Degree One Loading by Pressure Variations at the CMB

Hemispherical asymmetry in core dynamics induces degree-1 pressure variations at the core mantle boundary （CMB）, which in turn deforms the overlaying elastic mantle, at the same time keeps center of mass of the whole Earth stationary in space. We develop a systematic procedure to deal with the degree-1 CMB pressure loading. We find by direct calculation a surprisingly negative load Love number h1=-1.425 for vertical displacement. Further analysis indicates that the negative hi corre- sponds to thickening above the positive load that defies intuition that pressure inflation pushes over- laying material up and thins the enveloping shell. We also redefine the pressure load Love numbers in general to enable comparison between the surface mass load and the CMB pressure load for the whole spectrum of harmonic degrees. We find that the gravitational perturbations from the two kinds of loads at degrees n〉l are very similar in amplitude but opposite in sign. In particular, if the CMB pressure variation at degree 2 is at the level of -1 hpa/yr （1 cm water height per year）, it would perturb the variation of Earth＇s oblateness, known as the J2, at the observed level.

Simplification approaches for multi-level load spectra by using equivalent damage rule

Reasonable and effective fatigue load spectrum is key of aircraft structural fatigue test.Two kinds of load spectra simplification approaches based on statistical consistent fatigue damage model are proposed in the paper.One method is to simplify the original multi-level load spectra to spectral load with fewer level and was verified by the experimental data of five levels and seven levels load spectra.The equivalent damage here is not equivalent fatigue life,but equivalent number of spectral blocks.Moreover,it was proved that a section of low stress load cannot be converted into the highest stress load considering equivalent damage.The other is to convert the life distribution under multi-level load spectra into that of constant amplitude spectrum according to a certain principle,that is,equivalent damage is achieved through equivalent fatigue life,and two groups of three levels spectral data were used for experimental verification.The results show that equivalent damage simplification approach of multi-level load spectra is feasible,and it achieve that the damage of one loading block before and after the simplification is equal in probability statistics.The life distribution of load simplified as constant amplitude spectrum is consistent with test data.The simplification method presented in this paper can be generalized and is a predictive engineering method which does not depend on experimental data.