SEMI-INVERSE METHOD AND GENERALIZED VARIATIONAL PRINCIPLES WITH MULTI-VARIABLES IN ELASTICITY

Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.

POINCARE-LIGHTHILL-KUO METHOD AND SYMBOLIC COMPUTATION

This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method (PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, the difficulty of intermediate expression swell, often encountered in symbolic computation, is outlined. For overcoming the difficulty, a semi-inverse algorithm was proposed by the author, with which the lengthy ports of intermediate expressions are first frozen in the form of symbols till the Fnal stage of seeking perturbation solutions. Tn discuss the applications of the above algorithm, the related work of the author and his research group on nonlinear oscillations and waves is concisely reviewed. The computer-extended perturbation solution of the Duffing equation shows that the asymptotic solution obtained with the PLK method possesses the convergence radius of 1 and thus the range of validity of the solution is considerably enlarged. The studies on internal solitary waves in stratified fluid and on the head-on collision between two solitary waves in a hyperelastic rod indicate that by means of the presented methods, very complicated manipulation, unconceivable in hand calculation, can be conducted and thus result in higher-order evolution equations and asymptotic solutions. The examples illustrate that the algorithm helps to realize the symbolic computation on micro-commputers. Finally, it is concluded that,vith the aid of symbolic computation, the vitality of the PLK method is greatly. Strengthened and at least for the solutions to conservative systems of oscillations and waves, it is a powerful tool.

Modified Lagrange Multiplier Method and Generalized Variational Principle in Fluid Mechanics

The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.

Study on Top-Down Estimation Method of Software Project Planning

This paper studies a new software project planning method under some actual project data in order to make software project plans more effective. From the perspective of system theory, our new method regards a software project plan as an associative unit for study. During a top-down estimation of a software project, Program Evaluation and Review Technique （PERT） method and analogy method are combined to estimate its size, then effort estimation and specific schedules are obtained according to distributions of the phase effort. This allows a set of practical and feasible planning methods to be constructed. Actual data indicate that this set of methods can lead to effective software project planning.

VARIATIONAL PRINCIPLES FOR NONLOCAL CONTINUUM MODEL OF ORTHOTROPIC GRAPHENE SHEETS EMBEDDED IN AN ELASTIC MEDIUM

Equations governing the vibrations and buckling of multilayered orthotropic graphene sheets can be expressed as a system of n partial differential equations where n refers to the number of sheets. This description is based on the continuum model of the graphene sheets which can also take the small scale effects into account by employing a nonlocal theory. In the present article a variational principle is derived for the nonlocal elastic theory of rectangular graphene sheets embedded in an elastic medium and undergo- ing transverse vibrations. Moreover the graphene sheets are subject to biaxial compression. Rayleigh quotients are obtained for the frequencies of freely vibrating graphene sheets and for the buckling load. The influence of small scale effects on the frequencies and the buckling load can be observed qualiatively from the expressions of the Rayleigh quotients. Elastic medium is modeled as a combination of Winkler and Pasternak foundations acting on the top and bottom layers of the mutilayered nano-structure. Natural boundary con- ditions of the problem are derived using the variational principle formulated in the study. It is observed that free boundaries lead to coupled boundary conditions due to nonlocal theory used in the continuum formulation while the local （classical） elasticity theory leads to uncoupled boundary conditions. The mathematical methods used in the study involve calculus of variations and the semi-inverse method for deriving the variational integrals.

Variational principles for two kinds of extended Korteweg-de Vries equations

Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries （KdV） equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.

Equivalent Theorem of Hellinger-Reissner and Hu-Washizu Variational Principles

The paper has proved that Hellinger-Reissuer and Hu-Washizu variational principles are but equivalent principles in elasticity by following three ways: 1) Lagrange multiplier method. The paper points out that only a new independent variable can be introduced when one constraint equation has been eliminated by one Lagrange multiplier, which must be expressed as a function of the original variable(s) and/or the new introduced variable after identification. In using Lagrange multiplier method to deduce Hu-Washizu principle from the minimum potential energy principle, which has only one kind of independent variable namely displacement, by eliminating the constraint equations of stress-displacement relations, one can only obtain a principle with two kinds of variables namely displacement and stress; 2) involutory transformation, with such method Hu-Washizu variational principle can be deduce directly from the Hellinger-Reissner variational principle under the same variational constraints of Stress-strain relation, and vice verse; 3)semi-inverse method, by which both of the above variational principles can be deduced from the minimum potential energy principle with tile same variational constraints. So the three kinds of variational functions in Hu-Washizu variational principle are not independent to each other,the stress-strain relationships are still its constraint conditions.

Simulation of top-down crack propagation in asphalt pavements

Top-down crack in asphalt pavements has been reported as a widespread mode of failure.A solid understanding of the mechanisms of crack growth is essential to predict pavement performance in the context of thickness design,as well as in the design and optimization of mixtures.Using the coupled element free Galerkin (EFG) and finite element (FE) method,top-down crack propagation in asphalt pavements is numerically simulated on the basis of fracture mechanics.A parametric study is conducted to isolate the effects of overlay thickness and stiffness,base thickness and stiffness on top-down crack propagation in asphalt pavements.The results show that longitudinal wheel loads are disadvantageous to top-down crack because it increases the compound stress intensity factor (SIF) at the tip of top-down crack and shortens the crack path,and thus the fatigue life descends.The SIF experiences a process "sharply ascending—slowly descending—slowly ascending—sharply ascending again" with the crack propagating.The thicker the overlay or the base,the lower the SIF; the greater the overlay stiffness,the higher the SIF.The crack path is hardly affected by stiffness of the overlay and base.

不同全球变暖目标下中国气候变化风险区域格局

Climate change will bring huge risks to human society and the economy.Regional climate change risk assessment is an important basic analysis for addressing climate change,which can be expressed as a regional system of comprehensive climate change risk.This study establishes regional systems of climate change risks under the proposed global warming targets.Results of this work are spatial patterns of climate change risks in China,indicated by the degree of climate change and the status of the risk receptors.Therefore,the risks show significant spatial differences.The high-risk regions are mainly distributed in East,South,and central China,while the medium-high risk regions are found in North and southwestern China.Under the 2℃warming target,more than 1/4 of China’s area would be at high and medium-high risk,which is more severe than under the 1.5℃warming target,and would extend to the western and northern regions.This work provides regional risk characteristics of climate change under different global warming targets as a foundation for dealing with climate change.

Emerging porous nanosheets:From fundamental synthesis to promising applications

Metal-organic framework(MOF)nanosheets and covalent organic framework(COF)nanosheets as emerging porous materials nanosheets have captured increasing attention owing to their attractive properties originating from the advantages of large lateral size,ultrathin thickness,tailorable physiochemical environment,flexibility and highly accessible active sites on surface,and the applications of them have been explored in a wide range of fields.Although MOF and COF nanosheets own many similar properties,their applications in various fields show significant differences,probably due to their different compositions and bonding modes.Hence,we summarize the recent progress of MOF and COF nanosheets by comparative analysis on their advantages and limitations in synthesis and applications,providing a more profound and full-scale perspective for researchers or beginners to understand this field.Herein,the categories of preparation methods of MOF and COF nanosheets are firstly discussed,including top-down and bottom-up methods.Secondly,the applications of MOF and COF nanosheets for separation,catalysis,sensing and energy storage are summarized.Finally,based on current achievements,we put forward our personal insights into the challenges and outlooks on the synthesis,characterizations,and promising applications for future research of MOF and COF nanosheets.

Shanghai center project excavation induced ground surface movements and deformations

Empirical data on deep urban excavations can provide designers a significant reference basis for assessing potential deformations of the deep excavations and their impact on adjacent structures. The construction of the Shanghai Center involved excavations in excess of 33-m-deep using the top-down method at a site underlain by thick deposits of marine soft clay. A retaining system was achieved by 50-m-deep diaphragm walls with six levels of struts. During construction, a comprehensive instrumentation program lasting 14 months was conducted to monitor the behaviors of this deep circular excavation. The following main items related to ground surface movements and deformations were collected： （1） walls and circumferential soils lateral movements; （2） peripheral soil deflection in layers and ground settlements; and （3） pit basal heave. The results from the field instrumentation showed that deflections of the site were strictly controlled and had no large movements that might lead to damage to the stability of the foundation pit. The field performance of another 21 cylindrical excavations in top-down method were collected to compare with this case through statistical analysis. In addition, numerical analyses were conducted to compare with the observed data. The extensively monitored data are characterized and analyzed in this paper.

Two-dimensional covalent organic framework nanosheets:Synthesis and energy-related applications

Two-dimensional(2D)covalent organic framework nanosheets(CONs)are attracting increasing research attention because of their unique properties derived from their ultrathin thickness,high surface-tovolume atomic ratio,and extremely large surface area.2D CONs can provide high transport pathways for charge carriers(e.g.,electrons,holes and ions)through either the conjugated skeletons or the open channels.Therefore,they have shown great potential in energy related applications.In this review,we firstly introduce the recent developments and characteristics of 2D CONs by focusing on the two typical synthetic methods,i.e.,top-down and bottom-up methods.Then,the energy-related applications in energy storage and conversion of 2D CONs are summarized.Finally,we give our personal views on the challenges and perspectives for the future research of 2D CONs and their composites.

A VARIATIONAL MODEL FOR 2-D MICROPOLAR BLOOD FLOW

The micropolar fluid model is an essential generalization of thewell-established Navier-Stokes model in the sense that it takes into account the microstructure ofthe fluid. This paper is devolted to establishing a variational principle for 2-D incompressiblemicropolar blood flow.