In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh...In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.展开更多
Lightweight porous materials with high load-bearing,damage tolerance and energy absorption(EA)as well as intelligence of shape recovery after material deformation are beneficial and critical for many applications,e.g....Lightweight porous materials with high load-bearing,damage tolerance and energy absorption(EA)as well as intelligence of shape recovery after material deformation are beneficial and critical for many applications,e.g.aerospace,automobiles,electronics,etc.Cuttlebone produced in the cuttlefish has evolved vertical walls with the optimal corrugation gradient,enabling stress homogenization,significant load bearing,and damage tolerance to protect the organism from high external pressures in the deep sea.This work illustrated that the complex hybrid wave shape in cuttlebone walls,becoming more tortuous from bottom to top,creates a lightweight,load-bearing structure with progressive failure.By mimicking the cuttlebone,a novel bionic hybrid structure(BHS)was proposed,and as a comparison,a regular corrugated structure and a straight wall structure were designed.Three types of designed structures have been successfully manufactured by laser powder bed fusion(LPBF)with NiTi powder.The LPBF-processed BHS exhibited a total porosity of 0.042% and a good dimensional accuracy with a peak deviation of 17.4μm.Microstructural analysis indicated that the LPBF-processed BHS had a strong(001)crystallographic orientation and an average size of 9.85μm.Mechanical analysis revealed the LPBF-processed BHS could withstand over 25000 times its weight without significant deformation and had the highest specific EA value(5.32 J·g^(−1))due to the absence of stress concentration and progressive wall failure during compression.Cyclic compression testing showed that LPBF-processed BHS possessed superior viscoelastic and elasticity energy dissipation capacity.Importantly,the uniform reversible phase transition from martensite to austenite in the walls enables the structure to largely recover its pre-deformation shape when heated(over 99% recovery rate).These design strategies can serve as valuable references for the development of intelligent components that possess high mechanical efficiency and shape memory capabilities.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement i...A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.展开更多
Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain anal...Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.展开更多
A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic...A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange's approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.展开更多
Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.
We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions....We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.The main results show that the shape preserving approxi- mation has close relation to the shape preserving extension.One of our main results shows that if f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximated by polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap- proximation is Cω(f,n^(-β))with constants C,β>0.展开更多
In this paper, two new efficient fully nonconforming polynomial finite element methods on arbitrary convex quadrilaterals are constructed to solve the Brinkman problem. Both elements have 12 local degrees of freedom a...In this paper, two new efficient fully nonconforming polynomial finite element methods on arbitrary convex quadrilaterals are constructed to solve the Brinkman problem. Both elements have 12 local degrees of freedom and are uniformly first-order convergent. For the first element, we carefully design a shape function space of only degree four, which is convenient for practical computation. Meanwhile, the velocity solution obtained by our second element has O(h^(2)) convergence order in the case of Darcy limit. These new elements can be regarded as modifications of a known element to effectively improve the computational efficiency, only the shape function space is properly changed. We verify our theoretical findings by numerical examples.展开更多
翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function tr...翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function transformation)翼型参数化方法对Kriging模型的预测精度进行研究,并采用改进的粒子群优化算法构建气动优化设计系统。某亚声速机翼单点减阻设计及超临界翼型的稳健性设计表明该系统具有较高的设计质量,方法可靠,有较高的工程应用前景。展开更多
A novel envelope design for an envelope tracking(ET)power amplifier(PA)based on its derivatives is proposed,which can trade well off between bandwidth reduc-tion and tracking accuracy.This paper theoretically analyzes...A novel envelope design for an envelope tracking(ET)power amplifier(PA)based on its derivatives is proposed,which can trade well off between bandwidth reduc-tion and tracking accuracy.This paper theoretically analyzes how to choose an envelope design that can track the original envelope closely and reduce its bandwidth,and then demonstrates an example to validate this idea.The generalized memory polynomial(GMP)model is applied to compensate for the nonlinearity of ET PA with the proposed envelope design.Experiments are carried out on an ET system that is operated with the center fre-quency of 3.5 GHz and excited by a 20 MHz LTE signal,which show that the proposed en-velope design can make a good trade-off between envelope bandwidth and efficiency,and satisfactory linearization performance can be realized.展开更多
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 ele...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.展开更多
The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformatio...The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.展开更多
Based on the Joukowsky transformation and Theodorsen method, a novel parametric function （shape function） for wind turbine airfoils has been developed. The airfoil design space and shape control equations also have ...Based on the Joukowsky transformation and Theodorsen method, a novel parametric function （shape function） for wind turbine airfoils has been developed. The airfoil design space and shape control equations also have been studied. Results of the analysis of a typical wind turbine airfoil are shown to illustrate the evaluation process and to demonstrate the rate of convergence of the geometric characteristics. The coordinates and aerodynamic performance of approximate airfoils is rapidly close to the baseline airfoil corresponding to increasing orders of polynomial. Comparison of the RFOIL prediction and experimental results for the baseline airfoil generally show good agreement. A universal method for three-dimensional blade integration-＂ Shape function/Distribution function＂ is presented. By changing the parameters of shape function and distribution functions, a three dimensional blade can be designed and then transformed into the physical space in which the actual geometry is defined. Application of this method to a wind turbine blade is presented and the differences of power performance between the represented blade and original one are less than 0. 5%. This method is particularly simple and convenient for bodies of streamline forms.展开更多
A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement s...A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level （RL） to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.展开更多
Ni51Ti49 at.%bulk was additively manufactured by laser-directed energy deposition(DED)to reveal the microstructure evolution,phase distribution,and mechanical properties.It is found that the localized remelting,reheat...Ni51Ti49 at.%bulk was additively manufactured by laser-directed energy deposition(DED)to reveal the microstructure evolution,phase distribution,and mechanical properties.It is found that the localized remelting,reheating,and heat accumulation during DED leads to the spatial heterogeneous distribution of columnar crystal and equiaxed crystal,a gradient distribution of Ni4Ti3 precipitates along the building direction,and preferential formation of Ni4Ti3 precipitates in the columnar zone.The austenite transformation finish temperature(Af)varies from-12.65℃(Z=33 mm)to 60.35℃(Z=10 mm),corresponding to tensile yield strength(σ0.2)changed from 120±30 MPa to 570±20 MPa,and functional properties changed from shape memory effect to superelasticity at room temperature.The sample in the Z=20.4 mm height has the best plasticity of 9.6%and the best recoverable strain of 4.2%.This work provided insights and guidelines for the spatial characterization of DEDed NiTi.展开更多
The pull-in instability of a cantilever nano-actuator model incorporating the effects of the surface, the fringing field, and the Casimir attraction force is investigated. A new quartic polynomial is proposed as the s...The pull-in instability of a cantilever nano-actuator model incorporating the effects of the surface, the fringing field, and the Casimir attraction force is investigated. A new quartic polynomial is proposed as the shape function of the beam during the deflection, satisfying all of the four boundary values. The Gaussian quadrature rule is used to treat the involved integrations, and the design parameters are preserved in the evaluated formulas. The analytic expressions are derived for the tip deflection and pull-in parameters of the cantilever beam. The micro-electromechanical system （MEMS） cantilever actuators and freestanding nano-actuators are considered as two special cases. It is proved that the proposed method is convenient for the analyses of the effects of the surface, the Casimir force, and the fringing field on the pull-in parameters.展开更多
Abstract Reactivity measurement is an essential part of a zero-power physics test,which is critical to reactor design and development.The rod drop experimental technique is used to measure the control rod worth in a z...Abstract Reactivity measurement is an essential part of a zero-power physics test,which is critical to reactor design and development.The rod drop experimental technique is used to measure the control rod worth in a zero-power physics test.The conventional rod drop experimental technique is limited by the spatial effect and the difference between the calculated static reactivity and measured dynamic reactivity;thus,the method must be improved.In this study,a modified rod drop experimental technique that constrains the detector neutron flux shape function based on three-dimensional space–time dynamics to reduce the reactivity perturbation and a new method for calculating the detector neutron flux shape function are proposed.Correction factors were determined using Monte Carlo N-particle transport code and transient analysis code for a pressurized water reactor at the Ulsan National Institute of Science and Technology and Xi’an Jiaotong University,and a large reactivity of over 2000 pcm was measured using the modified technique.This research evaluated the modified technique accuracy,studied the influence of the correction factors on the modification,and investigated the effect of constraining the shape function on the reactivity perturbation reduction caused by the difference between the calculated neutron flux and true value,using the new method to calculate the shape function of the detector neutron flux and avoiding the neutron detector response function(weighting factor)calculation.展开更多
Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is ...Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.展开更多
In the exploitation of ocean oil and gas, many offshore structures may be damaged due to the severe environment, so an effective method of diagnosing structural damage is urgently needed to locate the damage and evalu...In the exploitation of ocean oil and gas, many offshore structures may be damaged due to the severe environment, so an effective method of diagnosing structural damage is urgently needed to locate the damage and evaluate its severity. Genetic algorithms have become some of the most important global optimization tools and been widely used in many fields in recent years because of their simple operation and strong robustness. Based on the natural frequencies and mode shapes of the structure, the damage diagnosis of a jacket offshore platform is attributed to an optimization problem and studied by using a genetic algorithm. According to the principle that the structural stiffness of a certain direction can be greatly affected only when the brace bar in the corresponding direction is damaged, an improved objective function was proposed in this paper targeting measurement noise and the characteristics of modal identification for offshore platforms. This function can be used as fitness function of a genetic algorithm, and both numerical simulation and physical model test results show that the improved method may locate the structural damage and evaluate the severity of a jacket offshore platform satisfactorily while improving the robustness of evolutionary searching and the reliability of damage diagnosis.展开更多
文摘In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.
基金supported by the National Natural Science Foundation of China(Grant No.52225503)National Key Research and Development Program of China(Grant No.2022YFB3805701)+1 种基金Development Program of Jiangsu Province(Grant Nos.BE2022069 and BE2022069-1)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX21-0207).
文摘Lightweight porous materials with high load-bearing,damage tolerance and energy absorption(EA)as well as intelligence of shape recovery after material deformation are beneficial and critical for many applications,e.g.aerospace,automobiles,electronics,etc.Cuttlebone produced in the cuttlefish has evolved vertical walls with the optimal corrugation gradient,enabling stress homogenization,significant load bearing,and damage tolerance to protect the organism from high external pressures in the deep sea.This work illustrated that the complex hybrid wave shape in cuttlebone walls,becoming more tortuous from bottom to top,creates a lightweight,load-bearing structure with progressive failure.By mimicking the cuttlebone,a novel bionic hybrid structure(BHS)was proposed,and as a comparison,a regular corrugated structure and a straight wall structure were designed.Three types of designed structures have been successfully manufactured by laser powder bed fusion(LPBF)with NiTi powder.The LPBF-processed BHS exhibited a total porosity of 0.042% and a good dimensional accuracy with a peak deviation of 17.4μm.Microstructural analysis indicated that the LPBF-processed BHS had a strong(001)crystallographic orientation and an average size of 9.85μm.Mechanical analysis revealed the LPBF-processed BHS could withstand over 25000 times its weight without significant deformation and had the highest specific EA value(5.32 J·g^(−1))due to the absence of stress concentration and progressive wall failure during compression.Cyclic compression testing showed that LPBF-processed BHS possessed superior viscoelastic and elasticity energy dissipation capacity.Importantly,the uniform reversible phase transition from martensite to austenite in the walls enables the structure to largely recover its pre-deformation shape when heated(over 99% recovery rate).These design strategies can serve as valuable references for the development of intelligent components that possess high mechanical efficiency and shape memory capabilities.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金supported by the Fulbright Colombia-Colciencias Scholarship and Universidad Militar Nueva Granada
文摘A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.
文摘Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.
基金Project(51105017)supported by National Natural Science Foundation of ChinaProject(2011BAG09B00)supported by the National Science and Technology Support Program,ChinaProject(2010DFB80020)supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China
文摘A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange's approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.
文摘Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.
文摘We establish the concept of shapes of functions by using partial differential inequalites. Our definition about shapes includes some usual shapes such as convex,subharmonic,etc.,and gives many new shapes of functions.The main results show that the shape preserving approxi- mation has close relation to the shape preserving extension.One of our main results shows that if f∈C(Ω)has some shape defined by our definition,then f can be uniformly approximated by polynomials P_n ∈p_n(n∈N)which have the same shape in Ω,and the degree of the ap- proximation is Cω(f,n^(-β))with constants C,β>0.
基金Supported by the National Natural Science Foundation of China(Grant No.12201254)。
文摘In this paper, two new efficient fully nonconforming polynomial finite element methods on arbitrary convex quadrilaterals are constructed to solve the Brinkman problem. Both elements have 12 local degrees of freedom and are uniformly first-order convergent. For the first element, we carefully design a shape function space of only degree four, which is convenient for practical computation. Meanwhile, the velocity solution obtained by our second element has O(h^(2)) convergence order in the case of Darcy limit. These new elements can be regarded as modifications of a known element to effectively improve the computational efficiency, only the shape function space is properly changed. We verify our theoretical findings by numerical examples.
文摘翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function transformation)翼型参数化方法对Kriging模型的预测精度进行研究,并采用改进的粒子群优化算法构建气动优化设计系统。某亚声速机翼单点减阻设计及超临界翼型的稳健性设计表明该系统具有较高的设计质量,方法可靠,有较高的工程应用前景。
文摘A novel envelope design for an envelope tracking(ET)power amplifier(PA)based on its derivatives is proposed,which can trade well off between bandwidth reduc-tion and tracking accuracy.This paper theoretically analyzes how to choose an envelope design that can track the original envelope closely and reduce its bandwidth,and then demonstrates an example to validate this idea.The generalized memory polynomial(GMP)model is applied to compensate for the nonlinearity of ET PA with the proposed envelope design.Experiments are carried out on an ET system that is operated with the center fre-quency of 3.5 GHz and excited by a 20 MHz LTE signal,which show that the proposed en-velope design can make a good trade-off between envelope bandwidth and efficiency,and satisfactory linearization performance can be realized.
基金the National Natural Science Foundation of China(No.50678093)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.51375424)
文摘The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.
基金Supported by the National Natural Science Foundation of China （ No. 50775227 ） and the Natural Science Foundation of Chongqing （ No. CSTC, 2008BC3029）.
文摘Based on the Joukowsky transformation and Theodorsen method, a novel parametric function （shape function） for wind turbine airfoils has been developed. The airfoil design space and shape control equations also have been studied. Results of the analysis of a typical wind turbine airfoil are shown to illustrate the evaluation process and to demonstrate the rate of convergence of the geometric characteristics. The coordinates and aerodynamic performance of approximate airfoils is rapidly close to the baseline airfoil corresponding to increasing orders of polynomial. Comparison of the RFOIL prediction and experimental results for the baseline airfoil generally show good agreement. A universal method for three-dimensional blade integration-＂ Shape function/Distribution function＂ is presented. By changing the parameters of shape function and distribution functions, a three dimensional blade can be designed and then transformed into the physical space in which the actual geometry is defined. Application of this method to a wind turbine blade is presented and the differences of power performance between the represented blade and original one are less than 0. 5%. This method is particularly simple and convenient for bodies of streamline forms.
基金financial support by the Open Foundation of Chongqing Key Laboratory of Geomechanics and Geoenvironment Protection(Logistical Engineering University)(No.GKLGGP 2013-02)
文摘A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level （RL） to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.
基金the financial support of the Hunan Innovation Platform and Talent Plan(2022RC3033)Natural Science Foundation of Shandong Province(ZR2020ZD04)Ganzhou Science and Technology Planning Project(Grant No.Ganshikefa[2019]60)。
文摘Ni51Ti49 at.%bulk was additively manufactured by laser-directed energy deposition(DED)to reveal the microstructure evolution,phase distribution,and mechanical properties.It is found that the localized remelting,reheating,and heat accumulation during DED leads to the spatial heterogeneous distribution of columnar crystal and equiaxed crystal,a gradient distribution of Ni4Ti3 precipitates along the building direction,and preferential formation of Ni4Ti3 precipitates in the columnar zone.The austenite transformation finish temperature(Af)varies from-12.65℃(Z=33 mm)to 60.35℃(Z=10 mm),corresponding to tensile yield strength(σ0.2)changed from 120±30 MPa to 570±20 MPa,and functional properties changed from shape memory effect to superelasticity at room temperature.The sample in the Z=20.4 mm height has the best plasticity of 9.6%and the best recoverable strain of 4.2%.This work provided insights and guidelines for the spatial characterization of DEDed NiTi.
基金supported by the National Natural Science Foundation of China(No.11201308)the Natural Science Foundation of Shanghai(No.14ZR1440800)the Innovation Program of the Shanghai Municipal Education Commission(No.14ZZ161)
文摘The pull-in instability of a cantilever nano-actuator model incorporating the effects of the surface, the fringing field, and the Casimir attraction force is investigated. A new quartic polynomial is proposed as the shape function of the beam during the deflection, satisfying all of the four boundary values. The Gaussian quadrature rule is used to treat the involved integrations, and the design parameters are preserved in the evaluated formulas. The analytic expressions are derived for the tip deflection and pull-in parameters of the cantilever beam. The micro-electromechanical system （MEMS） cantilever actuators and freestanding nano-actuators are considered as two special cases. It is proved that the proposed method is convenient for the analyses of the effects of the surface, the Casimir force, and the fringing field on the pull-in parameters.
文摘Abstract Reactivity measurement is an essential part of a zero-power physics test,which is critical to reactor design and development.The rod drop experimental technique is used to measure the control rod worth in a zero-power physics test.The conventional rod drop experimental technique is limited by the spatial effect and the difference between the calculated static reactivity and measured dynamic reactivity;thus,the method must be improved.In this study,a modified rod drop experimental technique that constrains the detector neutron flux shape function based on three-dimensional space–time dynamics to reduce the reactivity perturbation and a new method for calculating the detector neutron flux shape function are proposed.Correction factors were determined using Monte Carlo N-particle transport code and transient analysis code for a pressurized water reactor at the Ulsan National Institute of Science and Technology and Xi’an Jiaotong University,and a large reactivity of over 2000 pcm was measured using the modified technique.This research evaluated the modified technique accuracy,studied the influence of the correction factors on the modification,and investigated the effect of constraining the shape function on the reactivity perturbation reduction caused by the difference between the calculated neutron flux and true value,using the new method to calculate the shape function of the detector neutron flux and avoiding the neutron detector response function(weighting factor)calculation.
基金supported by the China Aviation Industry Corporation I Program (ATPD-1104-02).
文摘Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.
基金Supported by the National Natural Science Fundation of China (51079136)(51179179)
文摘In the exploitation of ocean oil and gas, many offshore structures may be damaged due to the severe environment, so an effective method of diagnosing structural damage is urgently needed to locate the damage and evaluate its severity. Genetic algorithms have become some of the most important global optimization tools and been widely used in many fields in recent years because of their simple operation and strong robustness. Based on the natural frequencies and mode shapes of the structure, the damage diagnosis of a jacket offshore platform is attributed to an optimization problem and studied by using a genetic algorithm. According to the principle that the structural stiffness of a certain direction can be greatly affected only when the brace bar in the corresponding direction is damaged, an improved objective function was proposed in this paper targeting measurement noise and the characteristics of modal identification for offshore platforms. This function can be used as fitness function of a genetic algorithm, and both numerical simulation and physical model test results show that the improved method may locate the structural damage and evaluate the severity of a jacket offshore platform satisfactorily while improving the robustness of evolutionary searching and the reliability of damage diagnosis.
