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Direct-to-indirect mapping for optimal low-thrust trajectories

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Astrodynamics 2024年第1期8卷 27-46页

作者： David Ottesen Ryan P.Russell department of aerospace engineering and engineering mechanics The University of Texas at AustinAustinTexas78712USA

Optimal,many-revolution spacecraft trajectories are challenging to solve.A connection is made for a class of models between optimal direct and indirect solutions.For transfers that minimize thrust-acceleration-squared,primer vector theory maps direct,many-impulsive-maneuver trajectories to the indirect,continuous-thrust-acceleration equivalent.The mapping algorithm is independent of how the direct solution is obtained and requires only a solver for a boundary value problem and its partial derivatives.A Lambert solver is used for the two-body problem in this work.The mapping is simple because the impulsive maneuvers and co-states share the same linear space around an optimal trajectory.For numerical results,the direct coast-impulse solutions are demonstrated to converge to the indirect continuous solutions as the number of impulses and segments increases.The two-body design space is explored with a set of three many-revolution,many-segment examples changing semimajor axis,eccentricity,and inclination.The first two examples involve a small change to either semimajor axis or eccentricity,and the third example is a transfer to geosynchronous orbit.Using a single processor,the optimization runtime is seconds to minutes for revolution counts of 10 to 100,and on the order of one hour for examples with up to 500 revolutions.Any of these thrust-acceleration-squared solutions are good candidates to start a homotopy to a higher-fidelity minimization problem with practical constraints.

关键词： direct optimization indirect optimization impulsive maneuvers Lambert's problem two-body dynamics primer vectortheory

硬/软复合材料结构防爆性能的实验及数值评估

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Acta Mechanica Sinica 2022年第1期38卷 27-36页

作者：杨丰源栗志杰庄茁柳占立 Applied mechanics Laboratory Department of Engineering MechanicsSchool of AerospaceTsinghua UniversityBeijing 100084China

现实防护工程中,硬1软复合结构在人员装甲(如头盔的外壳/衬里系统)中的应用可以有效减轻爆炸伤害.由于缺乏有效可靠的实验方法评估防护结构的防爆性能,直接接触型防护结构的发展受到限制,本文针对硬/软复合材料结构的防爆性能测试提出... 详细信息

现实防护工程中,硬1软复合结构在人员装甲(如头盔的外壳/衬里系统)中的应用可以有效减轻爆炸伤害.由于缺乏有效可靠的实验方法评估防护结构的防爆性能,直接接触型防护结构的发展受到限制,本文针对硬/软复合材料结构的防爆性能测试提出一种新的实验及数值评估方法,并对其防爆机理进行了分析.受测的硬/软结构由超高分子量聚乙烯(UHMWPE)复合材料和膨胀聚乙烯(EPE)泡沫组成.现场爆炸试验通过7.0 kg TNT球形炸药在3.8 m处产生的爆炸波来完成.设计了一种压力测试装置用于支撑被测结构并测量穿透防护结构的爆炸压力脉冲.实验结果表明,通过使脉冲波形更平坦、减小压力幅度和延迟脉冲到达时间,硬/软结构可以将爆炸压力脉冲减弱为三角形压力脉冲.7mmUHMWPE复合材料和20mmEPE泡沫的组合防护结构可将爆炸压力振幅降低40%.通过有限元模拟分析爆炸缓解机制.数值结果表明,爆炸压力脉冲的衰减主要发生在硬/软界面上,通过界面反射压力波和软材料层变形吸收动能来完成.在此基础上提出的理论模型可以很好地解释实验和数值结果,对评价和设计高性能的防爆结构具有重要意义.

关键词：防爆结构防爆性能接触型压力脉冲复合材料结构脉冲到达时间爆炸试验复合结构

Study on the prediction and inverse prediction of detonation properties based on deep learning

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Defence Technology（防务技术） 2023年第6期24卷 18-30页

作者： Zi-hang Yang Ji-li Rong Zi-tong Zhao department of mechanics School of Aerospace EngineeringBeijing Institute of TechnologyBeijing100081China

The accurate and efficient prediction of explosive detonation properties has important engineering significance for weapon design.Traditional methods for predicting detonation performance include empirical formulas,equations of state,and quantum chemical calculation methods.In recent years,with the development of computer performance and deep learning methods,researchers have begun to apply deep learning methods to the prediction of explosive detonation performance.The deep learning method has the advantage of simple and rapid prediction of explosive detonation properties.However,some problems remain in the study of detonation properties based on deep learning.For example,there are few studies on the prediction of mixed explosives,on the prediction of the parameters of the equation of state of explosives,and on the application of explosive properties to predict the formulation of explosives.Based on an artificial neural network model and a one-dimensional convolutional neural network model,three improved deep learning models were established in this work with the aim of solving these problems.The training data for these models,called the detonation parameters prediction model,JWL equation of state(EOS)prediction model,and inverse prediction model,was obtained through the KHT thermochemical code.After training,the model was tested for overfitting using the validation-set test.Through the model-accuracy test,the prediction accuracy of the model for real explosive formulations was tested by comparing the predicted value with the reference value.The results show that the model errors were within 10%and 3%for the prediction of detonation pressure and detonation velocity,respectively.The accuracy refers to the prediction of tested explosive formulations which consist of TNT,RDX and HMX.For the prediction of the equation of state for explosives,the correlation coefficient between the prediction and the reference curves was above 0.99.For the prediction of the inverse prediction model,the prediction error of the explosiv

关键词： Deep learning Detonation properties KHT thermochemical Code JWL equation of states Artificial neural network One-dimensional convolutional neural network

A thermal-flutter criterion for an open thin-walled circular cantilever beam subject to solar heating

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Chinese Journal of Aeronautics 2018年第9期31卷 1902-1909页

作者： Xiaode YUAN Zhihai XIANG department of engineering mechanics School of Aerospace EngineeringTsinghua University

The flexible attachments of spacecraft may undergo Thermally Induced Vibration(TIV)on orbit due to the suddenly changed solar heating. The unstable TIV, called thermal-flutter, can cause serious damage to the spacecraft. In this paper, the coupled bending-torsion thermal vibration equations for an open thin-walled circular cantilever beam are established. By analyzing the stability of these equations based on the first Lyapunov method, the thermal-flutter criterion can be obtained. The criterion is very different form that of closed thin-walled beams because the torsion has great impact on the stability of the TIV for open thin-walled beams. Several numerical simulations are conducted to demonstrate that the theoretical predictions agree very well with the finite element results, which mean that the criterion are reliable.

关键词： Fourier finite element Stability criteria Thermal flutter Thermally Induced Vibration（TIV） Thin-walled structures

Generalized covariant differentiation and axiom-based tensor analysis

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Applied Mathematics and mechanics(English Edition) 2016年第3期37卷 379-394页

作者： Yajun YIN department of engineering mechanics School of Aerospace EngineeringTsinghua University

This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

关键词： tensor analysis axiom of covariant form invariability generalized compo-nent generalized covariant differentiation covariant differential transformation group

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅱ):Lagrangian Description

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Acta Mechanica Solida Sinica 2016年第4期29卷 359-370页

作者： Yajun Yin department of engineering mechanics School of Aerospace Engineering Tsinghua University

The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.

关键词： Lagrangian description the postulate of covariant form invariability generalized Lagrangian component generalized covariant derivative with respect to time covariant differential transformation group

Real-time prediction of projectile penetration to laminates by training machine learning models with finite element solver as the trainer

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Defence Technology（防务技术） 2021年第1期17卷 147-160页

作者： Pushkar Wadagbalkar G.R.Liu department of aerospace engineering and engineering mechanics University of CincinnatiCincinnatiOH 45219USA

Studies on ballistic penetration to laminates is complicated,but important for design effective protection of structures.Experimental means of study is expensive and can often be dangerous.Numerical simulation has been an excellent supplement,but the computation is time-consuming.Main aim of this thesis was to develop and test an effective tool for real-time prediction of projectile penetrations to laminates by training a neural network and a decision tree regression model.A large number of finite element models were developed;the residual velocities of projectiles from finite element simulations were used as the target data and processed to produce sufficient number of training samples.Study focused on steel 4340tpolyurea laminates with various configurations.Four different 3D shapes of the projectiles were modeled and used in the training.The trained neural network and decision tree model was tested using independently generated test samples using finite element models.The predicted projectile velocity values using the trained machine learning models are then compared with the finite element simulation to verify the effectiveness of the models.Additionally,both models were trained using a published experimental data of projectile impacts to predict residual velocity of projectiles for the unseen samples.Performance of both the models was evaluated and compared.Models trained with Finite element simulation data samples were found capable to give more accurate predication,compared to the models trained with experimental data,because finite element modeling can generate much larger training set,and thus finite element solvers can serve as an excellent teacher.This study also showed that neural network model performs better with small experimental dataset compared to decision tree regression model.

关键词： Finite element simulations Machine learning Neural networks Impact analysis Protective laminates Projectile Decision tree

Generalized Covariant Derivative with Respect to Time in Flat Space(Ⅰ):Eulerian Description

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Acta Mechanica Solida Sinica 2016年第4期29卷 345-358页

作者： Yajun Yin department of engineering mechanics School of Aerospace EngineeringTsinghua University

This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.

关键词： Eulerian description covariant form invariability generalized Eulerian component generalized covariant derivative with respect to time covariant differential transformation group

The smoothed finite element method (S-FEM):A framework for the design of numerical models for desired solutions

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Frontiers of Structural and Civil engineering 2019年第2期13卷 456-477页

作者： Gui-Rong Liu department of aerospace engineering and engineering mechanics University of CincinnatiCincinnati 45219USA

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

关键词： computational method finite element method smoothed finite element method strain smoothing technique smoothing domain weakened weak form solid mechanics softening effect upper bound solution