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Research Papers: Design and Analysis

Exact, Hierarchical Solutions for Localized Loadings in Isotropic, Laminated, and Sandwich Shells

[+] Author and Article Information
E. Carrera

Department of Aeronautic and Space Engineering, Aerospace Structures and Aeroelasticity, Politecnico di Torino, Turin 10129, Italy

G. Giunta1

Department of Aeronautic and Space Engineering, Politecnico di Torino, Turin 10129, Italy; Department of Advanced Materials and Structures, Centre de Recherche Public Henri Tudor, 29, avenue John F. Kennedy, L-1855 Luxembourg-Kirchberg, Luxembourggaetano.giunta@polito.it

1

Corresponding author.

J. Pressure Vessel Technol 131(4), 041202 (Jun 10, 2009) (14 pages) doi:10.1115/1.3141432 History: Received May 13, 2008; Revised October 02, 2008; Published June 10, 2009

This paper presents closed form solutions for simply supported cylindrical and spherical shells subjected to uniform localized distributions of transverse pressure and bending moment. These distributions have been expanded in terms of Fourier’s series for which Navier type “exact” solutions have been found for the governing differential equations of the employed shell theories. Shells made of isotropic materials, composites laminates, and sandwich have been analyzed. Carrera’s unified formulation has been adopted in order to implement a large variety of two-dimensional theories. Classical, refined, zigzag, layerwise, and mixed theories are compared in order to evaluate the stress and deformation variables. Conclusions are drawn with respect to the accuracy of the various theories for the considered loadings and layouts. The importance of the refined shell models in order to describe accurately the three-dimensional stress state in the neighborhood of the localized loading application area is outlined.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry and reference system of (a) a curved panel and (b) a cylindrical shell

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Figure 2

Isotropic cylindrical shell under the opposite local forces

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Figure 3

u¯z,C versus z/h for (a) Rβ/h=20 and (b) 10 in the case of the isotropic cylindrical shell under the opposite forces

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Figure 4

Orthotropic cylindrical shell under the pinching opposite loads

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Figure 5

u¯z versus (a) α/a and (b) 2β/b at 2z/h=1 for the orthotropic cylindrical shell under the pinching loadings; Rβ/h=10

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Figure 6

(a) 10σ¯αz and (b) 10σ¯βz along z for the orthotropic cylindrical shell under the pinching loadings; Rβ/h=100

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Figure 7

(a) 10σ¯αz and (b) 10σ¯βz along z for the orthotropic cylindrical shell under the pinching loadings; Rβ/h=10

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Figure 8

Orthotropic cylindrical shell under local the bending moment

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Figure 9

u¯z versus α/a at 2z/h=1 for (a) Rβ/h=20 and (b) 10 in the case of the orthotropic cylindrical shell under the local bending moment

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Figure 10

Transverse shear stress σ¯βz along the thickness for (a) Rβ/h=100 and (b) 20 in the case of the orthotropic cylindrical shell under the local bending moment

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Figure 11

Transverse shear stress σ¯αz across the thickness for (a) Rβ/h=100 and (b) 20 in the case of the orthotropic cylindrical shell under the local bending moment

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Figure 12

Convergence analysis of (a) u¯z and (b) σ¯αz computed at the top of the center point via LM4∗

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Figure 13

Dimensionless stress σ¯αα versus z/h for (a) Rβ/h=10 and (b) 5 in the case of the sandwich spherical panel

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Figure 14

Dimensionless stress σ¯αz versus z/h for R/h=(a) 100, (b) 50, (c) 10, and (d) 5

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