calculation] / E.V.Amelina [et al.] // ICT SB RAS: Computational Technologies. 2015. Vol. 20. No. 5. Рp. 27–52. (rus)
8. Kayumov R.A. Identifikaciya mehanicheskih harakteristik armirovannih voloknami kompozitov [Identification of mechanical characteristics of fiber-reinforced composites] / R.A.Kayumov, S.A.Lukanin, V.N.Paimushin, S.A.Kholmogorov // Scientific notes of the Kazan University. Physical and mathematical sciences. – 2015. Vol. 157. book 4. Pp. 112–132. (rus)
9. Shafigullin L.N. Development of the recommendations on selection of glass-fiber reiforced polyurethanes for vehicle parts / L.N.Shafigullin, A.A.Bobrishev, V.T.Erofeev, A.A.Treshchev, A.N.Shafigullina // International Journal of Applied Engineering Research. 2015. Vol. 10. No.23. Рр. 43758–43762.
10. Rose A.V. Treharmirovannie tkanie materiali [Three-reinforced woven materials] / A.V.Rose, I.G.Zhigun, M.N.Dushin // Mechanics of polymers. 1970. No. 3. Pp. 471–476. (rus)
11. Jones R.M., Theoretical-experimental correlation of material models for non-linear deformation of graphite / R.M.Jones, D.A.R.Nelson // AIAA Journal. 1976. Vol. 14. No.10. Рр. 1427–1435.
12. Jones R.M. Stress-Strain Relations for Materials with Different Moduli in Tension and Compression / R.M.Jones // AIAA Journal. 1977. Vol. 15. No.1. Рр. 16–25.
13. Zolochevsky A.A. Raschot anizotropnih obolochek iz raznomodul’nih materialov pri neosesimmetrichnom nagrujenii [Calculation of anisotropic shells from multi-modular materials under nonaxisymmetric loading] / A.A.Zolochevsky, V.N.Kuznetsov // Dynamics and strength of heavy machines. – Dnepropetrovsk: DSU, 1989. Pp. 84–92. (rus)
14. Elsufyev S.A. Issledovanie deformirovaniya ftoroplasta-4 pri lineynom I ploskom napryajonnom sostoyaniyah [Investigation of deformation of fluoroplast-4 under linear and plane stress states] / S.A.Elsufyev // Mechanics of polymers. 1968. No. 4. Pp. 742–746. (rus)
15. Elsufyev S.A. Izuchenie deformirovaniya ftoroplasta v usloviyah ploskogo napryajonnogo sostoyaniya [The study of fluoroplast deformation in a plane stress state] / S.A.Elsufyev, V.M.Chebanov // Research. on elasticity and plasticity. L.: LSU Publishing House, 1971. Issue 8. Pp. 209–213. (rus)
16. Ainbinder S.B. Vliyanie gidrostaticheskogo davleniya na mehanicheskie svoystva polimernih materialov [The influence of hydrostatic pressure on the mechanical properties of polymer materials] / S.B.Ainbinder, M.G.Laka, I.Y.Majors // Mechanics of polymers. 1965. No. 1. Pp. 65–75. (rus)
17. Ainbinder S.B. Svoystva polymerov pri visokih davleniyah [Properties of polymers at high pressures] / S.B.Ainbinder, K.I.Alksne, E.L.Tyurina, M.G.Laka. M.: Nauka, 1973. 118 p. (rus)
18. Derevyanko N.I. Svoystva armirovannogo polistirola pri kratkovremennom rastyajenii, sjatii I izgibe [Properties of reinforced polystyrene under short-term stretching, compression and bending] / N.I.Derevyanko // Mechanics of polymers. 1968. No.6. Pp. 1059–1064. (rus)
19. Bazhanov P.V. Opredelenie prochnostnih kriteriev pri vozniknovenii plasticheskih deformaciy [Determination of strength criteria in the occurrence of plastic deformations in polycarbonate] / P.V.Bozhanov, A.A.Treshchev // Innovations and investments. 2018. No. 12. Pp. 323–326. (rus)
20. Bert C.W. Models for Fibrous Composite with Different Properties in Tension and Compression / C.W.Bert // Transaction of the ASME. 1977. Vol. 99 H. Ser. D. No. 4. Рр. 344–349.
21. Treshchev A.A. Teoriya deformirovaniya i prochnosti raznosoprotivlyayushchihsya materialov [Theory of deformation and strength of different resistant materials] / A.A. Treshchev // Tula: TulSU, 2020. 359 p. (rus)
22. Bazant Z.P. Endochronic Theory of Inelasticity and Failure of Concrete / Z.P.Bazant, P.D.Bhat // Journal of the Engineering Mechanics Division, ASCE. 1976. Vol. 102. No. EM4. Рр. 701–722.
23. Kupfer H.B. Das nicht-linear Verhalten des Betonsbei Zweiachsinger Beanspruchung / H.B.Kupfer // Beton und Stahlbetonbau. 1973. No.11. Рр. 269–274.
24. Tasuji M.E. Stress-Strain Response and Fracture of Concrete in Biaxial Loading / M.E.Tasuji, F.O.Slate, A.H.Nilson // ACI Journal. 1979. No.7. Рр. 806–812.
25. Ambartsumyan S.A. Osnovnie uravneniya i sootnosheniya raznomodul’noy teorii uprugosti anizotropnogo tela [Basic equations and relations of the multi-modulus theory of elasticity of an anisotropic body] / S.A. Ambartsumyan // Izv. of the USSR Academy of Sciences. MSB. 1969. No. 3. Рp. 51-61. (rus)
26. Lomakin E.V. Sootnosheniya teorii uprugosti anizotropnogo tela, deformacionnie harakteristiki kotorih zavisyat ot vida napryajonnogo sostoyaniya [Relations of the theory of elasticity for an anisotropic body, the deformation characteristics of which depend on the type of stress state] / E.A. Lomakin // Izv. of the USSR Academy of Sciences. MSB. 1983. No.3. Рp. 63–69. (rus)
27. Treshchev A.A. Variant modeli deformirovaniya ortotropnih kompozitnih materialov [Variant of the deformation model of orthotropic composite materials] / A.A. Treshchev, Yu.A. Zavyalova, M.A. Lapshina // Expert: Theory and Practice (Scientific and Practical journal). – Togliatti: ANO "Institute of Forensic Construction and Technical Expertise" 2020. No.3(6). Pp. 62–68. (rus)
28. Treshchev A.A. Izgib ortotropnih plastin sredney tolshchini s uchetom zavsimosti material’nih parametrov ot vida napryajonnogo sostoyaniya [Bending of orthotropic plates of medium thickness taking into account the dependence of material parameters on the type of stress state] / A.A. Treshchev, Yu.A. Zavyalova, M.A. Lapshina // Structural mechanics and constructions. Voronezh: VSTU. 2022. Issue 1. No. 32. Pp. 7–28. (rus)
29. Treshchev A.A. Opisanie deformirovaniya ortotropnih raznosoprotivlyayushchihsya materialov [Description of deformation of orthotropic materials with different resistance] / A.A. Treshchev, Yu.A.Monastyrev, V.D.Chibrikina, Yu.A.Zavyalova, M.A.Lapshina // Construction mechanics and structures. Voronezh: VSTU. 2019. No. 1(20). Pp. 7–13. (rus)
30. Treshchev A.A. Potential’naya zavisimost’ mejdu deformaciyami i napryajeniyami dlya ortotropnih fizicheski nelineynih materialov [Potential dependence between deformations and stresses for orthotropic physically nonlinear materials] / A.A.Treshchev // Fundamental and applied problems of engineering and technology. Eagle: OGU. 2017. № 4-1 (324). Pp. 71–74. (rus)
31. Treshchev A.A. Defining equations of deformation of materials with double anisotropy / A.A.Treshchev, Yu.A.Zavyalova, M.A.Lapshina, A.E.Gvozdev, O.V.Kuzovleva, E.S.Krupitsyn // Chebyshevskii sbornik. 2021. Vol. 22. No. 4. Рp. 369–383.
32. Timoshenko S.P. Plastinki i obolochki [Plates and shells] / S.P. Timoshenko, S. Voynvsky-Krieger. M.: Nauka, 1966. 636 p. (rus)
33. Batov P.A. Primenemiye modificirovannogo prostranstva dlya rascheta ortotropnih plastin s ispol’zovaniyem ANSYS i analiticheskih metodov [Application of modified space for calculation of orthotropic plates using ANSYS and analytical methods] / P.A.Batov, K.G.Batyrev, N.M.Matchenko // Collection of materials of the 2nd Russian-Ukrainian Symposium. Penza: PGUAS. 2002. Pp. 165–167. (rus)
34. Batyrev K.G. Osesimmetrichnaya zadacha izgiba transversal’no izotropnoy plastini pod deystviem poperechnoy nagruzki [Axisymmetric problem of bending a transversally isotropic plate under the action of a transverse load] / K.G.Batyrev // Izvestiya Tula State University. Series: Technology, mechanics and durability of building materials, structures and structures. Tula: TulSU. 2001. Issue 2. Pp. 10–18. (rus)
35. Pikul V.V. Mehanika obolochek [Mechanics of shells] / V.V.Pikul. Vladivostok: Dalnauka, 2009. 536 p. (rus)
36. Ambartsumyan S.A. Obshchaya teoriya anizotropnih obolochek [General theory of anisotropic shells] / S.A.Ambartsumyan. M.: Nauka, 1974. 446 p. (rus)
37. Treshchev A.A. Anizotropnite plastini i obolochki iz raznosopronivlyayushchihsya materialov [Anisotropic plates and shells made of highly resistant materials] / A.A. Treshchev. M.: Tula: RAASN; TulSU, 2007. 160 p. (rus)
38. Alfutov N.A. Raschot mnogosloynih plastin i obolochek iz kompozicionnih materialov [Calculation of multilayer plates and shells made of composite materials] / N.A.Alfutov, P.A.Zinoviev, B.G.Popov. M.: Mashinostroenie, 1984. 263 p. (rus)
39. Birger I.A. Soprotivleniye materialov [Resistance of materials] / I.A.Birger, R.R.Mavlyutov. M.: Nauka. Gl. ed. phys. - mate. lit, 1986. 560 p. (rus)
40. Pisarenko G.S. Uravneniya i kraevie zadachi teorii plastichnosti i polzuchesti [Equations and boundary value problems of the theory of plasticity and creep] / G.S.Pisarenko, N.S.Mozharovsky // Reference manual. Kiev: Nauk. dumka, 1981. 496 p. (rus)
Review
For citations:
TRESHCHEV A.A., ZAVYALOVA Y.A. DEFORMATION OF ANNULAR ORTHOTROPIC PLATES OF MEDIUM THICKNESS MADE OF MATERIALS SENSITIVE TO THE TYPE OF STRESS STATE. Building and Reconstruction. 2022;(3):60-74. (In Russ.) https://doi.org/10.33979/2073-7416-2022-101-3-60-74
Views:
156
Email this article 