Abstract:
The mechanism of local changes of thickness of a lithosphere as a result of instability of
deformation of an ellipsoidal lithospheric cover of Earth under the influence of the internal pressure and
volume forces of inertia of rotation is found. The main stressed-deformed state of an elastic and viscous
ellipsoid of rotation is considered. The equation of elastic balance and the main ratios are defined in
degenerate elliptic coordinates. The axisymmetric task about the stressed state of an ellipsoid of rotation is
solved at expansion under the influence of uniform pressure on its internal surface. The stressed-deformed
state of an expanding ellipsoid of the rotation subject to action of volume forces of inertia of rotation is
investigated. Stability of deformation is investigated by a Leybenzon-Ishlinsky method.The main stressed
and deformed state is considered at an invariable form of border of a body and revolted taking into account
turns of elements of borders of a body in the course of transition to an adjacent form of balance.
Asymmetric forms of the indignations leading to loss of stability of an ellipsoid of rotation are defined. The
common decision of the equations of balance is defined through the biharmonic functions expressed by
means of tesseral spherical functions. Components of indignations are expressed through three any
constants which are found from the corresponding boundary conditions. Exponential growth of components
of indignations in time, accompanied by oscillatory changes takes place.
