Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the random...Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.展开更多
This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So...This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.展开更多
A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous H...A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and e...This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.展开更多
A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysi...A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.展开更多
Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DN...Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis.展开更多
This study pioneers the integrated fabrication of magnesium corrugated-core sandwich structures using wire-arc directed energy deposition(WA-DED).Two sandwich structures—V-type and X-type—were designed with optimize...This study pioneers the integrated fabrication of magnesium corrugated-core sandwich structures using wire-arc directed energy deposition(WA-DED).Two sandwich structures—V-type and X-type—were designed with optimized deposition paths to achieve comparable grain morphology while enhancing strength.The compression properties and failure modes of the two corrugated-core sandwich structures were examined through quasi-static compression tests.Results showed that the V-type structure exhibited a higher specific compressive strength(93 MPa∙cm^(3)/g)than the X-type structure(72 MPa∙cm^(3)/g).Both finite element analysis and experimental compression tests indicated that failure occurred at the midsection of the corrugated core.This work offers valuable insights for the efficient fabrication of high-strength corrugated-core sandwich structures.展开更多
Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat...Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat systems(IEHS).While synergies in the electricity-heat market are known to enhance economic efficiency,it is hard to achieve cooperative operation due to the inherent differences among participants of IEHS and the absence of an incentive-compatible mechanism.To address this challenge,this paper proposes a Nash bargaining-based cooperative operation strategy for IEHS with AA-CAES.First,a cooperative alliance framework based on the Nash bargaining is proposed to optimize energy trading.Second,to overcome computational complexity,the non-convex,nonlinear Nash bargaining problem is decomposed into a two-stage optimization approach.In the first stage,a joint planning model maximizes the total profit of the alliance,determining the optimal energy interaction for each participant.In the second stage,a subsequent model ensures fair profit distribution by optimizing pricing and benefit-sharing mechanisms.Subsequently,a distributed solution strategy based on the self-adaptive alternating direction method of multipliers is utilized to preserve operator privacy and improve computational efficiency.Finally,case studies demonstrate that within the electricity-heat co-supply mode,the daily profit of AA-CAES can improve by approximately 4137.45 CNY.Meanwhile,through the proposed cooperative strategy,participants in the IEHS can obtain greater profits,which validates the effectiveness of this strategy.展开更多
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By...A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.展开更多
This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservatio...This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.展开更多
A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was ...A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.展开更多
This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time...This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.展开更多
The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode su...The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.展开更多
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ...Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.展开更多
A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a trunc...A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.展开更多
We develop a new procedure to improve the angular resolution of coded-mask telescopes by the Direct Demodulation Method （DDM）. DDM has been applied to both real and simulated data of INTEGRAL/IBIS. The angular resol...We develop a new procedure to improve the angular resolution of coded-mask telescopes by the Direct Demodulation Method （DDM）. DDM has been applied to both real and simulated data of INTEGRAL/IBIS. The angular resolution of IBIS/ISGRI has been improved from about 13＇ to 2＇.展开更多
基金supports of the National Natural Science Foundation of China(Nos.12032008,12102080)the Fundamental Research Funds for the Central Universities,China(No.DUT23RC(3)038)are much appreciated。
文摘Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.
基金Project supported by the Natural Science Foundation of China(10371009)Research Fund for the Doctoral Program Higher Education
文摘This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.
文摘A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
基金This work was supported by The National Key R&D Program of China(Grant No.2017YFC0804601)the National Natural Science Foundation of China(No.51741410)Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z017017).
文摘This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.
文摘A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.
基金National Natural Science Foundation of China(Nos.11262014,11962021 and 51965051)Inner Mongolia Natural Science Foundation,China(No.2019MS05064)+1 种基金Inner Mongolia Earthquake Administration Director Fund Project,China(No.2019YB06)Inner Mongolia University of Technology Foundation,China(No.2020015)。
文摘Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis.
基金supported by JCKY Project(Grant No.JCKY2023602B012).
文摘This study pioneers the integrated fabrication of magnesium corrugated-core sandwich structures using wire-arc directed energy deposition(WA-DED).Two sandwich structures—V-type and X-type—were designed with optimized deposition paths to achieve comparable grain morphology while enhancing strength.The compression properties and failure modes of the two corrugated-core sandwich structures were examined through quasi-static compression tests.Results showed that the V-type structure exhibited a higher specific compressive strength(93 MPa∙cm^(3)/g)than the X-type structure(72 MPa∙cm^(3)/g).Both finite element analysis and experimental compression tests indicated that failure occurred at the midsection of the corrugated core.This work offers valuable insights for the efficient fabrication of high-strength corrugated-core sandwich structures.
基金supported in part by the National Natural Science Foundation of China(No.52407115)State Key Laboratory of Power System Operation and Control(61011000223).
文摘Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat systems(IEHS).While synergies in the electricity-heat market are known to enhance economic efficiency,it is hard to achieve cooperative operation due to the inherent differences among participants of IEHS and the absence of an incentive-compatible mechanism.To address this challenge,this paper proposes a Nash bargaining-based cooperative operation strategy for IEHS with AA-CAES.First,a cooperative alliance framework based on the Nash bargaining is proposed to optimize energy trading.Second,to overcome computational complexity,the non-convex,nonlinear Nash bargaining problem is decomposed into a two-stage optimization approach.In the first stage,a joint planning model maximizes the total profit of the alliance,determining the optimal energy interaction for each participant.In the second stage,a subsequent model ensures fair profit distribution by optimizing pricing and benefit-sharing mechanisms.Subsequently,a distributed solution strategy based on the self-adaptive alternating direction method of multipliers is utilized to preserve operator privacy and improve computational efficiency.Finally,case studies demonstrate that within the electricity-heat co-supply mode,the daily profit of AA-CAES can improve by approximately 4137.45 CNY.Meanwhile,through the proposed cooperative strategy,participants in the IEHS can obtain greater profits,which validates the effectiveness of this strategy.
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
基金National Natural Science Foundation of China under Grant No.11372084
文摘A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001 the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.
基金Project supported by the Department of Industrial and Systems Engineering,The Hong Kong Polytechnic University (No.1-45-56-0000).
文摘A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.NRF-2020R1A2C2011955)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(No.2020R1A6A1A03046811)。
文摘This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.
文摘The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.
基金Project supported by the National Natural Science Foundation of China (No.10432030).
文摘Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.
文摘A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.
基金National Natural Science Foundation of China (10603004).
文摘We develop a new procedure to improve the angular resolution of coded-mask telescopes by the Direct Demodulation Method （DDM）. DDM has been applied to both real and simulated data of INTEGRAL/IBIS. The angular resolution of IBIS/ISGRI has been improved from about 13＇ to 2＇.
