Analytical solutions for flexure of rectangular orthotropic plates with opposite rotationally restrained and free edges

• Autorzy: Zhang S. , Xu L.

Identyfikatory

DOI

10.1016/j.acme.2018.02.005

• Języki publikacji: EN

Abstrakty

EN

The problem of flexural characteristics of rectangular orthotropic thin plates with opposite rotationally restrained and free edges subjected to arbitrary transverse loads is investigated in present study. By introducing a rotational fixity factor to simulate the elastic rotation restraint at plate edges, the finite integral transform method is employed to obtain exact analytical solution of the problem. Numerical solutions for rectangular plates with various aspect ratios and edge flexibility are investigated and compared to the results reported in previous research. The accuracy and convergence of the present formulation are assessed by comparing with previously reported results. The excellent agreement on the results between the proposed method and previous studies indicates that the proposed method is accurate and effective.

Słowa kluczowe

EN

rectangular orthotropic plate; flexural characteristics; finite integral transform; rotationally restrained edge; free edges

PL

płyta ortotropowa; zginanie; system podłogowy

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 18, no. 3
• Strony: 965--972
• Opis fizyczny: Bibliogr. 25 poz., rys., tab., wykr.

Twórcy

autor

Zhang S.

• Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1 Canada

autor

Xu L.

• Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1 Canada

Bibliografia

• [1] D.E. Allen, D.M. Onysko, T.M. Murray, Minimizing Floor Vibration, ATC Design Guide 1, Applied Technology Council, Redwood City, CA, 1999.
• [2] Y.H. Chui, Application of ribbed-plate theory to predict vibrational serviceability of timber floor systems, in: The Proceedings of 7th World Conference on Timber Engineering WCTE, vol. 4, 2002, 87–93.
• [3] J. Weckendorf, T. Toratti, I. Smith, T. Tannert, Vibration serviceability performance of timber floors, Eur. J. Wood Wood Prod. (2015) 1–15.
• [4] L. Xu, F. Tangorra, Experimental investigation of lightweight residential floors supported by cold-formed steel c-shape joists, J. Constr. Steel Res. 63 (3) (2007) 422–435.
• [5] A. Leissa, F. Niedenfuhr, Bending of a square plate with two adjacent edges free and the others clamped or simply supported, AIAA J. 1 (1) (1963) 116–120.
• [6] S.G. Lekhnitskii, Anisotropic Plates, Gordon and Breach, Science Publishers, Inc., 1968 Translated by S. W. Tsai and T. Cheron.
• [7] S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed., McGraw-Hill, Inc., New York, 1959.
• [8] K. Bhaskar, A. Sivaram, Untruncated infinite series superposition method for accurate flexural analysis of isotropic/orthotropic rectangular plates with arbitrary edge conditions, Compos. Struct. 83 (1) (2008) 83–92.
• [9] L.S.D. Morley, Bending of rectangular orthotropic plates under concentrated load with two opposite edges simply supported, Schweizerische Bauzeitung 84 (48) (1966) 843–848.
• [10] D.R. Thornton, H.D. Conway, The structural analysis of edge- loaded plates, Int. J. Mech. Sci. 22 (8) (1980) 481–490.
• [11] K. Bhaskar, B. Kaushik, Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges, Compos. Struct. 63 (1) (2004) 63–68.
• [12] C.W. Lim, S. Cui, W. Yao, On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported, Int. J. Solids Struct. 44 (16) (2007) 5396–5411.
• [13] R. Li, Y. Zhong, On a new symplectic geometry method for exact bending solutions of orthotropic rectangular plates with two opposite sides clamped, Acta Mech. 216 (1–4) (2011) 333–343.
• [14] X. Liu, J. Banerjee, Free vibration analysis for plates with arbitrary boundary conditions using a novel spectral-dynamic stiffness method, Comput. Struct. 164 (2016) 108–126.
• [15] R. Li, Y. Zhong, B. Tian, Y. Liu, On the finite integral transform method for exact bending solutions of fully clamped orthotropic rectangular thin plates, Appl. Math. Lett. 22 (12) (2009) 1821–1827.
• [16] R. Li, B. Tian, Y. Zhong, Analytical bending solutions of free orthotropic rectangular thin plates under arbitrary loading, Meccanica 48 (10) (2013) 2497–2510.
• [17] B. Tian, Y. Zhong, R. Li, Analytic bending solutions of rectangular cantilever thin plates, Arch. Civil Mech. Eng. 11 (4) (2011) 1043–1052.
• [18] C. An, J. Gu, J. Su, Exact solution of bending problem of clamped orthotropic rectangular thin plates, J. Braz. Soc. Mech. Sci. Eng. 38 (2) (2016) 601–607.
• [19] S. Zhang, L. Xu, Bending of rectangular orthotropic thin plates with rotationally restrained edges: a finite integral transform solution, Appl. Math. Modell. 46 (2017) 48–62.
• [20] I. Sneddon, The Use of Integral Transforms, McGraw-Hill, Inc, 1972.
• [21] M.R. Khalili, K. Malekzadeh, R. Mittal, A new approach to static and dynamic analysis of composite plates with different boundary conditions, Compos. Struct. 69 (2) (2005) 149–155.
• [22] J.R. Hutchinson, On the bending of rectangular plates with two opposite edges simply supported, J. Appl. Mech. 59 (3) (1992) 679–681.
• [23] A. Ramsay, E. Maunder, An error in Timoshenko's 'theory of plates and shells', NAFEMS Benchmark Mag. (2016).
• [24] J.N. Reddy, Theory and Analysis of Elastic Plates and Shells, 2nd ed., CRC press, 2006.
• [25] O.A. Bauchau, J.I. Craig, Structural Analysis: With Applications to Aerospace Structures, Vol. 163, Springer Science & Business Media, 2009.

Uwagi

PL

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