Calculation method for plates with discrete variable thickness under uniform loading or hydrostatic pressure

• Autorzy: Aryassov G. , Gornostajev D. , Penkov I.

Identyfikatory

DOI

10.2478/ijame-2018-0046

• Języki publikacji: EN

Abstrakty

EN

The article proposes a new analytical method for the calculation of plates with constant and variable rigidity parameters. This method renders it possible to decrease the weight of the plates working under hydrostatic pressure by using variable thicknesses. Firs, a short overview of existing calculation methods and their results are compared. It is shown that all existing methods depend on boundary conditions. Then is given the theory of the proposed calculation method is described and calculations for plates with constant and variable thickness worked under uniformly loaded forces and hydrostatic pressure are made. The results are compared to the FEM calculations and experimental results obtained by a tensile test machine and special equipment. Calculation results obtained by the proposed analytical method and FEM results are very close. Deviations are not more than 11%. Deviations between theoretical calculations and experimental results depend on loading type and design of the test specimens but maximum values are not more than 17%. The proposed calculation method does not depend on the boundary conditions and can be used for plate calculations. Especially for plates with difficult design and complex loading.

Słowa kluczowe

EN

plate calculation; deflection; hydrostatic pressure; boundary conditions

PL

ciśnienie hydrostatyczne; warunki brzegowe; ugięcie

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2018
• Tom: Vol. 23, no. 4
• Strony: 835--853
• Opis fizyczny: Bibliogr. 41 poz., rys., tab., wykr.

Twórcy

autor

Aryassov G.

• Department of Mechanical and Industrial Engineering, School of Engineering Tallinn University of Technology Ehitajate tee 5, 19086 Tallinn, ESTONIA

autor

Gornostajev D.

• Department of Mechanical and Industrial Engineering, School of Engineering Tallinn University of Technology Ehitajate tee 5, 19086 Tallinn, ESTONIA

autor

Penkov I.

• Department of Mechanical and Industrial Engineering, School of Engineering Tallinn University of Technology Ehitajate tee 5, 19086 Tallinn, ESTONIA

Bibliografia

• [1] Kanwal R.P. (1971): Linear Integral Equations Theory and Technique. – San Diego: Academic Press.
• [2] Cheney W. and Kincaid D. (2008): Numerical Mathematics and Computing. – 6th Ed. Brooks/Cole, Independence.
• [3] Agarwal R.P. and O’Regan D. (2009): Ordinary and partial differential equations with special functions, Fourier series and boundary value problems. – Ch. Lecture 14, Boundary Value Problems, Springer, New-York, pp.104–108.
• [4] Boyce W.E. and Di Prima R.C. (2009): Elementary Differential Equations and Boundary Value Problems. – 9th Ed. Wiley, Hoboken.
• [5] Reut Z. (2005): Solution of ordinary differential equations by successive integration by parts. – International Journal of Mathematical Education in Science and Technology, vol.26, No.10, pp.589-597.
• [6] Koroljev V., Slepov V. and Sokolov E. (1980): Method of successive integration of differential equations of plates and shells. – Proceedings of Saint-Petersburg University of Architecture and Civil Engineering, Structural Mechanics, Saint-Petersburg, pp.45-51.
• [7] Aryassov G. and Petritshenko A. (2009): Study of free vibration of ladder frames reinforced with plate. – Solid State Phenomena, Mechatronic Systems and Materials III, vols 147-149, pp.368-373.
• [8] Zienkiewicz O. and Taylor R. (2005): Finite Element Method for Solid and Structural Mechanics. – 6th Ed. Butterworth-Heinemann.
• [9] Vainberg D. and Vainberg E. (1970): Calculation of Plates. – Kiev: Budivelnic.
• [10] Sapountzakis E. and Katsikadelis J. (2008): Elastic deformation of ribbed plates under static, transverseand inplane loading. – J. of Computers and Structures, vol.74, pp.571-581.
• [11] Liew K. and Wang C. (2003): Rayleigh–Ritz method for general plate analysis. – Engineering Structures, vol.15, No.1, pp.55-60.
• [12] Guryanov N. (1968): The effect of local loads on the Shallow spherical shell. – Investigations on the Theory of Plates and Shells, vol.6, pp.186-193.
• [13] Shigalo J. (1975): Static of shells subjected to local loads. – Investigations on the Theory of Plates and Shells, vol.6, 62-91.
• [14] Shigalo J. and Guryanov N. (1966): The effect of local loads on simply supported cylindrical shell. – Investigations on the Theory of Plates and Shells, vol.6, pp.42-55.
• [15] Eek R. and Poverus L. (1967): Structural Mechanics. – Vol.2, Tallinn.
• [16] Timoshenko S. (1990): Theory of Plates and Shells. – New-York: McCraw-Hill Bool Company, Inc.
• [17] Mihailov B. (1980): Plates and shells with discontinuous parameters. – Saint-Petersburg.
• [18] Sharkov O. and Zolotov I. (2011): Influence of the geometric properties of an external housing on its stress-strain state. – Russian Engineering Research, vol.31, No.4, pp.335-337, doi:10.3103/S1068798X11040228.
• [19] Alfutov N., Zinovev P. and Popov B. (1984): Analysis of Multilayer Plates and Shells of Composite Materials. – Moscow: Mashinostroenie.
• [20] Gornostajev D., Aryassov G. and Penkov I. (2016): Calculation method for optimization of barge hull. – International Review of Mechanical Engineering, vol.10, No.2, pp.115-124.
• [21] Gornostajev D. (2014): Development of the Calculation Method of Barge Hull. – PhD Thesis, Tallinn University of Technology Press.
• [22] Alexandrov A., Lamper R. and Suvernev V. (1985): Calculation of Structural Elements of Aircraft. Sandwich Plates and Shells. – Moscow: Mashinostroenie.
• [23] Johnson R. (2010): Composite Structures of Steel and Concrete. – Vol.1: Beams, Slabs, Columns and Frames for Buildings, Blackwell Scientific Publishers, Oxford.
• [24] Kristek V. and Skaloud M. (2001): Advanced Analysis and Design of Plated Structures. – Elsevier, Amsterdam and New York, and Academia (Publishing House of the Czechoslovak Academy of Sciences), Prague.
• [25] Sharkov O., Koryagin S. and Velikanov N. (2016): Design Models for Shaping of Tooth Profile of External Fine-Module Ratchet Teeth. – IOP Conference Series: Materials Science and Engineering, Vol.124, 012165, doi:10.1088/1757-899X/124/1/012165.
• [26] Leissa A. (2004): Buckling of Laminated Composite Plates and Shell Panels. – New York: American Society of Mechanical Engineers.
• [27] Lewinski T. and Telega J. (2007): Plates, Laminates and Shells. Asymptotic Analysis and Homogenization. – Singapore: World Scientific Publishing.
• [28] Reddy J. (2006): Analysis of Laminated Composite Plates and Shells. – New York, Chichester: John Wiley and Sons (A Wiley-Interscience Publication).
• [29] Gilbert R. and Hackl K. (1995): Asymptotic Theories for Plates and Shells. – New York: John Wiley and Sons.
• [30] Ivanyi M. and Skaloud M. (1995): Steel Plated Structures. – Wien: Springer-Verlag.
• [31] Jawad M. (2004): Theory and Design of Plate and Shell Structures. – New York: Chapman and Hall.
• [32] Sokolov E. (2004): Integration of Differential Equations in Shell Theory by the Method of Particular Solutions. Mathematical Modelling. Numerical Methods and Complex Programs. – St.-Peterburg: Proc. St.-Peterburg Civil University.
• [33] Noor A., Burton W. and Bert C. (1996): Computational models for sandwich panels and shells. – Appl. Mech. Rev., vol.49, No.3.
• [34] Mac Neal R. (1994): Finite elements: Their Design and Performance. – New York: Marcel Decker.
• [35] Gould P. (1999): Analysis of Plates and Shells. Prentice Hall. – New Jersey: Upper Saddle River.
• [36] Rvatsjov V., Kurpa L., Sklepus N. and Ucisvilli L. (1973): R-function method in tasks of deflection and vibrations in plates with complex shapes. – Kiev.
• [37] Hutchinson J. (1991): Analysis of plates and shells by boundary collocations. – In: Boundary Element Analysis of Plates and Shells, Springer-Verlag, Berlin, pp.341–368.
• [38] Vasiljev V. (1998): Classical theory of plates: historical perspective and state-of-the-art. – Mechanics of Solids, vol.33, No.3, pp.35-45.
• [39] Rvatsjov V. and Kurpa L. (1987): R-Functions in Plate Theory. Kiev.
• [40] Ventsel E. (2007): An indirect boundary element method for plate bending analysis. – Int. J. Numer. Meth. Eng., vol.9, pp.1597-1611.
• [41] Aryassov G. and Zhigailov S. (2013): Optimal design of system of cross-beams. – Solid State Phenomena, Mechatronic Systems and Materials IY, vol.198, pp.675-680.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)