Buckling of doubly curved shallow thin shells.

AIAA Journal ◽  
1968 ◽  
Vol 6 (5) ◽  
pp. 982-984 ◽  
Author(s):  
H. M. HAYDL
Keyword(s):  
Thin Shells ◽  
Doubly Curved

The Shape of Helically Creased Cylinders

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
K. A. Seffen ◽  
N. Borner
Keyword(s):  
Large Deformation ◽  
Gaussian Curvature ◽  
Pitch Angle ◽  
Thin Shells ◽  
Flat Sheet ◽  
Cylindrical Form ◽  
Geometrical Concept ◽  
Mohr’S Circles ◽  
Doubly Curved ◽  
Mohr’S Circle

Creasing in thin shells admits large deformation by concentrating curvatures while relieving stretching strains over the bulk of the shell: after unloading, the creases remain as narrow ridges and the rest of the shell is flat or simply curved. We present a helically creased unloaded shell that is doubly curved everywhere, which is formed by cylindrically wrapping a flat sheet with embedded fold-lines not axially aligned. The finished shell is in a state of uniform self-stress and this is responsible for maintaining the Gaussian curvature outside of the creases in a controllable and persistent manner. We describe the overall shape of the shell using the familiar geometrical concept of a Mohr's circle applied to each of its constituent features—the creases, the regions between the creases, and the overall cylindrical form. These Mohr's circles can be combined in view of geometrical compatibility, which enables the observed shape to be accurately and completely described in terms of the helical pitch angle alone.

Free Vibration of Doubly Curved Thin Shells

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
April Bryan
Keyword(s):  
Differential Equation ◽  
Vibration Analysis ◽  
Equation Of Motion ◽  
Thin Shells ◽  
Numerical Examples ◽  
Normal Coordinates ◽  
Spatial Equation ◽  
Doubly Curved ◽  
Analytical Approaches ◽  
Numerical Approaches

While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.

Maysel's formula generalized for piezoelectric vibrations - Application to thin shells of revolution

1996 ◽  
Author(s):  
Hans Irschik ◽  
Franz Ziegler ◽  
Hans Irschik ◽  
Franz Ziegler
Keyword(s):  
Thin Shells ◽  
Shells Of Revolution
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