Static Mantle Density Distribution 3 Dimpling and Bucking of Spherical Crust

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Tian-Quan Yun
Tian-Quan Yun

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This paper is the third step of project “Static mantle distribution, Equation, Solution and Application”. It consists of , , and this paper. Our result on shape of core is a “X type”, which differs from the traditional view that core is a sphere. Which one is correct? or, both are not correct? The aim of this paper is to study dimpling and bucking of the spherical crust under mantle loading. Dimpling analysis depends on the outer solution of non-homogeneous non-linear D. E., while bucking analysis depends on non-linear Eigen value of the homogeneous D. E The results based on two models and governing equations show that crust dimpled at poles is proved theoretically and numerical result well consists with pole radius, while the non-linear bucking Eigen value boundary problem is solved by decomposition method. The results show that bucking can occur, and the un-continuity of internal force per unit length causes un-continuity of masses by mantle material emitting to crust at turning point of “X”. The growing of Tibet high-land might be viewed as an evidence of the mass m s (θ 0 ) increasing due to mantle emission. Both poles radius and equatorial radius have been used to support our analysis. Question: how the nature makes cold at poles?

18 Cites in Articles

References

  1. Tian-Quan Yun (2019). Static Mantle Distribution 1 Equation.
  2. Tian-Quan Yun (2020). Static Mantle Density Distribution 2 Improved Equation and Solution.
  3. Э Григолюк,В Кабанов (1978). Устойчивость 600 Оболочек.
  4. David Parker,Frederic Wan (1984). Finite Polar Dimpling of Shallow Caps Under Sub-Buckling Axisymmetric Pressure Distributions.
  5. F Wan (1980). Bending of Spherical Shells.
  6. D Updike,A Kalnins (1970). Axisymmetric Behavior of an Elastic Spherical Shell Compressed Between Rigid Plates.
  7. Nai-Chien Huang (1964). Unsymmetrical Buckling of Thin Shallow Spherical Shells.
  8. David Bushnell (1967). Bifurcation phenomena in spherical shells under concentrated and ring loads..
  9. James Fitch (1968). The buckling and post-buckling behavior of spherical caps under concentrated load.
  10. J Fitch,B Budiansky (1970). Bucking and post behavior of spherical caps under axisymmetric load.
  11. Ta-Cheng Loo,R Evan-Iwanowski (1962). Interaction of Critical Pressures and Critical Concentrated Loads Acting on Shallow Spherical Shells.
  12. F Penning (1966). Nonaxisymmetric Behavior of Shallow Shells Loaded at the Apex.
  13. Tian-Quan Yun (1989). Asymmetric Dynamic Instability of Axis-symmetric Polar Dimpling of Thin Shallow Spherical Shell.
  14. Tian-Quan Yun (1989). Dynamic Instability of Axis-symmetric Dimpled Shallow Spherical Shells.
  15. Structure of the Earth.
  16. Tian-Quan Yun (1991). Twenty-second midwestern mechanics conference.
  17. (1979). Table of Contents.
  18. N Barton (1979). Book Review: The Hand Book.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Tian-Quan Yun. 2020. \u201cStatic Mantle Density Distribution 3 Dimpling and Bucking of Spherical Crust\u201d. Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 20 (GJSFR Volume 20 Issue A8): .

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GJSFR Volume 20 Issue A8
Pg. 21- 38
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-A Classification: FOR Code: 010599
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v1.2

Issue date

July 22, 2020

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English

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This paper is the third step of project “Static mantle distribution, Equation, Solution and Application”. It consists of , , and this paper. Our result on shape of core is a “X type”, which differs from the traditional view that core is a sphere. Which one is correct? or, both are not correct? The aim of this paper is to study dimpling and bucking of the spherical crust under mantle loading. Dimpling analysis depends on the outer solution of non-homogeneous non-linear D. E., while bucking analysis depends on non-linear Eigen value of the homogeneous D. E The results based on two models and governing equations show that crust dimpled at poles is proved theoretically and numerical result well consists with pole radius, while the non-linear bucking Eigen value boundary problem is solved by decomposition method. The results show that bucking can occur, and the un-continuity of internal force per unit length causes un-continuity of masses by mantle material emitting to crust at turning point of “X”. The growing of Tibet high-land might be viewed as an evidence of the mass m s (θ 0 ) increasing due to mantle emission. Both poles radius and equatorial radius have been used to support our analysis. Question: how the nature makes cold at poles?

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Static Mantle Density Distribution 3 Dimpling and Bucking of Spherical Crust

Tian-Quan Yun
Tian-Quan Yun

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