Bending Analysis of Simply Supported Shear Deformable Skew Plates
Publication: Journal of Engineering Mechanics
Volume 123, Issue 3
Abstract
This paper presents the bending analysis of a simply supported, thick skew plate based on the first-order shear deformation Reissner/Mindlin theory. Using the geometric transformation, the governing differential equations and boundary conditions of the plate are first transformed from the physical domain into a unit square computational domain. A set of linear algebraic equations is then derived from the transformed differential equations via a numerical technique, the differential quadrature method (DQM), and the approximate solutions of the problem are obtained by solving the set of algebraic equations. The applicability, accuracy, and convergent properties of DQM for the bending analysis of simply supported skew plates are carefully examined for various skew angles and various relative plate thickness. In this paper, the central deflections and moments of the plate are presented for different thickness-to-span ratios, and skew angles for future references.
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References
1.
Argyris, J. H. (1965). “Continua and discontinua.”Proc., Conf. on Matrix Methods in Struct. Mech., Wright-Patterson Air Force Base, Ohio, 112–119.
2.
Bellman, R. E. (1973). Methods of nonlinear analysis, Vol. 2, Academic Press, New York, N.Y.
3.
Butalia, T. S., Kant, T., and Dixit, V. D.(1990). “Performance of heterosis element for bending of skew rhombic plates.”Comp. and Struct., 34, 23–49.
4.
Du, H., Lim, M. K., and Lin, R. M.(1994). “Application of generalized differential quadrature method to structural problems.”Int. J. Numer. Methods in Engrg., 37, 1881–1896.
5.
Ganga Rao, H. V. S., and Chaudhary, V. K.(1988). “Analysis of skew and triangular plates in bending.”Comp. and Struct., 28, 223–235.
6.
Hinton, E., and Huang, H. C.(1986). “A family of quadrilateral Mindlin plate elements with substitute shear strain fields.”Comp. and Struct., 23, 409–431.
7.
Kobayashi, H., and Sonoda, K. (1984). “Rectangular thick plates on linear viscoelastic foundations.”Proc., Japanese Soc. Civ. Engrs., JSCE, Tokyo, Japan, No. 341, 33–39.
8.
Kobayashi, H., Ishikawa, K., and Turvey, G. J. (1995). “On bending of rhombic plates.”J. Struct. Engrg., Tokyo, Japan, 41A, 41–48 (in Japanese).
9.
Li, W. Y., Cheung, Y. K., and Tham, L. G.(1986). “Spline finite strip analysis of general plates.”J. Engrg. Mech., ASCE, 112, 43–54.
10.
Liew, K. M., Han, J.-B., Xiao, Z. M., and Du, H.(1996a). “Differential quadrature method for Mindlin plates on Winkler foundations.”Int. J. Mech. Sci., 38, 405–421.
11.
Liew, K. M., Han, J.-B., and Xiao, Z. M.(1996b). “Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility.”Int. J. Solids Struct., 33, 2647–2658.
12.
Mindlin, R. D.(1951). “Influence of rotatory inertia and shear on flexural motion of isotropic, elastic plates.”J. Appl. Mech., 18, 31–38.
13.
Moeley, L. S. D. (1963). Skew plates and structures, international series of monographs on aeronautics and astronautics. Pergamon Press, New York, N.Y.
14.
Quan, J. R., and Chang, C. T.(1989). “New insights in solving distributed system equations by the quadrature method—I. Analysis.”Comp. Chemical Engrg., 13, 779–788.
15.
Reissner, E.(1945). “The effect of transverse shear deformation on the bending of elastic plates.”J. Appl. Mech., 12, 69–77.
16.
Sengupta, D.(1995). “Performance study of a simple finite element in the analysis of skew rhombic plates.”Comp. and Struct., 54, 1173–1182.
17.
Shu, C., and Richards, B. E.(1992). “Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations.”Int. J. Numer. Methods in Fluids, 15, 791–798.
18.
Tham, L. G., Li, W. Y., and Cheung, Y. K.(1986). “Bending of skew plates by spline-finite-strip method.”Comp. and Struct., 22, 31–38.
19.
Wang, G., and Hsu, C.-T. T.(1994). “Static and dynamic analysis of arbitrary quadrilateral flexural plates by B3-spline functions.”Int. J. Solids Struct., 31, 657–667.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 123 • Issue 3 • March 1997
Pages: 214 - 221
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Mar 1, 1997
Published in print: Mar 1997
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