Thermoelastic deformation of a transversally isotropic prolate spheroid

1987 ◽  
Vol 23 (12) ◽  
pp. 1126-1133
Author(s):  
Yu. N. Podil'chuk
Keyword(s):  
Prolate Spheroid ◽  
Thermoelastic Deformation ◽  
Transversally Isotropic

Thermoelastic deformation of transversally isotropic two-cavity hyperboloid of revolution

1988 ◽  
Vol 24 (9) ◽  
pp. 833-839
Author(s):  
Yu. N. Podil'chuk
Keyword(s):  
Thermoelastic Deformation ◽  
Transversally Isotropic

scholarly journals On thermoelastic deformation of a transversally isotropic medium in 3D construction printing

2021 ◽  
Vol 2131 (3) ◽  
pp. 032024
Author(s):  
Yu Chirkunov ◽  
E Pikmullina ◽  
I Gasenko
Keyword(s):  
Differential Equations ◽  
Isotropic Medium ◽  
Group Analysis ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Thermoelastic Deformation ◽  
Transversally Isotropic ◽  
Materials Used ◽  
And Function

Abstract A three-dimensional dynamic model of a thermoelastic transversely isotropic medium is used to describe the thermoelastic deformation of materials with anisotropy of elastic properties with a selected direction of anisotropy. Such materials are layered and composite materials used in construction, mechanical engineering, aircraft and shipbuilding, soils in permafrost conditions, glaciers, as well as rocks (basalt, sandstone, marble, limestone, shale, and others). The study of this model, in particular, is relevant in connection with the use of 3D printers in construction. This is due to the fact that it is necessary to select the heating mode of the 3D printer head, in which cracks will not form during the cooling of the polystyrene concrete layers.We study this model using the group analysis methods, which is one of the most powerful and effective tools for obtaining exact solutions. The group stratification of the system of second-order differential equations defining this model is carried out. A system of first-order differential equations is obtained, which is equivalent to the equations of the original model. The solution describing a traveling wave for this system is obtained, that depends on arbitrary elements: parameters and function. For the specific sets of these elements, we study a deformation of a sphere and cube located inside a thermoelastic transversely isotropic medium with increasing time is found. The corresponding graphs are given.

Separated flow surface pressure fluctuations and pressure-velocity correlations on prolate spheroid

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 266-274
Author(s):  
Michael C. Goody ◽  
Roger L. Simpson ◽  
Christopher J. Chesnakas
Keyword(s):  
Surface Pressure ◽  
Pressure Fluctuations ◽  
Separated Flow ◽  
Prolate Spheroid ◽  
Flow Surface

A possible modification of groundwater flow equation using coordinate transformations

2014 ◽  
Vol 15 (2) ◽  
pp. 278-287 ◽  
Author(s):  
Abdon Atangana ◽  
Ernestine Alabaraoye
Keyword(s):  
Groundwater Flow ◽  
Prolate Spheroid ◽  
Flow Equation ◽  
Time Space ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
Groundwater Flow Equation ◽  
Factor Α ◽  
Modified Equation ◽  
Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

Numerical investigation on the flow around an inclined prolate spheroid

2021 ◽  
Vol 33 (7) ◽  
pp. 074106
Author(s):  
Zhe Wang ◽  
Jianzhi Yang ◽  
Helge I. Andersson ◽  
Xiaowei Zhu ◽  
Minghou Liu ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Prolate Spheroid

scholarly journals Longitudinal, Near-Surface Maneuvering of a Prolate Spheroid

2019 ◽  
Vol 52 (21) ◽  
pp. 248-253
Author(s):  
Ying-Chun Chen ◽  
Seyong Jung ◽  
Craig Woolsey
Keyword(s):  
Prolate Spheroid ◽  
Near Surface
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