Spherically symmetric transient responses of functionally graded magneto-electro-elastic hollow sphere

2006 ◽  
Vol 23 (5) ◽  
pp. 525-542 ◽  
Author(s):  
H.M. Wang ◽  
H.J. Ding
Keyword(s):  
Hollow Sphere ◽  
Functionally Graded ◽  
Spherically Symmetric ◽  
Transient Responses

Transient Responses in a Piezoelectric Spherically Isotropic Hollow Sphere for Symmetric Problems

2003 ◽  
Vol 70 (3) ◽  
pp. 436-445 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Hollow Sphere ◽  
Electric Potential ◽  
Present Method ◽  
Interpolation Method ◽  
Separation Of Variables ◽  
Time Variable ◽  
Spherically Symmetric ◽  
Transient Responses ◽  
Arbitrary Thickness ◽  
Piezoelectric Hollow Sphere

By virtue of the separation of variables technique, the spherically symmetric electroelastic dynamic problem of a spherically isotropic hollow sphere is transformed to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to spherically symmetric electric potential and radial mechanical loads, that both can be arbitrary functions about the time variable, at the internal and external surfaces.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Functionally Graded Hollow Sphere With Piezoelectric Internal and External Layers Under Asymmetric Transient Thermomechanical Loads

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Hollow Sphere ◽  
Legendre Polynomials ◽  
Radial Direction ◽  
Energy Equation ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Piezoelectric Layers ◽  
Transient Thermal

In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

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