114
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

An alternative numerical solution of 900/00/900 cross-ply laminated composite plate using displacement potential approach

Pages 674-684 | Received 04 Aug 2015, Accepted 17 Jan 2016, Published online: 08 Nov 2016

References

  • S.G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco, CA, 1963.
  • S.G. Lekhnitskii, Anisotropic Plate, Gordon and Breach, New York, 1968.
  • A.N. Stroh, Dislocations and cracks in anisotropic elasticity, Philos. Mag., vol. 3, pp. 625–646, 1958.
  • A.N. Stroh, Steady-state problems in anisotropic elasticity, J. Math. Phys., vol. 41, pp. 77–103, 1962.
  • T.C.T. Ting, Anisotropic Elasticity, Oxford University Press, New York, 1996.
  • R.D. Mindlin, Influence of rotatory inertial and shear in flexural motion of isotropic elastic plates, J. Appl. Mech., vol. 18, pp. 1031–1036, 1951.
  • E. Reissner, On a variational theorem in elasticity, J. Math. Phys., vol. 29, pp. 90–95, 1950.
  • J.N. Reddy, A simple higher-order theory for laminated composite plates, J. Appl. Mech., vol. 51, pp. 745–752, 1984.
  • J.N. Reddy, A generalization of two-dimensional theories of laminated plates, Commun. Appl. Numer. Methods, vol. 3, pp. 173–180, 1987.
  • M. Cho and R.R. Parmerter, Efficient higher order plate theory for laminated composites, Compos. Struct., vol. 20, pp. 113–123, 1992.
  • M. Cho and R.R. Parmerter, Efficient higher order composite plate theory for general lamination configurations, AIAA J., vol. 31, pp. 1299–1306, 1993.
  • M.T. Kamali and S. Pourmghaddam, Three-dimensional analysis of multi-layer composite plates of arbitrary shape and boundary conditions with shear slip interfaces, Mech. Adv. Mater. Struct., vol. 23, pp. 481–493, 2016.
  • C.-P. Wu, K.-H. Chiu, and Y.-M. Wang, RMVT-base mesh less collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates, Compos. Struct., vol. 93, pp. 923–943, 2011.
  • S. Timoshenko and V.N. Goodier, Theory of Elasticity, 3rd Edition, McGraw-Hill, New York, 1979.
  • M.W. Uddin, Finite difference solution of two-dimensional elastic problems with mixed boundary conditions. M.Sc. Thesis, Carleton University, Canada, 1966.
  • H.D. Conway and N.Y. Ithaca, Some problems of orthotropic plane stress, J. Appl. Mech., vol. 52-A-4, pp. 72–76, 1953.
  • G.M. Kulikov and S.V. Plotnikova, Exact 3D stress analysis of laminated composite plates by sampling surface method, Compos. Struct., vol. 94, pp. 3654–3663, 2012.
  • M. Tahani and A. Andakhshideh, Interlaminar stresses in thick rectangular laminated plates with arbitrary laminations and boundary conditions under transverse loads, Compos. Struct., vol. 94, pp. 1793–1804, 2012.
  • C. Zhang and S.V. Hoa, A limit-based approach to the stress analysis of cylindrically orthotropic composite cylinders (00/900/00) subjected to pure bending, Compos. Struct., vol. 94, pp. 2610–2618, 2012.
  • J. Singh and K.K. Shukla, Nonlinear flexural analysis of laminated composite plates using RBF based meshless method, Compos. Struct., vol. 94, pp. 1714–1720, 2012.
  • M. Shahbazi, B. Borroomand, and S. Soghrati, A mesh free method using exponential basis functions for laminates modeled by CLPT, FSDT and TSDT—Part I: Formulation, Compos. Struct., vol. 93, pp. 3112–3119, 2011.
  • J.D. Rodrigues, C.M.C. Roque, A.J.M. Ferreira, E. Carrera, and M. Cinefra, Radial basis functions-finite differences collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami's zig-zag theory, Compos. Struct., vol. 93, pp. 1613–1620, 2011.
  • R. Stürzenbecher and K. Hofstetter, Bending of cross-ply laminated composites: An accurate and efficient plate theory based upon models of Lekhnitskii and Ren, Compos. Struct., vol. 93, pp. 1078–1088, 2011.
  • J.O. Dow, M.S. Jones, and S.A. Harwood, A new approach to boundary modeling for finite-difference applications in solid mechanics, Int. J. Numer. Methods Eng., vol. 30, pp. 99–113, 1990.
  • T.H. Richards and M.J. Daniels, Enhancing finite element surface stress prediction: A semi analytic technique for axisymmetric solids, J. Strain Anal., vol. 22, pp. 75–86, 1987.
  • J. Smart, On the determination of boundary stresses in finite elements, J. Strain Anal., vol. 22, pp. 87–96, 1987.
  • M.Z. Hossain, S.R. Ahmed, and M.W. Uddin, An efficient algorithm for finite-difference modeling of mixed-boundary-value elastic problems, Adv. Eng. Software, vol. 37, pp. 41–55, 2006.
  • A.M. Afsar, S.K. Deb Nath, S. Reaz Ahmed, and J.L. Song, Displacement potential based finite difference solution to elastic field in a cantilever beam of orthotropic composite, Mech. Adv. Mater. Struct., vol. 15, pp. 386–399, 2008.
  • S.K. Deb Nath and A.M. Afsar, Analysis of the effect of fiber orientation on the elastic field in a stiffened orthotropic panel under uniform tension using displacement potential approach, Mech. Adv. Mater. Struct., vol. 16, pp. 300–307, 2009.
  • S.K. Deb Nath, Development of single function potential approach of orthotropic composite materials for the case of the plane strain condition, Mech. Adv. Mater. Struct., vol. 23, pp. 1326--1334, 2016.
  • S.R. Ahmed, S.K. Deb Nath, and M.W. Uddin, Optimum shapes of tire-treads for avoiding lateral slippage between tires and roads, Int. J. Numer. Methods Eng., vol. 64, pp. 729–750, 2005.
  • S.K. Deb Nath, S.R. Ahmed, and A.M. Afsar, Displacement potential solution of short stiffened flat composite bars under axial loadings, Int. J. Appl. Mech. Eng., vol. 11, pp. 557–575, 2006.
  • S.K. Deb Nath, A.M. Afsar, and S.R. Ahmed, Displacement potential approach to solution of stiffened orthotropic composite panels under uniaxial tensile load, J. Aerosp. Eng., vol. 221, pp. 869–881, 2007.
  • S.K. Deb Nath, A.M. Afsar, and S.R. Ahmed, Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material, J. Strain Anal., vol. 42, pp. 529–541, 2007.
  • S.K. Deb Nath and S.R. Ahmed, Investigation of elastic field of a short orthotropic composite column by using finite-difference technique, J. Aerosp. Eng., vol. 222, pp. 1161–1169, 2008.
  • S.R. Ahmed and S.K. Deb Nath, A simplified analysis of the tire-tread contact problem using displacement potential based finite-difference technique, Comput. Model. Eng. Sci., vol. 44, pp. 35–63, 2009.
  • A.M. Afsar, N.M.L. Huq, and J.L. Song, Analytical solution to a mixed boundary value elastic problem of a roller-guided panel of laminated composite, Arch. Appl. Mech., vol. 80, pp. 401–412, 2010.
  • R.M. Jones, Mechanics of Composite Materials, McGraw-Hill Book Company, New York, 1975.
  • P.K. Mallick, Fiber-Reinforced Composites, Materials, Manufacturing, and Design, 2nd Edition (revised and expanded), Marcel Dekker, New York, 1993.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.