Static Mantle Density Distribution 3 Dimpling and Bucking of Spherical Crust

Abstract

This paper is the third step of project "Static mantle distribution, Equation, Solution and Application". It consists of < Static Mantle Distribution 1 Equation>, < Static Mantle Density Distribution 2 Improved Equation and Solution>, 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?