Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

Establishment of the "Fenlong Energy Theory" and Conjecture of the "Fenlong Dark Matter Flow"

It is the first time that the world’s first new method of farming,the"Fenlong farming technology,"has been systematically clarified,and the"Fenlong body integrating with natural science"has been created in terms of land resource activation,natural fertilization,natural water management,natural ecological improvement(including climate),and natural indirect activation of river water resources.Moreover,the"theory of Fenlong energy"has been established based on its effectiveness.The"theory of Fenlong energy"originates from the"multiplying and incremental utilization of three-dimensional spatial resources"in production practice.Its application to more than 40 kinds of crops such as rice,corn and wheat in 26 provinces including Guangxi,Xinjiang and Tibet shows that:the yield of arable land increases by 20%to 50%(the quality is improved by 5%),the yield of saline land increases by 20%to 100%,and it can retain 100%of water and resist or ease the disaster.The"theory of three-dimensional spatial resources","Fenlong science","Fenlong law"are the theoretical base for the establishment of the"theory of Fenlong energy".Based on the phenomena that the Fenlong crops have particularly developed root systems,white and more fibrous roots,and tall plants,it is proposed for the first time that Fenlong farming breaks the confinement of the bottom layer of the plow and realizes the holographic penetration of material,energy,and information flows,and there may be the speculation of"Fenlong dark matter flow".

Nonequilibrium Solvent Free Energy Curve from Molecular Theory in Electron Transfer Reaction

The microscopic moleeular theory for electron transfer in a model solvent ishahr developed. The nonlinear response of the solvent molecules is be computedquanitatively in a new way. Adopting computer simulation daa and choosingappropriate reaction coordinae, a reasonable free energy dinram is constructed and thercorganhaion energy for the product state is calculated.

Material,energy and spatial fields for metallogenic prediction:Theory and practice An example:Limu Sn polymetallic crisis mines

The Limu tin deposits located in the Nanling tin and tungsten-polymetallic ore belt are now facing resource depletion after decades of exploitation.Peripheral mineral exploration therefore has become an urgent task.Using mineral exploration around the Limu crisis mines as an example,we introduce a breakthrough method of how the three-field theory,i.e.,the material,energy and spatial fields,is applied to intensively studies areas,a history of years of mineral exploitation and complex ore-forming systems.Taking a cue from Limu regional metallogeny,we based our investigation on the metallogenic information from geology,geophysics,geochemistry and remote sensing.We conducted our study of the three-field integrated information system,associated with metallogenic prognoses from deposits,with assignments and calculations which correct and allocate synthetic metallogenic prognosis by relying on GIS.We submitted a synthetic metallogenic prognosis map of tin in Limu where we delineated three ore target areas.A breakthrough was achieved by finding about 4785 t of tin metal outside the Shiziling deposit,which has been confirmed by drilling.The successful application in Limu shows that this three-field theory is of scientific and practical importance and deserves to be extended to utilization.

Energy-based marine ecological footprint in Shandong province, China

An energy-based ecological footprint model was set up to monitor the sustainable development status of a specific marine system. This model used unit energy value and energy density to convert the consumption into ecological productive areas. It can reflect the utilization degree of resources in the regional development. Then, the quantitative analysis of sustainable development was done by comparing the size of the areas. We defined the concept of energy-based ecological footprint of marine and built energy-based ecological footprint model of marine. Then we applied this model to marine ecological system of Shandong province to evaluate its sustainable development statue. The results showed that the energy-based marine ecological footprint of the marine ecological system in Shandong province was 1.74 × 106 hm^2 in 2010, and the energy-based ecological carrying capacity of this area was 1.60×107 hm^2 per capita. Thus, the marine ecological system of Shandong province has strong sustainability.

A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

Failure analysis of polycrystalline diamond compact cutters for breaking rock by bending waves theory

The breakage mechanism of the polycrystalline diamond compact(PDC) cutters was analyzed by the energy theory of bending waves. The cutting tests of granite block were conducted on a multifunctional testing device by using the cutter at three kinds of negative fore angles of 30°, 45° and 60°. The results show that, when the edge of the PDC layer is broken, the layer of tungsten cobalt is broken a little under the angle of 30°, while the layer of tungsten cobalt is broken continuously under the angle of 60°, their maximum depths are about 2 and 7 mm respectively in the two cases. The eccentric distance mainly depends on the negative fore angle of the cutter. When the cutter thrusts into the rock under an attack angle of 60°, the energy of bending waves reaches the maximum since the eccentric distance is the maximum. So the damage of cutter is the most serious. This test result is consistent with the conclusion of theoretical analysis well. The eccentric distance from the axial line of cutter to the point of action between the rock and cutter has great effect on the breakage of the cutter. Thus during the process of cutting, the eccentric distance should be reduced to improve the service life of PDC cutters.

Studies on the Quantitative Structure-activity Relationship of Substituted Biphenyls by Density Function Theory (DFT)

Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic parameters obtained at this level was taken as theoretical descriptors, and corresponding equation predicting the toxicity of Daphnia magna （-lgEC5o） was thus obtained, in which three parameters were contained, i.e., n-octanol/water partition coefficients （lgKow）, dipole moment of the molecules（ μ） and entropy （S°）. For this equation, R^2 = 0.9582, q^2 = 0.8921 and SD = 0.102. The absolute t-scores of three variables are larger than the standard one in the confidence range of 95%, which confirms the creditability and stability of this model.

Generalised energy conservation law for chaotic phenomena

Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted.

Mechanical Properties of Simple s-p Metals, and Defect Energies from Electron Theory and from Interatomic Force Laws

The cleavage force F(z) needed to separate parallel atomic planes by a distance z is first discussed for simple s-p metals using density functional theory.For the s-p nearly free-electron metals the linearized Thomas-Fermi equation is solved self-consistently in the cases of (a) semi-infinite planes of jellium (i.e. smeared uniform positive ions) and (b) a semi-infinite cylinder of finite radius, cleaved by a plane perpendicular to its axis. In (a), the elastic region has the form F(z)=Az ∝ Zrs-11/2, where rs is the mean interelectronic distance in the jellium model. Size effects are then considered, with possible relevance to atomic force microscopy.Defect energies are treated, using both electron theory and pair force laws.

f(T) modified teleparallel gravity as an alternative for holographic and new agegraphic dark energy models

In the present work, we reconstruct different f（T）-gravity models corre- sponding to the original and entropy-corrected versions of the holographic and new agegraphic dark energy models. We also obtain the equation of state parameters of the corresponding f（T）-gravity models. We conclude that the original holographic and new agegraphic f （T）-gravity models behave like the phantom or quintessence model, whereas in the entropy-corrected models, the equation of state parameter can justify the transition from the quintessence state to the phantom regime as indicated by the recent observations.

Theoretical Calculation about the High Energy Density Molecules of Nitrate Ester Substitution Derivatives of Prismane

The nitrate ester substitution derivatives of prismane were studied at the B3LYP/6-311G＊＊ level. The sublimation enthalpies and heats of formation in gas phase and solid state were calculated. The detonation performances were also predicted by using the famous Kamlet-Jacbos equation. Our calculated results show that introducing nitrate ester group into prismane is helpful to enhance its detonation properties. Stabilities were evaluated through the bond dissociation energies, bond order, characteristic heights（H50） and band gap calculations. The trigger bonds in the pyrolysis process of prismane derivatives were confirmed as O–ON2 bond. The BDEs of all compounds were large, so these prismane derivatives have excellent stability consistent with the results of H50 and band gap.

Interacting two-fluid viscous dark energy models in a non-flat universe

We study the evolution of the dark energy parameter within the scope of a spatially non-fiat and isotropic Friedmann-Robertson-Walker model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions that do not have a Big Rip singularity, and concluded that in both non-interacting and interacting cases the non-fiat open Universe crosses the phantom region. We find that during the evolution of the Universe, the equation of state for dark energy ωD changes from ωDeff 〉 - 1 to ωDeff 〈 - 1, which is consistent with recent observations.

Time Intervals of the Energy Emission in Quantum Systems Obtained from the Conservation Rule of the Electron Momentum

The paper presents a non-probabilistic approach to the time interval associated with the energy emission produced by the electron transition in a quantum system. The calculations were performed for the hydrogen atom and the electron particle in a one-dimensional potential box. In both cases, the rule of conservation of the electron momentum has been applied. The results, limited to the time intervals of transitions between two neighbouring quantum energy levels, occur to be much similar to those obtained earlier with the aid of the Joule-Lenz energy emission theory.

Theoretical Study on the C-H Activation in Decarbonylation of Acetaldehyde by NiL_2(L=SO_3CH_3) Using Density Functional Theory

Density functional theory calculations were carried out to explore the potential energy surface（PES） associated with the gas-phase reaction of Ni L2（L=SO3CH3） with acetone. The geometries and energies of the reactants, intermediates, products and transition states of the triplet ground potential energy surfaces of [Ni, O, C2, H4] were obtained at the B3LYP/6-311＋＋G（d,p） levels in C,H,O atoms and B3LYP/ Lanl2 dz in Ni atom. It was found through our calculations that the decabonylation of acetaldehyde contains four steps including encounter complexation, C-C activation, aldehyde H-shift and nonreactive dissociation. The results revealed that C-C activation induced by Ni L2（L=SO3CH3） led to the decarbonylation of acetaldehyde.

Extend ethylene aromatization single-event kinetic modeling with physical and chemical descriptor based on ZSM-5 catalyst

The ethylene aromatization is critical for the methanol to aromatics and light alkane dehydroaromatization process.The single-event microkinetic(SEMK)model combining the linear free energy theory and solid acid distribution concept were established and extend for the ethylene aromatization process,which can reduce the kinetic parameters and simplify the reaction network by comparison with the SEMK model including subtype elementary steps based on the type of carbenium ions.Further introducing deactivation parametersφinto the model and applying the linear free energy model to the deactivation experimental data,the obtained deactivation parametersφindicate that the carbon deposition precursors have the greatest impact on reducing the reaction rate of single-molecular reactions and the smallest impact on the hydrogen transfer reaction.Meanwhile,according to the change of reaction enthalpy,effect of carbenium ion structure on methylation,ethylation,cyclization and endo-βscission was investigated by introducing linear free energy concept into the SEMK model.The effect of different acid strengths on elementary steps was investigated based on the acid strength distribution model,it was found that the methylation and oligomerization reactions,the ali-βscission reaction,endo-βscission reaction and the cyclization reaction were more sensitive to strong acidity sites.The physisorption and chemisorption heat are separated from the protonation heat in the linear free energy kinetic model and the acid strength distribution kinetic model,and the absolute values of the obtained physisorption and chemisorption heat increase with the carbon number of carbenium ions.Furthermore,the parameters of the acid strength distribution kinetic model were applied to propane dehydroaromatization on H-ZSM-5 and the ethane dehydroaromatization on Zn/ZSM-5 to confirm the independence of parameters in the SEMK model with the similar reaction network.

A cumulative damage model for predicting and assessing raveling in asphalt pavement using an energy dissipation approach

Raveling is a common distress of asphalt pavements,defined as the removal of stones from the pavement surface.To predict and assess raveling quantitatively,a cumulative damage model based on an energy dissipation approach has been developed at the meso level.To construct the model,a new test method,the pendulum impact test,was employed to determine the fracture energy of the stone-mastic-stone meso-unit,while digital image analysis and dynamic shear rheometer test were used to acquire the strain rate of specimens and the rheology property of mastic,respectively.Analysis of the model reveals that when the material properties remain constant,the cumulative damage is directly correlated with loading time,loading amplitude,and loading frequency.Specifically,damage increases with superimposed linear and cosine variations over time.A higher stress amplitude results in a more rapidly increasing rate of damage,while a lower load frequency leads to more severe damage within the same loading time.Moreover,an example of the application of the model has been presented,showing that the model can be utilized to estimate failure life due to raveling.The model is able to offer a theoretical foundation for the design and maintenance of anti-raveling asphalt pavements.

Studies on the Quantitative Structure-activity Relationship of Toxicity of Chlorophenol Serial Compounds in the ab initio Methods and Substitutive Position of Chlorine Atom (N_(PCS))

20 Quantum chemical parameters of chlorophenol compounds were fully optimized by using B3LYP method on both 6-31G^＊ and 6-311G^＊ basis sets. These structural parameters are taken as theoretical descriptors, and the experimental data of 20 compounds＇ aquatic photogen toxicity（-lgEC50） are used to perform stepwise regression in order to obtain two predicted -lgEC50 correlation models whose correlation coefficients R^2 are respectively 0.9186 and 0.9567. In addition, parameters of chlorine atom＇s substitutive positions and their correlations （NPCs） are taken as descriptors to obtain another predicted -lgEC50 model with the correlation coefficient R2 of 0.9444. Correlation degree of each independent variable in the three models is verified by using variance inflation factors （VIF） and t value. In the cross-validation method, cross-validation coefficients q^2 of 3 models are respectively 0.8748, 0.9119 and 0.8993, which indicates that the relativity and prediction ability of this model are superior to those of the model obtained by topological and BLYP methods.

Quantitative Correlation of Chromatographic Retention and Acute Toxicity for Alkyl(1-phenylsulfonyl) Cycloalkane Carboxylates and Their Structural Parameters by DFT

Twenty eight alkyl(1-phenylsulfonyl) cycloalkane carboxylates were computed at the B3LYP/6-31G* level. Based on linear solvation energy theory, two quantitative correlation equations of the molecular structures of alkyl(1-phenylsulfonyl) cycloalkane carboxylate com- pounds to their chromatographic retention (capacity factor lgKW) and the toxicity for photo- bacterium phosphoreum (–lgEC50) were developed by using the molecular structural parameters as theoretical descriptors (r2 = 0.9501, 0.9488). The two quantitative correlation equations were consequently cross validated by leave-one-out (LOO) validation method with q2 of 0.9113 and 0.9281, respectively. The result showed that the two equations achieved in this work by B3LYP/6-31G* are both more advantageous than those from AM1, and can be used to predict the lgKW and –lgEC50 of congeneric organics.

QSPR Studies on lgK_(ow) and lgK_(oc) of Fluorobenzenes and Property Parameters Based on HF and DFT Calculations

Quantum chemistry parameters of 22 fluorobenzenes were computed at six levels using Hartree-Fock and DFT methods. Based on the experimental data of n-octanol/water partition coefficient （lgKow）, a three-parameter （dipole moments （μ）, zero point energy （ZPE） and free energy （G°）） quantitative correlation equation that can predict IgKow was developed using structural and thermodynamic parameters as theoretical descriptors. Similarly, based on experimental data of soil organic carbon sorption coefficient （lgKoc）, the other three-parameter （the most negative atomic net charge of molecule （q^-）, dipole moments （μ） and molecular volume （Vi）） quantitative correlation equation that can predict lgKoc was given. Quantitative correlation equations based on B3LYP/6- 311 G^＊＊ calculation were validated by VIF （variance inflation factors） and t-test and used to predict IgKow and lgKoc of a series of compounds. The result showed that the correlation and prediction ability of lgKoc equations based on three levels of HF/STO-3G, B3LYP/6-31 G^＊ and B3LYP/6- 311G^＊＊ are all more advantageous than those based on AMI.