Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

Microwave-Assisted Au and Ag Nanoparticle Synthesis: An Energy Phase-Space Projection Analysis

Microwave-assisted synthesis of gold and silver nanoparticles, as a function of Green Chemistry, non Green Chemistry, and four applicator types are reported. The applicator types are Domestic microwave ovens, commercial temperature controlled microwave chemistry ovens (TCMC), digesters, and axial field helical antennae. For each of these microwave applicators the process energy budget where estimated (Watts multiplied by process time = kJ) and energy density (applied energy divided by suspension volume = kJ·ml-1) range between 180 ± 176.8 kJ, and 79.5 ± 79 kJ·ml-1, respectively. The axial field helical field an-tenna applicator is found to be the most energy efficient (0.253 kJ·m-1 per kJ, at 36 W). Followed by microwave ovens (4.47 ± 3.9 kJ·ml-1 per 76.83 ± 39 kJ), and TCMC ovens (2.86 ± 2.3 kJ·m-1 per 343 ± 321.5 kJ). The digester applicators have the least energy efficiency (36.2 ± 50.7 kJ·m-1 per 1010 ± 620 kJ). A comparison with reconstructed ‘non-thermal’ microwave oven inactivation microorganism experiments yields a power-law signature of n = 0.846 (R2 = 0.7923) four orders of magnitude. The paper provides a discussion on the Au and Ag nanoparticle chemistry and bio-chemistry synthesis aspects of the microwave applicator energy datasets and variation within each dataset. The visual and analytical approach within the energy phase-space projection enables a nanoparticle synthesis route to be systematically characterized, and where changes to the synthesis are to be mapped and compared directly with historical datasets. In order to help identify lower cost nanoparticle synthesis, in addition to potentially reduce synthesis energy to routes informed changes to potentially reduce synthesis energy budget, along with nanoparticle morphology and yield.

Renewable energy power generation projects started construction in Tibet

On March 19, the construction of a 10-MW photovoltaic power plant and a 1 000-kW new type geothermal power generation project were started by Guodian Longyuan Group in Yanbajing Town, Dangxiong County of Tibet.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD

The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.

Criterion of aerodynamic performance of large-scale offshore horizontal axis wind turbines

With the background of offshore wind energy projects, this paper studies aerodynamic performance and geometric characteristics of large capacity wind turbine rotors （1 to 10 MW）, and the main characteristic parameters such as the rated wind speed, blade tip speed, and rotor solidity. We show that the essential criterion of a high- performance wind turbine is a highest possible annual usable energy pattern factor and a smallest possible dimension, capturing the maximum wind energy and producing the maximum annual power. The influence of the above-mentioned three parameters on the pattern factor and rotor geometry of wind turbine operated in China＇s offshore meteoro- logical environment is investigated. The variation patterns of aerodynamic and geometric parameters are obtained, analyzed, and compared with each other. The present method for aerodynamic analysis and its results can form a basis for evaluating aerodynamic performance of large-scale offshore wind turbine rotors.

Mathematical analysis of EEP method for one-dimensional finite element postprocessing

For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has the accuracy O（h^min{2k,k＋4}） The theoretical analysis coincides the reported numerical results.

Emission reduction effects of the green energy investment projects of China in belt and road initiative countries

Investment and construction of power infrastructure are directly related to the achievement of sustainable development goals.China's trade and investment with BRI(Belt and Road Initiative)countries have maintained growth trend.The development and construction of these investment projects certainly have impacts on the economic development mode and sustainable development goals of the countries.On collecting the basic information of the renewable energy investment projects,this paper compares and calculates the current power technology structure and grid emission factors of the host countries,and analyses the carbon emission level of electricity generation from the perspective of the whole life cycle.Making it as the benchmark,this paper also analyzes the current China's invested wind and solar energy projects and the carbon emission reduction benefits to the host country.The results show that at present,China has about 36 renewable energy investment projects in BRI countries,with an installed capacity of 15.75GW(China as the project owner or investor),and achieve at least 48.69M tCO2 emission reduction.This shows that China's effective investment and implementation of the green projects will provide a strong impetus for the energy transformation and the improvement of their energy security in BRI countries.

Mass Production of Fujian's Largest New Energy Lithium-ion Battery Project

In early March,after nearly six months of trial operation,the lithium-ion battery project of Fujian Dynavolt Renewable Energy Technology Co.,Ltd.began mass production in Zhaoan County.This RMB 300 million and260-meter-long production line can

A 3 Billion Yuan Lithium Battery New Energy Vehicle Industrial Cluster Project Landed in Daye

On December 24,a new industrial partner entered the friend circle of new energy vehicle industrial cluster in Daye;a new material project with a total investment of 3 billion yuan held ground-breaking ceremony,signaling its formal landing in Daye.This Project is invested and constructed by Hubei Zhongxing New Advanced Material Co.,Ltd,the Project involves total investment of

Real option-based optimization for financial incentive allocation in infrastructure projects under publicprivate partnerships

Financial incentives that stimulate energy investments under public-private partnerships are considered scarce public resources,which require deliberate allocation to the most economically justified projects to maximize the social benefits.This study aims to solve the financial incentive allocation problem through a real option-based nonlinear integer programming approach.Real option theory is leveraged to determine the optimal timing and the corresponding option value of providing financial incentives.The ambiguity in the evolution of social benefits,the decision-maker’s attitude toward ambiguity,and the uncertainty in social benefits and incentive costs are all considered.Incentives are offered to the project portfolio that generates the maximum total option value.The project portfolio selection is formulated as a stochastic knapsack problem with random option values in the objective flinction and random incentive costs in the probabilistic budget constraint.The linear probabilistic budget constraint is subsequently transformed into a nonlinear deterministic one.Finally,the integer non-linear programming problem is solved,and the optimality gap is computed to assess the quality of the optimal solution.A case study is presented to illustrate how the limited financial incentives can be optimally allocated under uncertainty and ambiguity,which demonstrates the efficacy of the proposed method.