Comparative Analysis of Plasticity Theory Algorithms in Finite-Element Calculations of the Rotation Shell

Article Preview

Abstract:

Comparative analysis of the use of the defining equations of plasticity theories obtained at the loading step in three ways is performed. In the first method, the relations between strains increments and stresses increments are obtained by differentiating the governing equations of the small elastic-plastic deformations theory between full stresses and strains. In the second method, the authors based on the proportionality hypothesis between the component deviators of strains increments and the component deviators of stresses increments without separating the incremental strain into elastic and plastic parts obtain the determining equations at the loading step. In the third method, the relations between the incremental strain and the stresses increment of the plastic flow theory are used on the basis of the hypothesis about the proportionality of the plastic deformations increments to the components of the stress deviator. Based on the analysis of algorithms for obtaining the constitutive relations and the analysis of the numerical results of the calculation example, preference is given to the second method of obtaining expressions between stress increments and strain increments without separating the latter into elastic and plastic parts.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

608-613

Citation:

Online since:

December 2019

Export:

Price:

* - Corresponding Author

[1] S.N. Krivoshapko, V.N. Ivanov, Encyclopedia of analytical surfaces, Springer, International Publishing, Switzeland, (2015).

Google Scholar

[2] V. Andreev, A. Chepurnenko, B. Yazyev, Calculation of creep of circular cylindrical shell by bending theory, Procedia Engineering. 165 (2016) 1141-1146.

DOI: 10.1016/j.proeng.2016.11.831

Google Scholar

[3] A.S. Solodovnikov, S.V. Sheshenin, Numerical study of strength properties for a composite material with short reinforcing fibers, Moscow University Mechanics Bulletin. 72 (4) (2017) 94-100.

DOI: 10.3103/s0027133017040045

Google Scholar

[4] A.Yu. Kim, S.V. Polnikov, Application of iterative numerical methods for calculation of membrane-pneumatic structures taking into account nonlinear factors, Fundamental and applied research in the modern world. 13-1 (2016) 110-113.

Google Scholar

[5] A.M. Belostotsky, S.B. Penkovoy, S.V. Scherbina, P.A. Akimov, T.B. Kaytukov, Сorrect numerical methods of analysis of structural strength and stability of high-rise panel buildings part 1: theoretical foundations of modelling, Key Engineering Materials. 685 (2016) 217-220.

DOI: 10.4028/www.scientific.net/kem.685.217

Google Scholar

[6] I.B. Badriev, M.V. Makarov, V.N. Paimushin, Contact statement of mechanical problems of reinforced on a contour sandwich plates with transversally soft core, Russian Mathematics. 61 (1) (2017) 69-75.

DOI: 10.3103/s1066369x1701008x

Google Scholar

[7] R.A. Kayumov, F.R. Shakirzyanov, S.S. Gavryushin, Modeling of the deformation process and evaluation of the bearing capacity of the soil – thin-walled structure, Proceedings of higher educational institutions. Engineering. 6 (2014) 20-24.

Google Scholar

[8] V.V. Galishnikova, P.J. Pahl, Constrained construction of planar delaunay triangulations without flipping, Construction mechanics of engineering structures and structures. 14 (2) (2018) 154-174.

DOI: 10.22363/1815-5235-2018-14-2-154-174

Google Scholar

[9] V.P. Agapov, K.R. Aidemirov, Calculation of farms by the finite element method taking into account geometric nonlinearity, Industrial and civil engineering. 11 (2016) 4-7.

Google Scholar

[10] V. Lalin, V. Rybakov, A. Sergey, The finite elements for design of frame of thin-walled beams, Applied Mechanics and Materials. 578 (2014) 858-863.

DOI: 10.4028/www.scientific.net/amm.578-579.858

Google Scholar

[11] E.A. Storozhuk, A.V. Yatsura, Analytical-numerical solution of static problems for noncircular cylindrical shells of variable thickness, International Applied Mechanics. 53 (3) (2017) 313-325.

DOI: 10.1007/s10778-017-0813-7

Google Scholar

[12] A.V. Ignatiev, V.A. Ignatiev, E.A. Gamzatova, Calculation of thin plates by the finite element method in the form of the classical mixed method with the exception of finite element displacements as a rigid whole Proceedings of higher educational institutions. Construction. 3 (711) (2018) 5-13.

Google Scholar

[13] L.P. Zheleznov, V.V. Kabanov, D.V. Boiko, Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure, Russian Aeronautics. 57 (2) (2014) 118-126.

DOI: 10.3103/s1068799814020020

Google Scholar

[14] I.V. Stankevich, Numerical solution of the problem of elasticity theory with one-way connections using the finite element method in mixed formulation, Vestnik mashinostroeniya. 2 (2019) 3-9.

Google Scholar

[15] Yu.V. Klochkov, A.P. Nikolaev, O.V. Vakhnina, Numerical analysis of stress-strain state of thin shells when using a triangular finite element with Lagrange multipliers, Proceedings of the lower Volga agrodiversity complex: Science and higher professional education. 3 (23) (2011) 186-192.

DOI: 10.3103/s1068799816030041

Google Scholar

[16] N.N. Malinin, Applied theory of plasticity and creep, mechanical engineering, Moscow, (1975).

Google Scholar