Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Water use and wastewater discharge of industrial sector in China

Problem of water scarcity has been increasingly severe in China. Though industrial sectors play important role for the rapid economic growth, and they consumes water and discharge wastewater. The purpose of this study is to examine the efficiency of water use and wastewater discharge in comparison with those of other inputs and production output in Chinese industry. Measuring efficiency of each input and output factor from 2002 to 2008, we find the average inefficiencies of industrial water use and industrial wastewater discharge are higher than those of capital, labor, and production output in China. In addition, the productivity levels to save water in the water shortage areas are not higher compared to the others. The water use inefficiency has a high dispersion especially in the regions where the amounts of water resources per capita is less than 3000 cubic meter.

Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

The ovarian response to controlled stimulation in IVF cycles may be predictive of the age at menopause

STUDY QUESTION Can the number of oocytes retrieved in IVF cycles be predictive of the age at menopause? SUMMARY ANSWER The number of retrieved oocytes can be used as an indirect assessment of the extent of ovarian reserve to provide information on the duration of the reproductive life span in women of different ages. WHAT IS KNOWN ALREADY Menopause is determined by the exhaustion of the ovarian follicular pool. Ovarian reserve is the main factor influencing ovarian response in IVF cycles. As a consequence the response to ovarian stimulation with the administration of gonadotrophins in IVF treatment may be informative about the age at menopause. STUDY DESIGN, SIZE, DURATION In the present cross-sectional study, participants were 1585 infertile women from an IVF clinic and 2635 menopausal women from a more general population. PARTICIPANTS/MATERIALS, SETTING, METHODS For all infertile women, the response to ovarian stimulation with gonadotrophins was recorded. For menopausal women, relevant demographic characteristics were available for the analysis. MAIN RESULTS AND THE ROLE OF CHANCE A cubic function described the relationship between mean numbers of oocytes and age, with all terms being statistically significant. From the estimated residual distribution of the actual number of oocytes about this mean, a distribution of the age when there would be no oocytes retrieved following ovarian stimulation was derived. This was compared with the distribution of the age at menopause from the menopausal women, showing that menopause occurred about a year later. LIMITATIONS, REASONS FOR CAUTION The retrieved oocyte data were from infertile women, while the menopausal ages were from a more general population. WIDER IMPLICATIONS OF THE FINDINGS In the present study, we have shown some similarity between the distributions of the age when no retrieved oocytes can be expected after ovarian stimulation and the age at menopause. For a given age, the lower the ovarian reserve, the lower the number of retrieved oocytes would be and the earlier the age that menopause would occur.

Prediction of a large-gap quantum-spin-Hall insulator: Diamond-like GaBi bilayer

A quantum-spin-Hall (QSH) state was achieved experimentally, albeit at a low critical temperature because of the narrow band gap of the bulk material. Twodimensional topological insulators are critically important for realizing novel topological applications. Using density functional theory (DFT), we demonstrated that hydrogenated GaBi bilayers (HGaBi) form a stable topological insulator with a large nontrivial band gap of 0.320 eV, based on the state-of-the-art hybrid functional method, which is implementable for achieving QSH states at room temperature. The nontrivial topological property of the HGaBi lattice can also be confirmed from the appearance of gapless edge states in the nanoribbon structure. Our results provide a versatile platform for hosting nontrivial topological states usable for important nanoelectronic device applications.

Thermal properties and thermal shock resistance of γ-Y 2Si2O7

Thermal properties, namely, Debye temperature, thermal expansion coefficient, heat capacity, and thermal conductivity of γ-Y 2Si2O7, a high-temperature polymorph of yttrium disilicate, were investigated. The anisotropic thermal expansions of γ-Y2Si2O7 powders were examined using high-temperature X-ray diffractometer from 300 to 1373 K and the volumetric thermal expansion coefficient is (6.68±0.35) × 10-6 K-1. The linear thermal expansion coefficient of polycrystalline γ-Y2Si2O7 determined by push-rod dilatometer is (3.90±0.4) × 10-6 K-1, being very close to that of silicon nitride and silicon carbide. Besides, γ-Y2Si2O7 displays a low-thermal conductivity, with a κ value measured below 3.0 W·(m·K) -1 at the temperatures above 600 K. The calculated minimum thermal conductivity, κmin, was 1.35 W·(m·K) -1. The unique combination of low thermal expansion coefficient and low-thermal conductivity of γ-Y2Si2O7 renders it a very competitive candidate material for high temperature structural components and environmental/thermal-barrier coatings. The thermal shock resistance of γ-Y2Si2O7 was estimated by quenching dense materials in water from various temperatures and the critical temperature difference, ΔTc, was determined to be 300 K.