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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

COMPARISON OF FINDINGS OF THE FINITE ELEMENT ANALYSISWITH THE FINDINGS OF THE ASYMPTOTIC HOMOGENIZATIONMETHOD IN RESPECT OF THE PLATE IN ELASTOPLASTIC BENDING

Vestnik MGSU 8/2013
  • Savenkova Margarita Ivanovna - Lomonosov Moscow State University (MGU) postgraduate student, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sheshenin Sergey Vladimirovich - Lomonosov Moscow State University (MGU) Doctor of Physical and Mathematical Sciences, Professor, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zakalyukina Irina Mikhailovna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 42-50

The authors present numerical results of the asymptotic homogenization method for elastoplastic bending of the plate. The plate is supposed to be laminated and exposed to the transversal load. Stresses and displacements in the cylindrical bending problem are compared with those calculated using the 2D finite element method. The new trend in the mathematical simulation of structures, made of composite materials, contemplates accurate consideration of their nonlinear properties (for instance, plasticity or damage) on the micro-structural level of materials. The homogenization method provides for the coupling between the microstructural level and the level of the entire structure. The authors have developed a numerical implementation of this coupling. It represents a combination of the homogenization method and linearization with account for the loading parameter. The approach was implemented as a parallel algorithm and applied to the plastic bending simulation of the FGM plate. The parallel algorithm is based on the overlapping subdomain decomposition method and the Euler explicit and implicit integration methods. MPI was used for software development purposes.In this paper, the authors provide a concise description of the proposed method applied to the 3D boundary-value problem. The authors compare numerical solutions obtained through the application of the homogenization approach and the finite element method. Two types of laminated plates are taken as an example. Three-layered plate was exposed to uniformly distributed transversal loading. The second five-layered plate, that was a lot thinner than the first one, was exposed to piecewise constant transversal loading. All layers of both plates are homogenous; they are supposed to be elastic or bilinearly plastic. It was discovered that the asymptotic homogenization technique provides a more accurate solution for the five-layered plate than for the three-layered one. Edge effects near the edges of the plates are smaller for the thin five-layered plate if compared with the thick three-layered plate. The edge effect appears due to the large value of the plate height-to-length ratio. Nevertheless, the first order asymptotic homogenized method provides sufficient accuracy in both cases.

DOI: 10.22227/1997-0935.2013.8.42-50

References
  1. Savenkova M.I., Sheshenin S.V., Zakalyukina I.M. Primenenie metoda osredneniya v zadache uprugoplasticheskogo izgiba plastiny [Application of Homogenization Method to Elastoplastic Bending of a Plate]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 9, pp. 156—164.
  2. Sheshenin S.V., Savenkova M.I. Osrednenie nelineynykh zadach v mekhanike kompozitov [Averaging Method for Nonlinear Problems in Composites Mechanics]. Vestnik Moskovskogo universiteta. Matematika. Mekhanika [Proceedings of Moscow University. Mathematics. Mechanics]. 2012, no. 5, pp. 58—61.
  3. Barret R. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia, SIAM, 1994.
  4. Sadovnichy V., Tikhonravov A., Voevodin V.l., Opanasenko V. "Lomonosov": Super-computing at Moscow State University. In Contemporary High Performance Computing: from Petascale toward Exascale. Chapman & Hall/CRC Computational Science. 2013, Boca Raton, USA, CRC Press, pp. 283—307.
  5. Fish J., Shek K., Pandheeradi M., Shephard M.S. Computational Plasticity for Composite Structures Based on Mathematical Homogenization: Theory and Practice. Comput. Methods Appl. Mech. Engrg. 1997, no. 148, pp. 53—73.
  6. Ghosh S., Lee K., Moorthy S. Two Scale Analysis of Heterogeneous Elastic-plastic Materials with Asymptotic Homogenization and Voronoi Cell Finite Element Model. Comput. Methods Appl. Mech. Enrgr. 1996, no. 132, pp. 63—116.
  7. Gorbachev V.I., Pobedrya B.E. The Effective Characteristics of Inhomogeneous Media. J. Appl. Math. Mech. 1997, vol. 61, no. 1, pp. 145—151.
  8. Bakhvalov N.S. Osrednenie differentsial'nykh uravneniy s chastnymi proizvodnymi s bystro ostsilliruyushchimi koeffitsientami [Homogenization of Differential Equations Having Partial Derivatives with Rapidly Ocillating Coefficients]. Doklady AN SSSR [Reports of the Academy of Sciences of the USSR]. 1975, vol. 221, no. 3, pp. 516—519.
  9. Pobedrya B.E., Gorbachev V.I. Kontsentratsiya napryazheniy i deformatsiy v kompozitakh [Concentration of Stresses and Strains in Composites]. Mekhanika kompozitsionnykh materialov [Mechanics of Composite Materials]. 1984, no. 2, pp. 207—214.
  10. Kalamkarov A.L., Andrianov I.V., Danishevs'kyy V.V. Asymptotic Homogenization of Composite Materials and Structures. Applied Mechanics Reviews, 2009, v. 63, no. 3, pp. 1—20.
  11. Sheshenin S.V. Asimptoticheskiy analiz periodicheskikh v plane plastin [Asymptotical Analysis of In-plane Periodical Plates]. Izvestiya RAN. Mekhanika tverdogo tela [RAS News. Mechanics of Solids.], 2006, no. 6, pp. 71—79.
  12. Sheshenin S.V. Primenenie metoda osredneniya k plastinam, periodicheskim v plane [Application of the Homogenization Method for the In-Plane Periodical Plates]. Vestnik Moskovskogo universiteta. Matematika. Mekhanika [Proceedings of Moscow University. Mathematics. Mechanics]. 2006, no. 1, pp. 47—51.

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IDENTIFICATION OF MUTUAL INFLUENCE OF BENDING AND TORSIONAL STRAINS OF THE REINFORCED CONCRETE SPACE GRID FLOOR AS PART OF THE MONITORING OF ITS ERECTION

Vestnik MGSU 7/2012
  • Plotnikov Alexey Nikolaevich - Chuvash State University named after I.N. Ulyanov (ChuvSU) Associate Professor of Building Structures, +7 (8352) 62 45 96, Chuvash State University named after I.N. Ulyanov (ChuvSU), 15 Moskovskiy Prospekt, Cheboksary, 428015, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 82 - 89

The author presents the results of measurements of total deformations of the space-grid floor in relation to the torsional strain of beams and the rigidity of beams in bending and torsion while monitoring the erection of the floor of a building.
Any space grid system is utterly sensitive to changes in relations between the rigidity of elements. No experimental data covering space grid floors or any method of analysis of their stress-strain state are available.
The author performed the assessment of interrelations between the rigidity of some beams in the two directions by means of a full-scale loading test (monitoring) of the monolithic space grid floor, beam size 8.0 × 9.2 m. The purpose of the assessment was to confirm the bearing capacity and the design patterns based on deflections and stresses of elements to select the operational reinforcement value. Monolithic concrete was used to perform the load test.
As a result, the width of concrete ribs was found uneven. In the design of reinforced concrete space rib floors it is advisable to develop detailed models of structures through the employment of the finite element method due to the significant sensitivity of the system to distribution and redistribution of stresses.
Large spans of monolithic space rib floors require the monitoring of the stress-strain state and computer simulations to adjust the design pattern on the basis of the monitoring results.

DOI: 10.22227/1997-0935.2012.7.82 - 89

References
  1. Cao M., Ren Q., Qiao P. Nondestructive Assessment of Reinforced Concrete Structures Based on Fractal Damage Characteristic Factor», Journal of Engineering Mechanics, vol. 132, no. 9, pp. 924—931.
  2. Plotnikov A.N. Raspredelenie i pereraspredelenie usiliy v opertykh po konturu zhelezobetonnykh setchato-rebristykh sostavnykh perekrytiyakh [Distribution and Redistribution of Forces in Reinforced Concrete Space Grid Layered Floors Supported on Four Sides]. Proceedings of the All-Russian Conference of Young Scientists «Building Structures — 2000». State University of Civil Engineering, 2000.
  3. Plotnikov A.N. Izmenenie napryazhenno-deformirovannogo sostoyaniya zhelezobetonnoy perekrestno-rebristoy sistemy v protsesse ee vklyucheniya v sostav sloistogo perekrytiya vysotoy 2,1 m [The Change of the Stress-strain State of the Reinforced Concrete Space Rib System in the Course of Its Incorporation into the Layered Floor, Height 2.1 m]. Industrial and Civil Engineering in the Modern World. Collections of research projects of the Institute of Construction and Architecture. Moscow State University of Civil Engineering, 2011.
  4. Plotnikov A.N. Modelirovanie metodom konechnykh elementov (MKE) zhelezobetona pri kruchenii s izgibom [Simulation of Reinforced Concrete in the event of Torsion with Bending by the Method of Finite Elements (FEM)]. International Journal for Computational Civil and Structural Engineering. Vol. 6, no. 1 and 2, 2010. Moscow State University of Civil Engineering, pp.177-178. Available at: URL:http://www.mgsu.ru/images/stories/ nash_universitet/ Vestnik/IJCCSE _v6_i12_2010.pdf/ Date of Access: 22.11.2011.
  5. Aivazov R.L., Plotnikov A.N. Modelirovanie napryazhennogo sostoyaniya perekrestnykh elementov s razlichnym sootnosheniem zhestkostey na izgib metodom konechnykh elementov [Simulation of the Stress State of Cross Elements with Different Ratios of Bending Rigidity by the Finite Element Method]. New in Architecture, and Reconstruction of Structures: Proceedings of the Sixth All-Russian Conference NASKR - 2005. Chuvash State University, Cheboksary, 2005.
  6. Plotnikov A.N., Ezhov A.V., Sabanov A.I. Obsledovanie zhelezobetonnykh perekrytiy, obrazovannykh perekrestnymi rebrami s tsel’yu otsenki ikh napryazhenno-deformirovannogo sostoyaniya [Examination of Reinforced Floors Formed by Cross Ribs in order to Assess Their Stress-Strain State]. Prevention of Accidents of Buildings and Structures — 2011. Moscow. 2011. Available at: http://pamag.ru/pressa/deformat-status/ Date of Access: 21/11/2011.
  7. Bailey C.G., Toh W.S., Chan B.M., Simplified and Advanced Analysis of Membrane Action of Concrete Slabs. ACI JOURNAL, vol. 105, no. 1, 2008, pp. 30—40.
  8. SP 52-101—2003. Betonnye i zhelezobetonnye konstruktsii bez predvaritel’nogo napryazheniya armatury [Building Rules 52-101—2003. Concrete and Reinforced Concrete Structures without Prestressing of Reinforcement]. Moscow, 2004.
  9. Tekhnicheskiy kodeks ustanovivsheysya praktiki [Technical Code of Practice]. EN 1992-1-1:2004 Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings. Ministry of Architecture and Construction of Belarus. Minsk, 2010.
  10. JSCE Guideline for Concrete no. 15. Standard Specifications for Concrete Structures — 2007. JSCE Concrete Committee. Design Publ., Japan, 2010.
  11. Aivazov R.L., Plotnikov A.N. Zhestkost’ zhelezobetonnykh perekrestnykh sistem na kruchenie i vliyanie ee izmeneniya na obshchee NDS [Rigidity of Reinforced Concrete Cross-Systems in Torsion and Its Effect on the Overall Change in the Stress-Strain State]. New in Architecture, and Reconstruction of Structures. Proceedings of the Sixth All-Russian Conference NASKR - 2007. Chuvash State University, Cheboksary, 2009.
  12. Plotnikov A.N., Ezhov A.V., Sabanov A.I. Pereraspredelenie usiliy v perekrestno-rebristom zhelezobetonnom perekrytii pri ekspluatatsii [Redistribution of Forces within Reinforced Concrete Space Rib Floors in the Course of Operation]. Industrial and Civil Engineering in the Modern World. Collections of research projects of the Institute of Construction and Architecture. Moscow State University of Civil Engineering, 2011.

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DETERMINATION OF STRESS-STRAIN STATE OF A THREE-LAYER BEAM WITH APPLICATION OF CONTACT LAYER METHOD

Vestnik MGSU 4/2016
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Turusov Robert Alekseevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Physical and Mathematical Sciences, Professor, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Tsybin Nikita Yur’evich - Moscow State University of Civil Engineering (National Research University) (MGSU) postgraduate student, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 17-26

The article deals with the solution for the stress-strain state of a multilayer composite beam with rectangular cross-section, which is bended by normally distributed load. The intermolecular interaction between layers is accomplished by the contact layer, in which the substances of adhesive and substrate are mixed. We consider the contact layer as a transversal anisotropic medium with such parameters that it can be represented as a set of short elastic rods, which are not connected to each other. For simplicity, we assume that the rods are normally oriented to the contact surface. The contact layer method allows us to solve the problem of determining the concentration of tangential stresses arising at the boundaries between the layers and the corner points, their changes, as well as to determine the physical properties of the contact layer basing on experimental data. Resolving the equations obtained in this article can be used for the solution of many problems of the theory of layered substances. These equations were derived from the fundamental laws of the theory of elasticity and generally accepted hypotheses of the theory of plates for the general case of the bending problem of a multilayer beam with any number of layers. The article deals with the example of the numerical solution of the problem of bending of a three-layer beam. On the basis of this solution the curves were obtained, which reflect the stress-strain state of one of the layers. All these curves have a narrow area of the edge effect. The edge effect is associated with a large gradient tangential stresses in the contact layer. The experimental data suggest that in this zone the destruction of the samples occurs. This fact allows us to say that the equations obtained in this article can be used to construct a theory of the strength layered beams under bending.

DOI: 10.22227/1997-0935.2016.4.17-26

References
  1. Turusov R.A., Manevich L.I. Metod kontaktnogo sloya v adgezionnoy mekhanike. Odnomernye zadachi. Sdvig soedineniya vnakhlestku [Contact Layer Method in Adhesion Mechanics. One-Dimensional Tasks. Lap Shear]. Klei. Germetiki, Tekhnologii [Adhesives. Sealants]. 2009, no. 6, pp. 2—12. (In Russian)
  2. Turusov R.A., Kuperman A., Andreev V.I. Determining the True Strength of the Material of Fiberglass Thick Rings When Stretched with Half-Disks. Advanced Materials Research. 2015, no. 1102, pp. 155—159. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMR.1102.155.
  3. Yazyev B.M., Andreev V.I., Turusov R.A. Nekotorye zadachi i metody mekhaniki makroneodnorodnoy uprugoy sredy [Some Problems and Methods of Macroheterogeneous Elastic Medium Mechanics]. Rostov-on-Don, RGSU Publ., 2009. (In Russian)
  4. Turusov R.A. Elastic and Temperature Behavior of a Layered Structure. Part I. Experiment and Theory. Mechanics of Composite Materials. 2014, vol. 50, no. 6, December, pp. 801—808. DOI: http://dx.doi.org/10.1007/s11029-015-9469-8.
  5. Turusov R.A. Elastic and Temperature Behavior of a Layered Structure. Part II. Calculation Results. Mechanics of Composite Materials. 2015, vol. 51, no. 1, January, pp. 127—134. DOI: http://dx.doi.org/ 10.1007/s11029-015-9484-9.
  6. Zhao L.G., Warrior N.A. and Long A.C. A Micromechanical Study of Residual Stress and Its Effect on Transverse Failure in Polymer-Matrix Composites. International Journal of Solids and Structures. 2006, vol. 43, no. 18—19, pp. 5449—5467. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2005.08.012.
  7. Andreev V.I., Barmenkova E.V. Modelirovanie real’noy sistemy zdanie — fundament — osnovanie dvukhsloynoy balkoy peremennoy zhestkosti na uprugom osnovanii [Modeling of the Real System “Structure—Foundation—Bedding” through the Employment of a Model of a Two-Layer Beam of Variable Rigidity Resting on the Elastic Bedding]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 6, pp. 37—41. (In Russian)
  8. Aleksandrov A.V., Potapov V.D., Derzhavin B.P. Soprotivlenie materialov [Strength of Materials]. 7th edition. Moscow, Vysshaya shkola Publ., 2003, 560 p. (In Russian)
  9. Manevich L.I., Pavlenko A.V. Ob uchete strukturnoy neodnorodnosti kompozita pri otsenke adgezionnoy prochnosti [Account of Structural Inhomogeneity of a Composite when Estimating Adhesive Stability]. Prikladnaya mekhanika i tekhnicheskaya fizika [Applied Mechanics and Technical Physics]. 1982, no. 3 (133), pp. 140—145. (In Russian)
  10. Lakes Roderic. Viscoelastic Materials. Cambridge University Press, April 27, 2009, pp. 344—350. DOI: http://dx.doi.org/10.1017/CBO9780511626722.
  11. Bolotin V.V., Novichkov Yu.N. Mekhanika mnogosloynykh konstruktsiy [Mechanics of Multilayered Stryctures]. Moscow, Mashinostroenie Publ., 1980, 375 p. (In Russian)
  12. Rabinovich A.L. Vvedenie v mekhaniku armirovannykh polimerov [Introduction into Mechanics of Reinforced Polymers]. Moscow, Nauka Publ., 1970, 482 p.
  13. Ellyin F., Xia Z., Zhang Y. Micro/Meso-Modeling of Polymeric Composites with Damage Evolution. Solid Mechanics and Its Applications. 2006, vol. 140, pp. 505—516. DOI: http://dx.doi.org/10.1007/1-4020-4891-2_42.
  14. Turusov R.A. Adgezionnaya mekhanika [Adhesive Mechanics]. Moscow, MGSU Publ., 2015, 230 p. (In Russian)
  15. Bower Allan F. Applied Mechanics of Solids. 1 edition, CRC Press, October 5, 2009, 112 p.
  16. Mallick P.K. Fiber-Reinforced Composites: Materials, Manufacturing, and Design. 3d ed. Taylor & Francis Group, LLC, 2007. 617 p.
  17. Moiseev E.I., Lur’e S.A. Nefedov P.V. Ob usloviyakh sushchestvovaniya resheniya dlya kraevykh zadach v modelyakh adgezionnykh vzaimodeystviy [On the Existence Conditions of Solutions for Boundary Problems in Models of Adhesive Interactions]. Mekhanika kompozitsionnykh materialov i konstruktsiy [Mechanics of Composite Materials and Structures]. 2013, no. 19 (1), pp. 87—96. (In Russian)
  18. Altenbach H., Eremeyev V.A., Lebedev L.P. On the Existence of Solution in the Linear Elasticity with Surface Stresses. Z. Angew. Math. Mech. (ZAMM). 2010, vol. 90 (3), pp. 231—240. DOI: http://dx.doi.org/10.1002/zamm.200900311.
  19. Ma H.M.,Gao X.-L., Reddy J.N. A Microstructure-Dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory. Journal of the Mechanics and Physics of Solids. 2008, vol. 56, no. 12, pp. 3379—3391. DOI: http://dx.doi.org/10.1016/j.jmps.2008.09.007.
  20. Belov P.A., Lur’e S.A. Teoriya ideal’nykh adgezionnykh vzaimodeystviy [Theory of Ideal Adhesive Interactions]. Mekhanika kompozitsionnykh materialov i konstruktsiy [Mechanics of Composite Materials and Structures]. 2007, no. 13 (4), pp. 519—536. (In Russian)

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Application of the homogenization method to the elastoplastic bending of a plate

Vestnik MGSU 9/2012
  • Savenkova Margarita Ivanovna - Lomonosov Moscow State University postraduate student, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, MSU Main Building, Vorobevy gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sheshenin Sergey Vladimirovich - Lomonosov Moscow State University (MGU) Doctor of Physical and Mathematical Sciences, Professor, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zakalyukina Irina Mikhaylovna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Assosiate Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-24-01; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 156 - 164

The authors present a method of homogenization used to solve nonlinear equilibrium problems
of laminated plates exposed to transversal loads.
The homogenization technique is a general and mathematically rigorous solution to elasticity
problems. It describes the processes of deformation of composite structural elements. It was originally
developed for linear problems. This method encompasses the calculation of all characteristics
related to deflection by combining solutions to local and global homogenization problems. Thus, it
implements the general idea of the domain decomposition into subdomains.
The homogenization method has been most widely used in cases of periodical heterogeneity
because of significant simplification that happens due to periodicity. This simplification implies that
any cell of periodicity appears to be the material representative volume element (RVE). Therefore,
it is sufficient to solve local problems within a single periodicity cell. Hence, with reference to local
problems, conditions of periodicity are a mere consequence of the periodicity of the material
structure. Decomposition of the domain causes decomposition of the solution. The latter means that
displacements, stresses and strains are represented by functions that depend on both global and local
coordinates. Global coordinates are associated with the whole body scale and local coordinates
vary in the periodicity cell, i.e. in RVE only.
If the material structure is not periodic, but its properties do not depend on global coordinates,
material effective properties can be determined by solving local problems in any RVE. That is not the ase of nonlinear materials. Now local problems have to be solved in every RVE because of the homogenized
properties dependence on global coordinates. Another complication arises due to nonlinearity.
Indeed, the homogenization method employs the superposition principle to represent the solution to the
elasticity problem as summarized solutions to global and local problems. This principle doesn't work in
the case of nonlinearity. We suggest combining the standard homogenization technique with linearization
by using the loading history to solve the nonlinear problem. On the contrary, local linear problems
have to be solved in every RVE. Certainly, this method involves numerous calculations.
As for the problem considered in the paper, its nonlinearity is caused by material plastic properties.
Most plasticity-related principles are formulated as tensorial linear relationships between the
stress and strain rates. Hence, here we identify a perfect opportunity to employ the homogenization
method combined with linearization with regard to the load parameter. This combined technique is
implemented to resolve the heterogeneous plate bending problem. Heterogeneous materials are of
the two types: laminates and functionally graded materials (FGM).
The computer code is developed for the purpose of numerical plate bending simulation. It employs
the parallel programming MPI technique and the Euler type explicit and implicit methods. For
example, laminated plate bending due to the distributed transversal load was the subject of research.
Each layer of the plate was composed of FGM or a homogeneous material. The authors have discovered
that FGM plates have a higher yield stress then the plates composed of homogeneous layers.

DOI: 10.22227/1997-0935.2012.9.156 - 164

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