Solution of a Three-Dimensional Thermoelasticity Problem for an Infinite Transversely Isotropic Body

2021 ◽  
Author(s):  
Yu. V. Tokovyy ◽  
D. S. Boiko
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Isotropic Body ◽  
Thermoelasticity Problem ◽  
Transversely Isotropic Body

Free Vibrations of Transversely Isotropic Cylinders and Cylindrical Shells

1998 ◽  
Vol 120 (4) ◽  
pp. 321-324 ◽  
Author(s):  
W. Q. Chen ◽  
J. Ying ◽  
Q. D. Yang
Keyword(s):  
Orthogonal Series ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Isotropic Body ◽  
Free Vibrations ◽  
Function Solution ◽  
Isotropic Cylindrical Shell ◽  
Complex Eigenvalues ◽  
Transversely Isotropic Body

Three displacement functions are introduced to decompose three displacement components so that the three-dimensional equations of motion of a transversely isotropic body are uncoupled. Expanding these functions in terms of orthogonal series, the equations of free vibration problem of a transversely isotropic cylindrical shell with ends simply supported are further simplified to be readily dealt with. As contrast to previous works, modified Bessel function solution with complex arguments is directly adopted for the case of complex eigenvalues. Moreover, for solid cylinders, (modified) Bessel functions of the first kind, even with pure imaginary arguments, are used because of their peculiar properties. Two numerical examples are given to check the correctness of the present method by comparing the results with those of others. Because no assumption is introduced in the paper, the method developed is completely three-dimensionally exact.

An Inverse Transient Thermoelastic Problem for a Transversely-Isotropic Body

1989 ◽  
Vol 56 (4) ◽  
pp. 791-797 ◽  
Author(s):  
Naotake Noda ◽  
Fumihiro Ashida ◽  
Tomoaki Tsuji
Keyword(s):  
Inverse Problem ◽  
Lateral Surface ◽  
Fourier Transforms ◽  
Heating Temperature ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Isotropic Body ◽  
Thermoelastic Problem ◽  
Shear Stresses ◽  
Transversely Isotropic Body

The present paper discusses an analytical method for an inverse problem of three-dimensional transient thermoelasticity in a transversely-isotropic solid. The inverse thermoelastic problem consists of the determination of the condition of heating when the conditions of displacements and stresses are given at some points of the solid considered. Applying the Laplace and Fourier transforms as well as the new potential function method, the temperature, displacements, and stresses are represented by the potential functions alone, and they are determined from the prescribed conditions. The heating condition is obtained from the boundary condition for the temperature field. As a practical example of an inverse problem, the heating temperature of a transversely-isotropic infinite circular cylinder is determined in the case where the radial displacement is given at an arbitrary cylindrical section and the radial and shear stresses are free on the lateral surface of the cylinder. Numerical calculations are carried out to illustrate the heating temperature of the cylinder as well as the temperature and stresses on the lateral surface of the cylinder.

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