Full Text:   <1416>

CLC number: TU2; TU3

On-line Access: 2008-04-15

Received: 2007-05-17

Revision Accepted: 2007-12-25

Crosschecked: 0000-00-00

Cited: 20

Clicked: 4004

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.5 P.600~613


Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings

Author(s):  Erasmo CARRERA, Gaetano GIUNTA

Affiliation(s):  Aeronautic and Space Engineering Department, Politecnico di Torino, Torino, Italy

Corresponding email(s):   erasmo.carrera@polito.it, gaetano.giunta@polito.it

Key Words:  Failure load, von Mises&rsquo, equivalent stress, Isotropic plates, Higher order theories (HOTs), Exact 3D solution

Erasmo CARRERA, Gaetano GIUNTA. Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings[J]. Journal of Zhejiang University Science A, 2008, 9(5): 600~613.

@article{title="Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings",
author="Erasmo CARRERA, Gaetano GIUNTA",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings
%A Gaetano GIUNTA
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 5
%P 600~613
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A072110

T1 - Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings
A1 - Erasmo CARRERA
A1 - Gaetano GIUNTA
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 5
SP - 600
EP - 613
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A072110

The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations. von Mises&rsquo; equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 (thin plates) and as low as 2 (very thick plates). Results are obtained via several 2D plate models. Classical theories (CTs) and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories (HOTs), HOTsd models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed: by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Carrera, E., 2002. Theories and finite elements for multilayered plates and shells. Archives of Computational Methods in Engineering, 9(2):87-140.

[2] Carrera, E., 2003. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Archives of Computational Methods in Engineering, 10(3):215-296.

[3] Carrera, E., Giunta, G., 2007. Hierarchical closed form solutions for plates bent by localized transverse loadings. Journal of Zhejiang University SCIENCE A, 8(7):1026-1037.

[4] Cauchy, A.L., 1828. Sur l’euilibre et le mouvement d’une plaque solide. Exercises de Matematique, 3:328-355.

[5] Demasi, L., 2007. 3D closed form solution and exact thin plate theories for isotropic plates. Composites Structures, 80(2):183-195.

[6] Kam, T.Y., Jan, T.B., 1995. First-ply failure analysis of laminated composite plates based on the layerwise linear displacement theory. Composites Structures, 32(1-4):583-591.

[7] Kirchhoff, G., 1850. Über das Gleichgewicht und die Bewegung einer elastishen Sceibe. J. Reine Angew. Math., 40:51-88.

[8] Librescu, L., 1975. Elasto-statics and Kinematics of Anisotropic and Heterogeneous Shell-type Structures. Nordhoff Int., Leiden, The Netherlands.

[9] Love, A.E.H., 1959. A Treatise on Mathematical Theory of Elasticity. Cambridge University Press, UK.

[10] Mindlin, E., 1951. Influence of the rotatory inertia and shear in flexural motions of isotropic elastic plates. J. Appl. Mech., 18:1031-1036.

[11] Pandey, A.K., Reddy, J.N., 1987. A Post First-ply Failure Analysis of Composites Laminates. Structures, Structural Dynamics and Materials Conference, Monterey, CA, USA, p.788-797.

[12] Poisson, S.D., 1829. Memoire sur l’euilibre et le mouvement des corps elastique. Mem. Acad. Sci., 8:357.

[13] Reddy, J.N., 1984. A simple higher-order theory for laminated composite plates. J. Appl. Mech., 51:745-752.

[14] Reddy, J.N., 1997. Mechanics of Laminated Composites Plates. Theory and Analysis. CRC Press, Boca Raton, Florida.

[15] Reddy, J.N., Pandey, A.K., 1987. A first-ply failure analysis of composites laminates. Computers and Structures, 25(3):371-393.

[16] Reddy, Y.S.N., Reddy, J.N., 1987. Linear and Non Linear Failure Analysis of Composites Laminates with Transverse Shear. American Institute of Aeronautics and Astronautics, Inc.

[17] Reissner, E., 1945. The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech., 12:69-76.

[18] Turvey, G.J., 1980a. An initial flexural failure analysis of symmetrically laminated cross-ply rectangular plates. International Journal of Solids and Structures, 16(5):451-463.

[19] Turvey, G.J., 1980b. Flexural failure analysis of angle-ply laminates of GFRP and CFRP. The Journal of Strain Analysis for Engineering Design, 15:43-49.

[20] Turvey, G.J., 1980c. A study on the onset of flexural failure in cross-ply laminated strips. Fibre Science and Technology, 13(5):325-336.

[21] Turvey, G.J., 1981. Initial flexural failure of square, simply supported, angle-ply plates. Fibre Science and Technology, 15(1):47-63.

[22] Turvey, G.J., 1982. Uniformly loaded, antisymmetric cross-ply laminated, rectangular plates: an initial flexural failure analysis. Fibre Science and Technology, 16(1):1-10.

[23] Turvey, G.J., 1987. Effect of Shear Deformation on the Onset of Flexural Failure in Symmetric Cross-ply Laminated Rectangular Plates. In: Marshall, I.H. (Ed.), Composites Structures. Elsevier Applied Science, London, p.141-146.

[24] Washizu, K., 1968. Variational Methods in Elasticity and Plasticity. Pergamon Press, NY.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE