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20 August 2019, Volume 41 Issue 4
Review
APPLICATIONS AND CHALLENGES OF STRUCTURAL OPTIMIZATION IN HIGH-SPEED AEROCRAFT 1)
QUAN Dongliang, SHI Guanghui, GUAN Chengqi, WANG Jian, LUO Junhang, SONG Feng, WANG Bo, GAO Tong, ZHU Jihong, ZHANG Weihong
2019, 41(4):  373-381.  doi:10.6052/1000-0879-18-448
Abstract ( 340 )   HTML( 283 )   PDF (2880KB) ( 283 )

With its great national strategic importance and socio-economic benefits, the high-speed vehicle always plays a specific role in the field of aerospace. In this paper, the structural optimization technique and its application in the aircraft design are reviewed firstly. Then, the specific applications of structural optimization techniques in the high-speed vehicle design are then discussed in the context of the typical service environment and the design requirement. We show typical cases subsequently with applications in the concept design of the high-speed vehicle and in the innovative and improved design of their parts over the last years. In view of the solid theoretical foundations as well as the numerous successful engineering practices of the structural optimization, it not only provides an effective tool, but also brings about revolutionary changes for the design of high-speed vehicle structures. It is anticipated that the structural optimization supplemented by the empirical design will surely be a standard procedure for the aircraft design, and the practice-oriented research will undoubtedly enhance the core competitiveness of the aerospace industry in China

Applied Research
2019, 41(4):  382-387.  doi:10.6052/1000-0879-19-086
Abstract ( 167 )   HTML( 72 )   PDF (1386KB) ( 72 )

In view of the fact that the Extend Kalman Filter (EKF) is prone to be divergent in the autonomous navigation by X-ray pulsars, this paper proposes an algorithm utilizing the fading memory filter. Based on the study of the error pattern of the EKF with the increase of iterations, some possible reasons for the divergency are analyzed. The fading memory filter can be used to reduce the peak of error, while delaying the divergence

HEAT-PIPE-COOLED THERMAL PROTECTION FOR THE LEADING EDGE OF THE WING
ZHU Xiaojun, LI Feng, OU Dongbin, CHEN Lianzhong, ZHOU Kai
2019, 41(4):  388-392.  doi:10.6052/1000-0879-18-471
Abstract ( 195 )   PDF (1573KB) ( 60 )
2019, 41(4):  393-397.  doi:10.6052/1000-0879-19-073
Abstract ( 268 )   HTML( 147 )   PDF (1550KB) ( 147 )

When driving on a bend, due to the high gravity center and the heavy load, large trucks or lorries are easy to roll-over if their speed is high. This paper proposes a simplified theoretical model of the roll-over process of a truck during its turning, based on the dynamics analysis. Two critical velocities are defined to evaluate the state of the truck: the tilting critical velocity and the roll-over critical velocity. For a truck of given parameters, the main factors that affect the roll-over process are analyzed, including the weight of the truck, the height of the gravity center, and the turning radius of the road. Finally, some qualitative driving suggestions are given about how to avoid roll-over of large trucks.

SPONTANEOUS CAPILLARY IMBIBITION MODEL IN TIGHT OIL RESERVOIRS 1)
YANG Liu, ZHAO Yiqing, JIANG Rongmin, ZHANG Xuhui, LU Xiaobing
2019, 41(4):  398-404.  doi:10.6052/1000-0879-18-449
Abstract ( 279 )   PDF (328KB) ( 74 )
The fracturing construction shows that the lower flowback efficiency is often accompanied with a high production in tight oil reservoirs, which may be due to the spontaneous imbibition of the fracturing fluid. However, the tight oil reservoir has poor physical properties with a complex permeable mechanism. A spontaneous imbibition model for tight oil reservoirs is desirable. Based on the oil-water flow theory, a mathematical model of the spontaneous imbibition is established. The numerical difference method is used to solve the equations and analyze the influencing factors. The results show that the imbibition volume and the imbibition front position of the tight oil reservoir are linear functions of the square root of time, as is consistent with the prediction of the classical Handy imbibition model. It indicates that the imbibition model is reliable. The numerical results show that the phase diffusion coefficient is the main control parameter of the imbibition rate and has a positive correlation with the imbibition rate. The phase diffusion coefficient increases first and then decreases with the water saturation; it increases with the increase of the irreducible water saturation, and the relative endpoint permeability of the oil and the water; it decreases with the increase of the permeability characteristic index, the oil-water viscosity ratio and the residual oil saturation. The results of this paper can help to understand the fracturing fluid imbibition mechanism in the tight oil reservoirs, and can be used for optimizing the flowback regime and improving the production of the tight oil.
2019, 41(4):  405-415.  doi:10.6052/1000-0879-19-084
Abstract ( 74 )   PDF (489KB) ( 52 )
Based on Gibson's theory for the large-strain consolidation, the governing equations for the void ratio and the excessive pore pressure for the large-strain consolidation of foundation with sand drains are derived by introducing the Hansbo's flow model with consideration of the sedimentary effect of the soil layer. By comparing with the existing research results, the reliability of the proposed method and the equivalence of the two description methods of the large deformation consolidation equation of the sand well foundation are verified. The numerical solutions of the equations are obtained by using the FlexPDE software, then the differences of the consolidation behaviors among the large-strain, the small-strain and the Barron's consolidation are investigated. And the effect of the parameters ($m$ and $I_1$) of the Hansbo's flow model on the consolidation behaviors is analyzed in detail. Finally, the consolidation behaviors of the axisymmetric consolidation, the radial consolidation and the 1D vertical consolidation are compared. The results show that the large-strain consolidation rate with the Hansbo's flow is smaller than that of any other consolidation models, and the average degree of the consolidation of the consolidation models with the Hansbo's flow tends to be the same with a comparatively long time. And the consolidation rate decreases with the increase of the parameters $m$ and $I_1$ and of the Hansbo's flow. Moreover, the difference of the average degree of the consolidation between the axisymmetric consolidation and the radial consolidation increases with the increase of the influence radius of the sand drains, and during the early stage of the consolidation, the consolidation rate of the 1D vertical consolidation is larger than those of the axisymmetric consolidation and the radial consolidation.
2019, 41(4):  416-423.  doi:10.6052/1000-0879-19-117
Abstract ( 85 )   PDF (291KB) ( 74 )
For the problem of buckling and free vibration of piezoelectric/piezomagnetic laminated nano-beams, a mechanical model is established based on the non-local theory and the sinusoidal shear deformation beam theory. The motion equations and the boundary conditions of the laminated beam are derived by the Hamilton's principle. The critical buckling load and the free vibration frequency of the laminated beam are obtained by the numerical method. The numerical results show that the effects of the magneto-electro-elastic interlayer on the buckling and the free vibration of the piezoelectric/piezomagnetic laminated nano-beam cannot be ignored. The volume fraction of the piezoelectric materials or piezomagnetic materials and the thickness of the interlayer are the main influencing factors. The influence analysis can provide a theoretical reference for the application of such materials in engineering.
2019, 41(4):  424-428.  doi:10.6052/1000-0879-19-119
Abstract ( 217 )   PDF (201KB) ( 53 )
This paper analyzes the thermal buckling of the circular plate embedded in an infinite elastic plate. As the temperature changes, the compressive stress will be generated in the circular plate due to the difference of the thermal expansion coefficient between the circular plate and the infinite elastic plate. When the compressive stress reaches the critical value, the thermal buckling will occur. Firstly, based on the theory of the plane stress problem of elasticity, the stress and the displacement of the circular plate and the infinite elastic plate are obtained. Then, the governing differential equation of the thermal buckling of the circular plate is derived. Analytical and numerical solutions of the critical buckling temperature are obtained. The effect of the difference of the material properties between the circular plate and the infinite elastic plate on the critical buckling temperature is discussed.
ULTIMATE STRENGTH OF MENTAL HOOK OF UNIFORM CROSS SECTION
ZHU Tianc, LI Liyun, WANG Hongwei, WEI Mengxi
2019, 41(4):  429-435.  doi:10.6052/1000-0879-19-114
Abstract ( 255 )   PDF (859KB) ( 97 )
In order to study the stress distribution and the ultimate strength of the hook of uniform cross section subjected to load, a stress distribution model of the hook is established as a curved beam. The numerical method of ANSYS is used to test the theoretical solution of the hook, which also helps to identify the dangerous section. Three failure principles are established based on the displacement, the limit of elasticity and the principle of plastic design, providing a theoretical basis for the factory to produce hooks of different sizes under different ultimate loads.
2019, 41(4):  436-441.  doi:10.6052/1000-0879-19-072
Abstract ( 166 )   PDF (239KB) ( 78 )
The motion by the inertia force of an eccentric rotor is affected by the ground friction, as is different from the theoretical results of the smooth case. If the inertia force of the rotor rotating in the counter-clockwise direction uniformly is less than the total weight of the component, the base will be in four states with the increase of the friction factor: the continuous state, the one-stop state, the two-stop vibration state and the completely static state. Due to the influence of inertia force on the normal pressure and the friction force as well, the displacement of the base to the right direction is larger than that to the left direction, when the vibration is continuous and stopping for one time. When the base of the eccentric rotor jumps up, it moves to the left just like a frog rammer''.
Research on Education
2019, 41(4):  442-444.  doi:10.6052/1000-0879-19-185
Abstract ( 205 )   HTML( 84 )   PDF (252KB) ( 84 )

This is the preface to Calculus II, a textbook to be published by Peking University Press. We explore the purpose and the pedagogy for teaching calculus in theoretical and applied mechanics curriculun.

2019, 41(4):  445-448.  doi:10.6052/1000-0879-18-486
Abstract ( 576 )   HTML( 273 )   PDF (239KB) ( 273 )

The stress transformation formula, which is also called the Cauchy's formula for stresses on slanted surfaces, is widely used in solid mechanics. No explicit statement has been found on its limitations in application. The stresses at the sharp point of a V-shaped free-surface notch on a bar under axial loading at both ends are examined as an example. With the two intersecting surfaces being free, it is deduced from the transformation equations that the sharp point is stress free. This deduction is however contradictory to the fact that the stress concentrates near the sharp point. Clearly the stress transformation formula leads to incorrect results and thus is not valid at that sharp point. It is known that if the stress transformation formula is valid, the stress components constitute a stress tensor, but the stress at the sharp concave corner is shown to be discontinuous and double-valued. It is further pointed out that stress transformation formula is not applicable to any point where a stress component has discontinuity or lacks of uniqueness at a surface passing through that point. The tip of any crack is the case.

2019, 41(4):  449-452.  doi:10.6052/1000-0879-19-035
Abstract ( 313 )   PDF (2852KB) ( 143 )
The principle of virtual work is used to better understand the role of support reactions in the appliction of Castigliano theorem. The essencial explanation is made to the question why the support reactions should be considered to be independent varibles in statically determinate structures, while they can be regarded as either independent or dependent varibles in statically indeterminate structures. This paper may help to learn the nature of Castigliano theorem besides using it freely.
TORSIONAL CENTER OF BEAMS OF ARBITRARY COMPLEX CROSS-SECTION 1)
LU Xiaoming*, 2), CAO Hai, GONG Yaoqing
2019, 41(4):  453-457.  doi:10.6052/1000-0879-18-453
Abstract ( 194 )   PDF (234KB) ( 69 )
In order to determine the position of the torsional center of a beam of arbitrary complex non-circular section, the shape of all the out-of-plane deformation of the beam of non-circular section caused by non-uniform torsion is expressed by the nodal-line method as a family of surfaces containing unknown functions of the nodal lines. After establishing the governing equations of the beam caused by its non-uniform torsion, the numerical solutions of these unknown functions are obtained by using an ODE (ordinary differential equation) solver for a torque and a transverse load separately. Finally, the position of the torsional center of the beam of a complex cross section is derived by using the principle of stiffness equivalence. The computational results of examples show that the method is reliable for computing the torsional center position of a beam of arbitrary complex non-circular section.
2019, 41(4):  458-462.  doi:10.6052/1000-0879-19-032
Abstract ( 202 )   PDF (155KB) ( 106 )
The uniqueness law of solution is the theoretical basis of the inverse method or the semi- inverse method for solving elasticity problems. The stress function method, the stress method and the stress sum function method are used for solving plane problems of elasticity to let students understand the true meaning of the uniqueness law of solution, and to enrich the solution methods and enlarge the application scope of elasticity.
2019, 41(4):  463-469.  doi:10.6052/1000-0879-18-489
Abstract ( 227 )   PDF (693KB) ( 85 )
The finite element simulation is now an important link in the engineering education for students majored in mechanics and mechanical engineering. This paper proposes a heuristic and example-driven method for teaching the finite element simulation courses. Through the practice of a teaching case of stretching a rectangular plate with a central hole, the contents and the key points of the example-driven method are illustrated in details. The incarnation of heuristics in the activities of teaching this example is discussed. Based on the teaching practice in Tongji University, the effectiveness of the proposed teaching method is demonstrated.
2019, 41(4):  470-474.  doi:10.6052/1000-0879-18-504
Abstract ( 144 )   PDF (1196KB) ( 65 )
With the reform of college enrolment policy based on the specialty categories, the recruitment of students majored in mechanics becomes difficult, which implies the quality and quantity of students both decline. This is really harmful to the overall development of mechanics. In this paper, the problem is explored from three aspects, i.e. the current situation, the advantages of mechanics, and the recruitment practice. Some methods and suggestions are proposed to solve this problem according to our experiences in recent years.
THE NEW ASSESSMENT METHOD FOR THE COURSE OF STRENGTH OF MATERIALS 1)
WU Mengmeng, YANG Shaohong, ZHANG Xiangming
2019, 41(4):  475-477.  doi:10.6052/1000-0879-19-002
Abstract ( 228 )   PDF (186KB) ( 73 )
The existing assessment methods focus on the final exam and ignore the process assessment. For the course of strength of materials, a new evaluation system is explored, that emphasizes the process evaluation to comprehensively evaluate students' mastery of the course. That is to reduce the proportion of the final exam grade in the overall evaluation from 70% to 50% , and the after-class homework, quizzes, module tests, laboratory tests and case studies each accounts for 10% . The new assessment method pays more attention to the assessment of the students' learning process, so that the students can maintain a high degree of tension throughout the course of learning, the timeliness and the purpose of learning can be improved, and thereby, the enthusiasm of learning the course and the classroom teaching effect are improved.
The Field of Mechanics
2019, 41(4):  478-482.  doi:10.6052/1000-0879-18-343
Abstract ( 244 )   HTML( 115 )   PDF (6287KB) ( 115 )

In the appreciation of the ancient poem for dragonflies, we discuss the magical hydrodynamic characteristics of dragonflies, which have evolved for hundreds of millions of years. The dragonfly's compound eye, the wings' ability of eliminating chatter, the superhydrophobicity of its epidermis, the drag reduction by its scales, and the mechanical characteristics of the water-jet propulsion of the dragonfly larvae; and their inspiration to the development of engineering technology are discussed. At the same time, the development status of the dragonfly robots is introduced as well.

2019, 41(4):  483-487.  doi:10.6052/1000-0879-18-051
Abstract ( 1336 )   HTML( 421 )   PDF (1460KB) ( 421 )

In this paper, the paper folding problem is simplified to a three-point bending model of a simply supported beam with a rectangular cross section under the concentrated force acting on the middle position. The maximal folding times of a sheet of A4 printing paper and octavo newspaper under a normal human force are related with the maximum bending deflections and the minimum folding loads. The results show that for an ordinary A4 printing paper, an adult can only fold 6 times, or up to 7 times under extreme circumstances. For an octavo newspaper, an adult can easily fold 7 times, but not 8 times. The test results are in good agreement with the theoretical predictions.

2019, 41(4):  488-497.  doi:10.6052/1000-0879-19-283
Abstract ( 335 )   HTML( 347 )   PDF (2852KB) ( 347 )

The China Trajectory Optimization Competition (CTOCorganized by The Chinese Society of Theoretical and Applied Mechanics, has been successfully held for ten years since its initiation in 2009. With unremitting efforts during the past ten years, CTOC has become a communication platform for domestic universities and research institutions on space trajectory design and optimization research. It not only identifies research talents for space exploration, but also provides knowledge and ideas for this field. This article reviews the development history and achievements of CTOC following the timeline from 2009 to 2019, and summarizes the main features and innovations of the competition.

2019, 41(4):  498-504.  doi:10.6052/1000-0879-19-292
Abstract ( 345 )   HTML( 152 )   PDF (7000KB) ( 152 )

The 10th Global Trajectory Optimisation Competition hosted by Jet Propulsion Laboratory (JPL) came to an end in June 2019, and the Chinese team won the championship for the first time. For the first time in history, this competition is based on the sci-fi mission, designing the optimal orbit to settle in 100000 Milky Way stars. This paper introduces the tasks, gravity model and spacecraft maneuver model of the Galaxy settlement mission, and analyzes the merit function of this competition specifically. The tree structure is introduced to represent the settlement solution, and the design method of the initial settler distribution is described. Simultaneously, the forward and reverse tree generation strategies are introduced and compared. The methods of local optimization and topology reconstruction of settlement trees used in the competition are briefly introduced. In the galaxy-s stars map, the champion solution was presented in tree structures. The significance of this competition was summarized and some useful inspirations were obtained.