Geodesic
Approximate analytical solution of~the~problem for~the~tube with~elliptic outer contour under~steady-state creep condition
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 65-84

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The boundary value problem of steady-state creep for thick-walled outer elliptic contour's tube under internal pressure is considered. The approximate analytical solution of this problem for the state of plane deformation by the method of small parameter including the second approach is under construction. The hypothesis of incompressibility of material for creep strain is used. As a small parameter the value of flattening factor of the ellipse for external contour is used. Analysis of analytical solution is executed depending on the steady-state creep nonlinearity parameter and flattening factor of ellipse that is ratio of the difference of the semi-major and semi-minor axis to the semi-major axis which is outer radii of the unperturbed thick-walled tube. It is shown that with increasing of value of flattening factor to $0.1$ of outer radii of tube tangential stresses in weakest section at $\theta=\pi/2$ increase by $1.7$–$1.8$ times. The results of computations are presented in tabular and graphic form.
Mots-clés : elliptic outer contour of tube
Keywords: steady-state creep, approximate analytical solution, small parameter method, first and second approximation. 
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     author = {A. D. Moskalik},
     title = {Approximate analytical solution of~the~problem for~the~tube with~elliptic outer contour under~steady-state creep condition},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {65--84},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_4_a6/}
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A. D. Moskalik. Approximate analytical solution of~the~problem for~the~tube with~elliptic outer contour under~steady-state creep condition. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 65-84. http://geodesic.mathdoc.fr/item/VSGTU_2014_4_a6/