A. Ertepinar

Stability and asymmetric vibrations of pressurized compressible hyperelastic cylindrical shells

Abstract Cylindrical shells of arbitrary wall thickness subjected to uniform radial tensile or compressive dead-load traction are investigated. The material of the shell is assumed to be homogeneous, isotropic, compressible and hyperelastic. The stability of the finitely deformed state and small, free, radial vibrations about this state are investigated using the theory of small deformations superposed on large elastic deformations. The governing equations are solved numerically using both the multiple shooting method and the finite element method. For the finite element method the commercial program ABAQUS is used. 1 The loss of stability occurs when the motions cease to be periodic. The effects of several geometric and material properties on the stress and the deformation fields are investigated.

Finite deformations of compressible hyperelastic tubes subjected to circumferential shear

Abstract Finite deformations of homogeneous, isotropic, hyperelastic and compressible tubes subjected to circumferential shearing forces are studied using the theory of finite elasticity. The coupled, non-linear differential equations governing the problem are solved numerically to obtain the angle of twist and radial displacement. The qualitative difference of the present problem from the corresponding problem with incompressible material being the presence of radial deformations. the significance of this coupling is studied for various material constants. Limiting cases of infinitesimal deformations and incompressible material are compared with the findings of this work.

Large amplitude radial oscillations of inhomogeneous tubes of arbitrary wall thickness

Finite radial oscillations of inhomogeneous tubes with arbitrary wall thickness subjected to a suddenly applied uniform internal pressure are investigated. The material is assumed to be of neo-Hookean type with radially varying material constant. The theory of finite elastic deformations is used in the formulation of the problem. The equation of motion written in an integrated form is solved partially to yield the frequency-pressure curves. As a special case, the problem of small, free vibrations of thick, inhomogeneous tubes is formulated.

Compressible, hyperelastic spinning tubes subjected to circumferential shear

Abstract The finite strain behavior of cylindrical tubes, made of a polynomial compressible material and subjected to the simultaneous action of constant spin and uniform external circumferential shear, is investigated using the theory of finite elasticity. The inner surface of the tube is assumed to be perfectly bonded to a rigid shaft. The governing quasi-linear system of two ordinary differential equations is solved using a shooting method. Numerical results are generated to analyze, qualitatively, the effects of the material constants related to the amount of compressibility of the material and the second strain invariant-dependent behavior to the response of the tubes.

Finite deformations of compressible hyperelastic tubes subjected to external pressure

Abstract The behavior of a cylindrical tube made of a polynomial compressible material under a uniformly distributed external pressure is examined using the theory of finite elasticity. The non-linear differential equation of equilibrium is solved numerically by the method of adjoints. A large range of dilatation ratio is studied to compare the present results with the existing results for incompressible materials and for compressible Hookes material undergoing small or moderately large deformations.

Stability and vibrations of spinning tubes subjected to uniform radial pressure

Abstract The theory of small motions superposed on large, elastic, static deformations is used to investigate the stability and small vibrations of circular cylindrical tubes of arbitrary wall thickness. The tube is assumed to rotate about its axis with constant angular speed and be simultaneously subjected to a uniform radial pressure. The material of the tube is of Mooney-Rivlin type which is elastic, isotropic, homogeneous and incompressible. The effect of angular speed on the frequency of small vibrations and the buckling pressure is illustrated with several examples.

Finite, free torsional oscillations of hollow circular cylinders made of a mooney material

Abstract Finite, free torsional oscillations of hollow circular cylinders of arbitrary wall thickness and of arbitrary length are investigated. The material of the cylinder is assumed to be homogeneous, isotropic, elastic and incompressible. The governing differential equations of motion are obtained by the use of finite elasticity theory. While the exact solution of the problem requires a rather unrealistic body force distribution in the axial direction, it is shown that, in the solutions corresponding to long tubes and hollow disks, the error introduced by ignoring the body force distribution is negligibly small for large wavelengths.

Breathing motions and loss of stability of pre-stressed compressible hyperelastic cylindrical shells

The stability and breathing motions about finitely deformed states of cylindrical shells of arbitrary wall thickness subjected to uniform dead load traction are investigated. The material is assumed to be a polynomial compressible material which is homogeneous, isotropic and hyperelastic. The stability of the finitely deformed state and small, free, radial vibrations about this state are investigated using the theory of small deformations superposed on large elastic deformations The loss of stability occurs when the motions cease to be periodic. Numerical results are provided to study the effect of several geometric and material parameters.

SYMMETRIC AND ASYMMETRIC VIBRATIONS OF CYLINDRICAL SHELLS

The stability of cylindrical shells of arbitrary wall thickness subjected to uniform radial tensile or compressive dead-load traction is investigated. The material of the shell is assumed to be a polynomial compressible material which is homogeneous, isotropic, and hyperelastic. The governing equations are solved numerically using the multiple shooting method. The loss of stability occurs when the motions cease to be periodic. The effects of several geometric and material properties on the stress and the deformation fields are investigated.

Compressible, hyperelastic, spinning tubes subjected to radial pressure

Abstract The theory of finite elasticity is used to investigate the behaviour of cylindrical tubes made of compressible, hyperelastic materials and subjected to the simultaneous action of spin and radial tractions on the outer curved surface while the inner curved surface is perfectly bonded to a rigid shaft. The second order quasi-linear ordinary differential equation governing the system is solved numerically by the method of adjoints. The effects of the material compressibility, the second strain invariant dependent behaviour and the spin speed on the response of the tubes are studied by considering several numerical examples.