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TECHNICAL BRIEFS

# Why Do Shallow Caps Deflect More Than Deep Ones?

[+] Author and Article Information
B. Ostraich, E. Kochavi, E. Nizri, I. Cohen

Faculty of Engineering Sciences, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel

J. Pressure Vessel Technol 128(3), 476-478 (Nov 04, 2005) (3 pages) doi:10.1115/1.2218354 History: Received May 06, 2005; Revised November 04, 2005

## Abstract

The deflection of a clamped thin shell spherical cap is evaluated by the finite element method. Elastic material properties are assumed. The ratio of the center height to the base radius of the cap is used to distinguish shallow from deep caps. Comparing the deflection of clamped shallow caps to deep ones resulted in a very interesting behavior which may contradict the intuition of some engineers. For example, the deflection of a shallow clamped cap is considerably larger than that of a sphere or hemisphere with the same radius of curvature. The causes for this behavior are discussed. Results are presented for a wide range of geometries, pressures, and material properties for design purposes.

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## Figures

Figure 1

The definition of cases

Figure 2

Relative displacement as function cap’s angle, Cases (a), (b), and (c), p∕E=5×10−7, R∕t=100, and ν=0.3

Figure 3

The displaced shape of a 45deg sphere

Figure 4

Relative displacements of a clamped cap as a function of angle θ for some values of R∕t, p∕E=5×10−7, and ν=0.3

Figure 5

Relative displacements of a clamped cap as a function of angle θ for some values of R∕t, p∕E=5×10−5, and ν=0.3

Figure 6

Relative displacements of a clamped cap as a function of angle θ for some values of p∕E, R∕t=100, and ν=0.3

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