Another approach of WKB method for the stability analysis of the bending of an elastic rubber block

Sanjaranipour, M.; Hatami, Ali; Abdolalian, N.

doi:10.1016/j.ijengsci.2012.07.004

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…Their analysis started from the discrete monomer level and extended to the polymer chain at the macroscopic level. Accordingly, three models were developed simulating the local relations between molecular dipoles and their corresponding electric fields, introducing the electro-elasticity of polymer networks as a new concept (Sanjaranipour et al (2013)). Expanding on their previous works, Su et al (2019) addressed deformations caused by bending a dielectric-elastic bilayer reacting to voltage variations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the bending of a neo-Hookean electro-elastic shell of arbitrary thickness under an externally-applied hydrostatic pressure

Teymoori

Hatami

2022

Lat. Am. j. solids struct.

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The present study analyzes the bending of a simple electro-elastic cylindrical shell by the compound matrix method. The cross-section of the circular cylindrical shell is a non-circular curved shape, with 𝜇𝜇 1 a function of 𝐴𝐴 𝐵𝐵 � and the mode number, where 𝐴𝐴 and 𝐵𝐵 are the pre-deformation inner and outer radii of the cylindrical shell, and 𝜇𝜇 1 is the ratio of the deformed inner radius to 𝐴𝐴 . In the first step, a numerical model of the problem is developed to obtain specific differential equations. The modeling yields a system of two Ordinary Differential Equations with three boundary conditions of the same type. Next, it is shown that the dependence of 𝜇𝜇 1 to 𝐴𝐴 𝐵𝐵 � has a boundary layer structure. Simple numerical observations were made for bifurcation conditions. The analysis is, in fact, based on the variations of the inner and outer radii 𝐴𝐴 and 𝐵𝐵 , assuming 𝑎𝑎 = 𝜇𝜇 1 𝐴𝐴 and 𝑏𝑏 = 𝜇𝜇 2 𝐵𝐵, and based on the bifurcation of 𝜇𝜇 1 and 𝜇𝜇 2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.

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Section: Introductionmentioning

confidence: 99%