A FINITE ELEMENT MODEL FOR CALCULATING A NON-THIN ORTHOTROPIC CYLINDRICAL SHELL, TAKING INTO ACCOUNT THE INDUCED INHOMOGENEITY
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Abstract
The formulation of a model for the deformation and strength calculation of an open cylindrical shell of circular shape rigidly pinched along contour planes formed by generators is considered. The ratios of the geometric parameters of the shell differ significantly from thin-walled structures, to which traditional technical hypotheses could be applied. The formulation of a mathematical model defining the stress-strain states of a thick-walled structure was carried out within the framework of a nonlinear three-dimensional theory. The peculiarity of the developed model was that orthotropic composites were adopted as the structural materials of the shell, the deformation and strength properties of which manifest themselves in different ways in accordance with the types of stress states being realized. The manifestation of such mechanical properties of materials is interpreted as induced heterogeneity, which significantly complicates the methodology for calculating spatial structures. Due to the specified features of the research object, isoparametric finite elements of a three-dimensional tetrahedral shape, the nodes of which had three degrees of freedom, were used to develop a computational model. In order to adequately account for the stiffness properties of orthotropic composites exhibiting induced heterogeneity, the basis of the determining relationships for them was the deformation potential formulated in the normalized stress tensor space associated with the main axes of orthotropy of materials. Due to the nonlinearity of the problem under consideration, the process of solving it was based on the method of variable elasticity parameters. As a result of the implementation of the computational model, comprehensive information was obtained on the stresses, deformations and displacements of the shell, the main of which are presented in the text of the article with the addition of their analysis.
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References
Treshchev A.A. Potential dependence between deformations and stresses for orthotropic physically nonlinear materials / A.A.Treshchev // Fundamental and applied problems of engineering and technology. – 2017. – No. 4-1 (324). – рр. 71–74.
Treshchev A.A. 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). – Tolyatti: ANO “Institute of Forensic Construction and Technical Expertise” – 2020. – No. 3(6). – P. 62 – 68.
Treschev A.A. Defining equations of deformation of materials with double anisotropy / A.A.Treschev, Yu.A.Zavyalova, M.A.Lapshina, A.E.Gvozdev, O.V.Kuzovleva, E.S.Krupitsyn // Chebyshevskiisbornik. – 2021. – Vol. 22. – No. 4. – pp. 369 – 383.
Treshchev A.A. Theory of deformation and strength of materials with initial and induced sensitivity to the kind of stress state. Defining relations / A.A. Treshchev. – M.; Tula: RAASN; Tula State University, 2016. – 326 p.
Treschev A.A. Theory of deformation and strength of different resistant materials / A.A.Treschev. – Tula: Publisher Name TulSU. – 2020. – 359 p.
Schmueser D.W. Nonlinear Stress-Strain and Strength Response of Axisymmetric Bimodulus Composite Material Shells / D.W.Schmueser // AIAA Journal. – 1983. – Vol. 21. – №12. – рр. 1742 – 1747.
Reddy L.N. On the Behavior of Plates Laminated of Bimodulus Composite Materials / L.N.Reddy, C.W.Bert // ZAMM. – 1982. – Vol. 62. – № 6. – рр. 213 – 219.
Jones R.M. A Nonsymmetric Compliance Matrix Approach to Nonlinear Multimodulus Ortotropic Materials / R.M.Jones // AIAA Journal. – 1977. – Vol. 15. – № 10. – рр. 1436 – 1443.
Jones R.M. Modeling Nonlinear Deformation of Carbon-Carbon Composite Material / R.M.Jones // AIAA Journal. – 1980. – Vol. 18. – № 8. – рр. 995 – 1001.
Rose A.V. Three-reinforced woven materials / A.V. Rose, I.G. Zhigun, M.N. Dushin // Polymer mechanics. – 1970. – No. 3. – рр. 471–476.
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 – №10. – рр. 1427–1435.
Jones R.M. Stress-Strain Relations for Materials with Different Moduli in Tension and Compression / R.M.Jones // AIAA Journal. – 1977. – Vol. 15. – №1. – рр. 16–25.
Zolochevsky A.A. Calculation of anisotropic shells from different modulus materials under non-axisymmetric loading / A.A. Zolochevsky, V.N. Kuznetsov // Dynamics and strength of heavy machines. – Dnepropetrovsk: DSU, 1989. – pp. 84–92.
Ambartsumian S.A. Basic equations and of the ratio of the heterogeneous theory of elasticity of an anisotropic body / S.A.Ambartsumian // News USSR Academy of Sciences. Solid State Mechanics. – 1969. – No. 3. – рр. 51 – 61.
Kayumov R.A. Identification of mechanical characteristics of fiber-reinforced composites / R.A.Kayumov, S.A.Lukankin, V.N.Paimushin, S.A.Kholmogorov // Scientific Notes of the Kazan University. Physical and mathematical sciences. – 2015. – Vol. 157. – Book 4. – pp. 112 – 132.
Treshchev A.A. Theory of deformation of spatial reinforced concrete structures / A.A. Treshchev, V.G. Telichko. – M.; Tula: RAASN; Tula State University, 2019. – 386 p.
Treshchev A.A. Finite element model for calculating spatial structures made of materials with complex properties / A.A. Treshchev, V.G. Telichko, A.N. Tsarev, P.Yu. Khodorovich // Izvestia of Tula State University. Technical science. – Tula: Tula State University Publishing House, 2012. – Issue. 10. − pp. 106 – 114.
Green A. Large elastic deformations and nonlinear mechanics of a continuous medium / A.Green, J.Adkins. – Moskow: Publisher Name Mir. – 1976. – 416 p.