A Strain-Energy Expression for Thin Cylindrical Shells

1953 ◽  
Vol 20 (3) ◽  
pp. 448-449
Author(s):  
H. H. Bleich ◽  
F. DiMaggio
Keyword(s):  
Strain Energy ◽  
Cylindrical Shells ◽  
Energy Expression

On the Strain Energy of Shells

1954 ◽  
Vol 21 (1) ◽  
pp. 81-82
Author(s):  
H. L. Langhaar ◽  
D. R. Carver
Keyword(s):  
Power Series ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Energy Expression ◽  
Circular Cylindrical Shells

Abstract In a previous paper, the strain energy of a shell was derived with the aid of the assumption that only the linear terms in the thickness co-ordinate z need be retained in the expressions for the strains. Recently, Bleich and DiMaggio derived a strain-energy expression for circular cylindrical shells without using power series in z. The present paper shows that power series in z may be eliminated, in general, and that the errors caused by linearizing approximations are frequently significant.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Cylindrical Shells: Energy, Equilibrium, Addenda, and Erratum

1955 ◽  
Vol 22 (1) ◽  
pp. 111-116
Author(s):  
E. H. Kennard
Keyword(s):  
Cylindrical Shell ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Uniform Thickness ◽  
Energy Equilibrium

Abstract The strain energy in a homogeneous cylindrical shell of uniform thickness is calculated from equations obtained by Epstein’s method. The indeterminateness of the equations of equilibrium is further discussed and simplified forms of these equations and of the expressions for the stress resultants are given. Addenda and an erratum to a prior paper are included.

An Expression of Strain Energy with Couple Stresses

1984 ◽  
Vol 8 (2) ◽  
pp. 63-69
Author(s):  
S.K. Lakhanpal
Keyword(s):  
Material Properties ◽  
Strain Energy ◽  
Load Transfer ◽  
Modern Technology ◽  
Material Behavior ◽  
Couple Stresses ◽  
Energy Expression

Modern Technology has required a continuous search for better materials. Hence, the desire among engineers to study the material properties rigorously. Throughout the literature, the concept of load transfer is based on linear stresses. However, the material behavior is better defined when load transfer is considered to be by couple stresses, in addition to linear stresses. The strain energy expression is an important tool for the study of the material. With this in mind, an expression with couple stresses included is developed.

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