On the Singularity of the Liquid-Gas Coexistence Curve Diameter

A simplified Anisimov–Wang variant of the complete scaling approach makes it possible to determine the amplitudes of singularities for the diameter of the phase coexistence curve (CXC) on the basis of the coefficients in the power series expansion of the mean-field free energy in the reduced temperature and pressure near the critical point. This method is applied to obtain the amplitudes for the leading critical singularities of the CXC diameter in the case of a fluid described in the framework of the mesoscopic mean-field model. The results obtained demonstrate that the amplitudes of leading singularities of the CXC diameter are determined by the mesoscopic asymmetry parameters of the heterophase fluid.

The Dynamic Similitude Design Method of Thin Walled Structures and Experimental Validation

For the applicability of dynamic similitude models of thin walled structures, such as engine blades, turbine discs, and cylindrical shells, the dynamic similitude design of typical thin walled structures is investigated. The governing equation of typical thin walled structures is firstly unified, which guides to establishing dynamic scaling laws of typical thin walled structures. Based on the governing equation, geometrically complete scaling law of the typical thin walled structure is derived. In order to determine accurate distorted scaling laws of typical thin walled structures, three principles are proposed and theoretically proved by combining the sensitivity analysis and governing equation. Taking the thin walled annular plate as an example, geometrically complete and distorted scaling laws can be obtained based on the principles of determining dynamic scaling laws. Furthermore, the previous five orders’ accurate distorted scaling laws of thin walled annular plates are presented and numerically validated. Finally, the effectiveness of the similitude design method is validated by experimental annular plates.

The similitude design method of thin-walled annular plates and determination of structural size intervals

For the design problem of dynamic similitude models of an aero engine’s turbine discs, distorted scaling laws and structural size intervals of thin walled annular plates are established in the research. According to the governing equation, the geometrically complete scaling law of thin walled annular plates is firstly established. In order to determine accurate distorted scaling laws of thin walled annular plates, three significant principles are proposed and theoretically proved combining the governing equation and the sensitivity analysis. According to results of the sensitivity analysis, accurate distorted scaling laws of thin walled annular plates are obtained based on significant principles. In addition, structural size intervals of distorted scaling laws of thin walled annular plates are calculated by the numerical method. Finally, the previous six orders’ natural frequencies of thin walled annular plates are discussed as examples to verify the theory presented in this research, and distorted scaling laws of each order’s natural frequency are obtained and the corresponding structural size intervals are analyzed.

On shakedown and ratchetting of conforming frictional systems

Conforming contact is found on many important areas: materials with cracks, inclusions, layered structures, pinned geometries, etc. Coulomb friction is non-associative i.e. does not satisfy Drucker’s postulates for stability in plasticity theory, and this does not permit to use the classical Melan and Koiter theorems for cyclic loading which however remain obvious necessary conditions. On the other hand, the Coulomb friction cone has a peculiarity, its linear self-similarity, and this permits few general results, quite different but also powerful. For example, we show that for conforming contact, the Bree interaction diagram is open and sectors-shaped, and therefore there is no lower and upper bounds as in plasticity, since there is linear dependence on a load parameter \(\lambda\), and not a limit on \(\lambda\). As there is dependence on initial conditions in general, the Bree diagram doesn’t have the same profound meaning as in plasticity, since multiple steady states are possible. However, there is a complete scaling of the possible states (elastic shakedown, cyclic slip, ratchetting) with load factor \(\lambda\), and hence a worst-scenario can be defined. However, in order to develop residual stresses (which generally will take many cycles of steady cyclic loading), the load cannot go to zero, at least for friction coefficient below the critical value for "wedging". More in general, there needs to be a "permanent stick region" in the steady state.Almost conforming contacts, and in particular, in the case of initial interference, loose the independence on \(\lambda\) at low \(\lambda\) only, but "gain" greater possibilities to develop residual stresses. However, their study can be greatly simplified by developing a master curve approach to study the dependence on \(\lambda\). The theorems can also be considered the extension to cyclic loadings of the Dundurs results for conforming contacts under monotonic loading, in which case the contact area doesn’t vary in time and hence the problem is linear (from which the denomination "receding contacts"). However, here the problems remain fully non-linear, and the contact are not in general receding, nor there is a unique steady state, not even in the case of proportional loading. In the latter case it is nevertheless possible to derive some special results.