MODELING OF LOCAL BUCKLING OF PERFORATED BEAMS WITH CIRCULAR OPENINGS: COMPUTATION BY FEM AND EXPERIMENTS ON TIN-PLATE STRUCTURES

Vestnik MGSU 10/2017 Volume 12
  • Lavrova Anna Sergeevna - Kaliningrad Marine Design Institute - branch of AO "31st State Design Institute of Special Construction" engineer, Kaliningrad Marine Design Institute - branch of AO "31st State Design Institute of Special Construction", 15 Artilleriyskaya str., Kaliningrad, 236015, Russian Federation.
  • Pritykin Aleksey Igorevich - Kaliningrad State Technical University (KGTU) Doctor of Technical Sciences, Professor, Department of Shipbuilding, Kaliningrad State Technical University (KGTU), 1 Sovetskiy prospect, Kaliningrad, 236040, Russian Federation.

Pages 1115-1124

Subject: investigation of local stability of cellular beams with circular openings, which are widely used in civil engineering. The main problem in this field is the absence of analytical relations for evaluation of critical load of perforated beams. Research objectives: show effectiveness of studying the local stability of perforated beams on small-scale models made of tin; obtain a relationship for recalculating the results of the model tests onto the full-scale structure; check the reliability of numerical calculations of the critical load by the finite element method (FEM). Materials and methods: tests were performed on the tin models of small beams of 32 cm length and on the full-scale steel structure of 4 m length. As for research methods, we used similarity theory, experiments and numerical modeling of stability by the finite element method with help of the software package ANSYS. Results: it was shown that the tests of small-scale models give reliable results for estimation of critical load for full-scale structures that experience local buckling in elastic stage of loading. Obtained relationship for recalculation of critical load of the model onto the full-scale structure does not require strict observance of similarity with respect to Poisson’s ratio and size of flanges because their influence on the critical load is small. Comparison of data obtained from the model tests with the results of structure analysis by the finite element method showed that FEM calculations give reliable results for prediction of stability, and the testing of models is needed only for examining the effect of initial imperfections in the form of small buckles, inaccuracy of manufacture or variation in thicknesses, or the influence of residual stresses due to welding. Discrepancy between the results of tests of the models and numerical calculations of the critical load by FEM does not exceed 6 %. Conclusions: the relationship obtained on the basis of similarity theory allows us to efficiently recalculate the critical load of the model onto the full-scale structure, for which only similarity of geometry of the perforated web from the side view, identity of boundary conditions and the loading type should be respected. Critical load of the cellular beam is proportional to the cube of the web thickness.

DOI: 10.22227/1997-0935.2017.10.1115-1124

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STABILITY ANALYSIS OF ORTHOTROPIC RECTANGULAR PLATES USING THE FORM FACTOR

Vestnik MGSU 12/2017 Volume 12
  • Savin Sergey Yur’evich - South-West State University (SWSU) Сandidate of Technical Sciences, Associate Professor, South-West State University (SWSU), 94 50 let Oktyabrya str., Kursk, 305040, Russian Federation.
  • Ivlev Ivan Andreevich - Orel State University named after I.S. Turgenev Post-graduate Student, Orel State University named after I.S. Turgenev, Orel State University named after I.S. Turgenev, 95 Komsomol’skaya str., Orel, 302026, Russian Federation.

Pages 1333-1341

The article describes the problem of stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported, and two other sides have boundary with either simple supports or fixed supports, which are arbitrarily combined. The plate that is simply supported all over the contour is not considered in the article since the authors described it in the earlier publication. The external load is uniformly distributed along the side and is applied to the shorter side of the plate. To solve the stability problem, the authors use an approximate analytical method - the form factor interpolation method, which is based on the functional relationship between an integral geometric parameter of the mid-plane surface (the form factor) and an integral mechanical parameter (the critical force of buckling). Subject: stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported and two other sides have combination of simple supports and fixed supports arbitrarily combined. Materials and methods: the form factor interpolation method (FFIM) is used to solve the stability problem of elastic orthotropic rectangular plates. The solutions which were obtained by the FFIM method were compared with the results of calculations by FEM (the program SCAD Office 11.5). Results: for orthotropic rectangular plates with combined boundary conditions, we obtained analytical expressions for critical force surfaces and they depend on an integral geometric parameter - form factor and flexural stiffness ratio. To the authors’ knowledge, these expressions are obtained for the first time. The critical force surface for orthotropic rectangular plates constitutes one of the boundaries of this integral physicomechanical parameter for the entire set of orthotropic plates with arbitrary convex contour. Therefore, this surface can be used for obtaining reference solutions by the form factor interpolation method. We demonstrated how to obtain the solution of the stability problem for orthotropic rectangular plates by the form factor interpolation method using the results obtained from the aforementioned analytical expressions as the reference solutions. The solutions obtained by the form factor interpolation method are compared with the results of calculations by the finite element method and show a good accuracy. Conclusions: the analytical expressions for critical loads presented in this work can be used directly for the stability analysis of orthotropic rectangular plates loaded in one direction as well as to obtain one of the reference solutions by the form factor interpolation method for plates with arbitrary convex contour and combined boundary conditions. The proposed approach can be extended to other forms of plates, boundary conditions and loading types.

DOI: 10.22227/1997-0935.2017.12.1333-1341

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DETERMINATION OF DEFLECTIONS OF BEAMS WITH RHOMBIC PERFORATION OF THE WEB

Vestnik MGSU 7/2018 Volume 13
  • Pritykin Aleksey Igorevich - Kaliningrad State Technical University (KSTU) Doctor of Technical Sciences, Professor, Department of Shipbuilding; ORCID ID 0000-0002-6597-8558, Kaliningrad State Technical University (KSTU), 1 Sovetsky avenue, Kaliningrad, 236040, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Emelianov Konstantin Anatol’evich - «Litana» Leading Design Engineer, «Litana», 10 Vodnaya st., Kaliningrad, 236004, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 814-823

Subject: due to a wide spread in construction practice of castellated beams with the rhomb-shaped perforation of the web, influence of parameters of such openings on beam’s deflections was investigated. Currently, in the Design Codes, both domestic and international, and also in Eurocode 3, the recommendations on determination of deflections of such beams are absent although they contain regulatory requirements. Research objectives: elaboration of analytical relationship, convenient for engineering calculations, for estimation of deflections of castellated beams with rhombic perforation of the web. Materials and methods: derivation of the deflection formula was carried out using one of the efficient methods for calculating deformations of perforated I-beams, based on the use of the theory of compound bars. Several numerical coefficients included in the expression for the stiffness coefficient of the elastic layer, formed by web-posts, were refined by means of finite element calculations. As a criterion for reliability of the analytical expression for deflections, the results of the finite element analysis of the beam, obtained with the ANSYS software complex, are used. Results: results of the study constitute the analytical relation for engineering calculations of deflections of castellated beams with the rhombic perforation of the web. The applicability of the proposed dependence to the calculation of deflections for beams with different shapes of rhombic perforation is verified by varying both the height of the openings and the width of the web-posts. In all cases, only the angle of inclination of the hexagonal sides, taken equal to 60°, remains fixed. An example of analysis of a perforated beam according to the method considered is given. For beams made by wasteless technology, when the width of the web-posts is equal to the horizontal side of the opening, for a rhomb-shaped perforation with a constant relative height of the openings, the total cut-out area remains practically unchanged for any width of the web-posts. A consequence of this is the weak influence of the relative width of the web-posts on deflections of beams with a fixed height of the openings. Conclusions: obtained engineering relationship will certainly be of practical interest to designers and can be recommended for including into the Design Codes of the Russian Federation.

DOI: 10.22227/1997-0935.2018.7.814-823

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Essential FEM statements applied to structural mechanics problems. Part 1

Vestnik MGSU 11/2014
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 37-57

In the article, the author shares his classification of FEM statements that may serve as a guide in respect of the huge number of works that are published and being published with a view to the FEM efficiency improvement. The author provides a summarized history of the finite element method, and classifies its configurations and versions. The author also provides FEM statements applicable to the deflection method. Derivation of the rigidity matrix designated for shaft-based finite elements is demonstrated in the article. The author employs one-dimensional framing as an example aimed to demonstrate the convergence of the FEM method in terms of deflections, if the finite element grid is refined. However it is also noteworthy that in the event of a fine grid, the finite element designed for plates does not coincide with the finite element of a thin plate designed as the initial physical model. However, the system of equations, provided by the author, takes account of the influence produced by the load onto the finite element and generates the exact solution irrespective of any finite values of the length that are equal to the physical model of a finite element.

DOI: 10.22227/1997-0935.2014.11.37-57

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  30. Adini A. Analysis of Shell Structures by the Finite Element Method. Ph. D. Dis. Dept. Civil Eng. Univ. of California, Berkeley, 1961.
  31. Bogner F., Fox R., Schmit L. A Cylindrical Shell Discrete Element. AIAA. 1967, vol. 5, no. 4, pp. 745—750. DOI: http://dx.doi.org/10.2514/3.4056.
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  33. Clough R. Comparison of Three-Dimensional Finite Elements. Symp. Application of FEM in Civil Eng. Nashville, Ten. 1969, pp. 1—26.
  34. Pian T., Tong P. Basis for Finite Element Methods for Solid Continua. Int. J. Num. Meth. Eng. 1969, vol. 1, no. 1, pp. 3—28. DOI: http://dx.doi.org/10.1002/nme.1620010103.
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  36. Prato C. A Mixed Finite Element Method for Thin Shell Analysis. Ph. D. Th. Dept. Civil Eng. MIT, 1968.
  37. Connor J., Will D. A mixed finite element shallow shell formulation. Matrix Meth. Str. Anal. Design. Univ. Alabama, 1971, pp. 105—137.
  38. Poceski A. From Deformation to Mixed and Hybrid Formulation of the Finite Element Method. J. Theor. App. Mechanics, Yug. Society of Mechanics. Belgrade, 1979, no. 5.
  39. Poceski A., Simonee V. Metodot na koneeni elementi i hegovata primena. Gradezen fakultet, Skopje, 1972.
  40. Poceski A. A mixed finite element method for bending of plates. Int. J. Num. Meth. Eng. 1975, vol. 9, no. 1, pp. 3—15. DOI: http://dx.doi.org/10.1002/nme.1620090102.
  41. Poceski A. Meovit metod na koneni elementi (111). 12 Jug. Kon. Teor. Prim. Mehanike, Ohrid, 1974.
  42. Brezzi F., Douglas J., Marini L.D. Two Families of Mixed Finite Elements for Second Order Elliptic Problems. Numer. Math. 1985, vol. 47, pp. 217—235. DOI: http://dx.doi.org/10.1007/BF01389710.
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  44. Maslennikov A.M. Raschet stroitel’nykh konstruktsiy chislennymi metodami [Calculation of Building Structures by Numerical Method]. Leningrad, LGU Publ., 1987, 224 p. (In Russian).
  45. Belkin A.E., Gavryushkin S.S. Raschety plastin metodom konechnykh elementov [Calculation of Plates by Finite Element Method]. Moscow, MGTU named after N.E. Baumana Publ., 2008, 232 p. (In Russian).
  46. Visser V. Uluchshennyy variant diskretnogo elementa smeshannogo tipa plastiny pri izgibe [Improved Variant of the Discreet Element of Mixed Type of a Plate at Bending]. Raketnaya tekhnika i kosmonavtika [Rocket Enineering and Space Technologies]. 1969, no. 9, pp. 172—174. (In Russian).
  47. Ayad R., Dhatt G., Batoz J.L. A New Hybrid-mixed Variational Approach for Reissner-Mindlin plates. The MiSP model. International J. for Numerical Methods in Engineering. 1998, vol. 42, no. 7, pp. 1149—1179. DOI: http://dx.doi.org/10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2
  48. Nedelec J.C. Mixed Finite Elements in R3. Numerische Mathematik, September 1980, 35(3), pp. 315—341.
  49. Poceski A. Mixed Finite Element Method. Springer-Verlag Berlin Heidelberg, 1992, 356 p.
  50. Sekulovich M. Metod konechnykh elementov [Finite Element Method]. Translation from Serbian. Moscow, Stroyizdat Publ., 1993, 664 p.
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  52. Bathe K.-Yu. Metody konechnykh elementov [Finite Elements Methods]. Transl. Into Russian. Moscow, FIZMATLIT Publ., 2010, 1024 p.
  53. Bathe K.J. Finite Element Procedures. Prentice Hall, Englewood Cliffs, 1996, 1036 p.
  54. Bathe K.J., Wilson E.L. Numerical Methods in Finite Element Analysis. Prentice-Hall Inc., New Jersey, 1976.
  55. Vasidzu K. Variatsionnye metody v teorii uprugosti i plastichnosti [Variation Methods in Plasticity Theory]. Moscow, Mir Publ., 1987, 542 p. (In Russian).
  56. Gallager R. Metod konechnykh elementov. Osnovy [Finite Element Method. Basics]. Moscow, Mir Publ., 1984, 428 p. (In Russian).
  57. Zenkevich O.K., Morgan K. Konechnye elementy i approksimatsiya [Finite Elements and Approximation]. Moscow, Mir Publ., 1986, 318 p. (In Russian).
  58. Morrey D.O. O skhodimosti resheniy v metode konechnykh elementov [On Solutions’ Convegence in Finite Element Method]. Raketnaya tekhnika i kosmonavtika [Rocket Enineering and Space Technologies]. 1970, no. 4, pp. 112—114. (In Russian).
  59. Bazeley G.P., Cheung Y.K., Irons B.M., Zienkiewicz O.C. Triangular Elements in Plate Bending — Conforming and Non-conforming Solutions. Proc. Conf. On Matrix Methods in Structural Mechanics. Air Force Inst. of Tech., Wright Patterson A. F. Base, Ohio, 1965, pp. 547—576.
  60. Marchuk G.I., Agoshkov V.I. Vvedenie v proektsionno-setochnye metody [Introduction into Projective Grid Methods]. Moscow, Nauka Publ., 1981, 416 p. (In Russian).
  61. Zenkevich O.K. Metod konechnykh elementov v tekhnike [Finite Element Method in Technology]. Transl. into Russian. Moscow, Mir Publ., 1975, 541 p.
  62. Ignat’ev V.A. Metod konechnykh elementov v zadachakh stroitel’noy mekhaniki [Finite Element Method in Problems of Structural Mechanics]. Saratov, Saratov University Publ., 1980, 87 p. (In Russian).
  63. Chuvikovskiy V.S. Chislennye metody raschetov v stroitel’noy mekhanike korablya [Numerical Calculation Methods in Structural Mechanics of Ships]. Leningrad, Sudostroenie Publ., 1976, 376 p.

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Healthmonitoring of building constructions with crack-like defects

Vestnik MGSU 12/2013
  • Korgin Andrey Valentinovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Supervisor, Scientific and Educational Center of Constructions Investigations and Examinations, Department of Test of Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 183-54-29; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zeyd Kilani Leys Zeydovich - Moscow State University of Civil Engineering (MGSU) Junior Research Worker, Scientific and Research Center of Engineering Investigations and Monitoring of Building Structures, 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 .
  • Ermakov Valentine Alekseevich - Moscow State University of Civil Engineering (MGSU) Junior Research Worker, Scientific and Research Center of Engineering Investigations and Monitoring of Building Structures, 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 77-83

This article deals with structural inspection of the flaws caused by such factors as overloading, differential settlements of construction’s foundation, etc. In order to detect them and define their type and size, modern non destructive equipment such as ultrasonic tomography mira1040 and ultrasonic flaw detector A 1212 MASTER are used. Since cracks increase the stress, they are one of most dangerous defects, so some calculation for analyzing stresses distributions near the crack tip and the whole construction stress redistribution caused by cracking are required. Such calculations are rather complicated, that's why the most suitable methods are computational methods.Practical application of FEM is known as finite element analysis (FEA). FEA is applied in engineering as a computational tool for performing engineering analysis. In this research Finite Element Method is used for defining danger level caused by cracking in a construction, whether it is a through crack or a surface crack. Two types of meshing near the crack tip were considered. The first is refined mesh near the crack tip, it is done using finite elements of smaller size therefore increasing the number of elements and calculation time. The second mesh is done by skewing mid side nodes of the first row of elements to the 1/4 point for crack tip, so the elements number does not increase, the same as calculation time, while accuracy of calculating stresses near the crack tip matches the accuracy in case of refined mesh.As a research result this article describes the methods of detecting and analyzing the structures that have been flawed during the building operation.

DOI: 10.22227/1997-0935.2013.12.77-83

References
  1. Posobie po obsledovaniyu stroitel'nykh konstruktsiy zdaniy [Guidebook on Structural Inspection]. AO «TsNIIPROMZDANIY» Publ., Moscow, 2004.
  2. Andrianov A.A. Vliyanie poverkhnostnykh treshchin na prochnost' betonnykh elementov [Influence of Surface Cracks on the Strength of Concrete Elements]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 3, pp. 140—142.
  3. Hoegh K., Khazanovich L., Yu H.T. Ultrasonic Tomography Technique for Evaluation of Concrete Pavements. Transportation Research Record: Journal of the Transportation Research Board. 2011, no. 2232, pp. 85—94.
  4. Hoegh K., Khazanovich L., Worel B.J., Yu T. Subsurface Joint Deterioration Detection: A MnROAD Blind Test Comparison of Ultrasound Array Technology with Conventional Nondestructive Methods. Transportation Research Board Annual Meeting 2013. Available at: http://docs.trb.org/prp/13-2048.pdf. Date of access 10.10.2013.
  5. Michaux C., Grill M. NDT 3D Tomographic Testing Cases on Concrete and National Heritage Buildings. Available at: http://www.germann.org/Publications/Sevilla/NDT%203D%20Tomography,%20Michaux%20and%20Grill.pdf. Date of access: 10.10.2013.
  6. Korgin A.V., Ermakov V.A. Avtomatizirovannaya aktualizatsiya MKE-modeli sooruzheniya v khode monitoringa [Automated Updating of a FEM-model of a Structure in the Process of Monitoring]. Mekhanizatsiya stroitel'stva [Mechanization of Construction]. 2011, no. 7, pp. 2—4.
  7. Korgin A.V., Zakharchenko M.A., Ermakov V.A. Metodika aktualizatsii raschetnoy skhemy sooruzheniya, podvergaemogo protsedure monitoringa [Methods of Updating the Calculation Model of a Construction under Monitoring]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering]. 2011, no. 3, pp. 28—31.
  8. Basko E.M., Afonin A.S. O kriteriyakh otsenki soprotivleniya khrupkomu razrusheniyu elementov stal'nykh konstruktsiy s uchetom treshchinopodobnykh defektov [On the Evaluation Criteria of Brittle Fracture Resistance of the Elements of Steel Structures with Account for Crack-like Defects]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering]. 2010, ¹ 9, pp. 41—43.
  9. Silant'ev A.S. Raschet prochnosti naklonnykh secheniy izgibaemykh zhelezobetonnykh elementov metodom konechnykh elementov v KE-kompleksakh Ansys i Abaqus [Strength Calculation of Oblique Sections of Bending Reinforced Concrete Elements by the FEM in Ansys i Abaqus ]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering]. 2012, no. 2, pp. 71—74.
  10. Robert Ravi S., Prince Arulraj G. Finite Element Modeling on Behavior of Reinforced Concrete Beam Column Joints Retrofitted with Carbon Fiber Reinforced Polymer Sheets. International Journal of Civil and Structural Engineering. 2010, vol. 1, no. 3, pp. 576—582. Available at: http://www.ipublishing.co.in/ijcserarticles/ten/articles/volone/EIJCSE2027.pdf. Date of Access: 10.10.2013.

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STRESS DISTRIBUTION AND CONCENTRATION IN CASTELLATED BEAMS WITH SINUSOIDAL WALL PERFORATION

Vestnik MGSU 8/2017 Volume 12
  • Pritykin Aleksej Igorevich - Kaliningrad State Technical University, 1 Sovetskij prospekt, Kaliningrad Doctor of Technical Sciences, Professor, Kaliningrad State Technical University, 1 Sovetskij prospekt, Kaliningrad, 236040, Russian Federation.
  • Misnik Aleksandr Vladislavovich - Immanuel Kant Baltic Federal University, 14 A. Nevskogo str., Kaliningrad postgraduate student, Department of Urban Development, Land Management and Design, Immanuel Kant Baltic Federal University, 14 A. Nevskogo str., Kaliningrad, 14 A. Nevskogo str., Kaliningrad, 236022, Russian Federation.

Pages 876-884

N wide spread beams with hexagonal openings, the stress concentration level is rather high. Aiming to reduce the stress level by means of rounding corner openings brings to introduction of beams with sinusoidal perforation (BSP). However, the studies of stress level in such beams depending on perforation parameters are not known. Development of empirical relation for estimation of stress level in castellated beams with sinusoidal perforation was fulfilled on the base of analysis of the results of BSP calculation by the finite element method. Results of study have allowed to establish the empirical relation for estimation of distribution regularities of equivalent stresses on Mises in castellated beams with sinusoidal perforation useful for engineering calculations. The established relation differentiates the role of every force factor: transverse force V and constant bending moment M. Calculation of hinged beams are performed under action of one pointed load applied in the mid-span and also under simple bending. The developed relation allows to determine the level of stress build-up in perforated double-tee beams with sinusoidal openings under constant transverse force V and constant bending moment M. Application of established relation to calculation of stresses in beams with the same perforation pattern was verified when varying the height of openings. The value of rounding corner radius remained unchanged. FEM calculations have shown that under constant transverse force and lineally changing bending moment, the maximum values of equivalent stresses on Mises near the contour of openings along the beam length are also changing lineally. The obtained empirical relation, in spite of its simplicity, allows to estimate the level and stress buildup in the openings zone under constant transverse force and simple bending depending on parameters of beam perforation.

DOI: 10.22227/1997-0935.2017.8.876-884

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