Stability of equilibrium of several simple floating bodies and ship models was investigated, and the maximal allowed external torque for ship models was analyzed and calculated. The analysis and calculation procedure was generalized and applied to real ships of any shapes. This may help to improve ship design. 6 criteria for stable equilibrium of floating bodies were compared, and the advantage and limitation for each as well as their possible relations were pointed out. This helps to clarify some basic concepts and may benefit teaching and research in this field.

In this paper, we adopt machine learning techniques to design artificial boundary conditions for one-dimensional linear atomic chain. Training a feedforward neural network with a small amount of numerical solutions, we obtain artificial boundary conditions. This approach requires little prior information, and programming and computation are fast. Numerical examples illustrate a relatively small reflection.

Measurement of the angular velocity of flight vehicles is one of the most important problem in the aerospace field. However, the gyroscope, as the dominating measuring device for the angular velocity measurement, is expensive. In this paper, a method for obtaining the angular velocity of the rigid body is proposed, based on measuring the accelerations of three non-collinear points. The angular velocity is calculated by using the base-point method in mechanics of rigid bodies, and the errors of the angular velocity are also analyzed. In order to validate the new model, a numerical simulation is carried out to analyze the applicability of this method for a spacecraft in the high angular velocity situation or for a satellite in the low angular velocity situation. The result indicates that this method can be applied for the spacecraft with a high angular velocity and in a steady state.

In order to study the principle of the water reflow phenomenon in the Mariotte bottle, the calculation formula for the amount of the water reflow is derived by using the Ideal Gas Law and the theories of pressure in this paper. And the validity of the formula is verified by experiments. It is found that the calculated value of the supplementary water amount is basically consistent with the actual value, which shows that the formula is applicable. At the same time, the results show that the returned water enters not only the intake pipe, but also the Mariotte bottle. The water reflowed to the Mariotte bottle will compress the air above the water surface and reduce the volume of the cavity in the bottle, which further reveals the mechanism of the water reflow process in the Mariotte bottle.

When the stress reaches a certain level, the rock would undergo accelerated creep failure after the attenuation and stable creep processes, but the traditional Nishihara model could not reflect the accelerated creep stage effectively. In order to solve this problem, a non-linear rheological element is introduced and connected in series to the traditional Nishihara model to form a new six-element model, which could fully reflect the three stages of the rock creep. Based on the improved constitutive equation of the Nishihara model and the Laplace transformation, the variations of the radial displacement of the surrounding rock of the shield circular roadway are obtained. Based on the measured data of the convergence deformation of the surrounding rock of the roadway, the viscoelastic-plastic creep parameters of the rock are obtained by inversion. The comparison between the calculation results of the radial displacement of the surrounding rock and the measured data shows that when $t\leq 25$ d, the surrounding rock of the roadway is in the stage of the accelerated deformation, and the rate of change of the radial displacement is increased with time; the surrounding rock of the roadway enters the stage of the stable deformation when $t>25$ d, and the rate of change of the displacement of the radial surrounding rock is gradually stabilized with the passage of time.

In order to explore the scale effect of the shale tensile strength and the origin of the scale effect of the rock strength in general, the outcrop of the continental shale of Chang 7 of Yanchang Formation in Ordos Basin is collected to make rock samples of 50 mm in diameter and 15.32 mm, 20.39 mm, 25.46 mm and 30.28 mm in length for the Brazilian splitting test. On the basis of analyzing the rock tensile strength, a new understanding of the origin of the scale effect is proposed. It is shown that the maximum load on the shale and the number of rupture surfaces increase with the increase of the sample size, while the tensile strength decreases with the increase of the sample size, and the correlation between the fracture time and the sample size is poor. The heterogeneity and the end friction effect are the main causes of the scale effect of the rock strength. The obvious scale effect of the tensile strength in the Brazilian shale splitting test results indicates that the scale effect of the rock strength is not entirely rooted in the end friction between the specimen and the indenter. The scale effect of the rock strength is formed by the interaction of the heterogeneity and the end friction effect. For small scale rock samples, the end friction effect plays the dominant role, and for large scale rock samples, the heterogeneity plays the dominant role. For various types of rocks, the size of rock samples may be neither "small" nor "large". The study of the scale effect and its origin for the rock strength is helpful to improve the accuracy of the rock strength prediction and for revealing the rock failure mechanism.

Based on the bench strain test method, the stress state of the car wheel in the fatigue test is studied. The results show that the tire has a great influence on the load on the wheel during the radial fatigue test. The compression deformation and the clockwise and counterclockwise rotations of the tire and the drum will affect the stress state of the wheel. During the radial fatigue test of the wheel, the maximum load on the wheel occurs at the contact position of the wheel rim and the tire along the wheel circumference, and the load at the position near the wheel center is small. In the wheel bending fatigue test, the maximum load on the wheel appears at the position of the spoke near the wheel center, and the maximum strain is along the length of the spoke. Different loads have no effect on the variation rule of the wheel stress, but will have an impact on the maximum and minimum peak values.

For simplifying the mechanical models and the loading patterns in structural mechanics and the design of engineering structures, three methods, including a semi-static loading method, a three-step loading method for simulating the construction process and a multi-layer method, are adopted to study the simplification and the calculation of the mechanical models of frame structures under the action of vertical load. The assumptions made in the calculation by the three methods and the calculation results are analyzed, and reasonable scopes for the application are suggested. The results demonstrate that the semi-static load method is more suitable for the analysis of the progressive collapse and the design and the calculation of the building structure modification while the three-step loading method is more applicable for the design and the calculation of new projects. In addition, as a simplified calculation method by hand, the multi-layer method can be used as a basic method for understanding the principles of structural mechanics.

The slag entrapment in the continuous casting process is a key and difficult issue in the teaching of the metallurgical fluid mechanics. The complex theory is difficult for students to master. In this paper, it is suggested to use the existing simulation devices of the continuous casting mould at the Key Laboratory of Vanadium and Titanium Resources of Sichuan Province to create visual observations of the flow in the mould and to improve the teaching of the metallurgical fluid mechanics through the water-based experiment and numerical simulation.

The mechanical behavior of air conditioning under drop conditions is studied. Firstly, the LS-DYNA material model is established by material tests with different strain rates. Then the continuous drop finite element model of air conditioning is established by the DYNAIN method. In the meantime, the drop simulation and the test are benchmarked. The benchmark data show that the correlation between the continuous drop simulation and the experimental acceleration curve is over 93%, and the damage location is consistent. The results show that the method can accurately simulate the mechanical behavior of air conditioning under continuous drop conditions, which may serve as a guidance for the research and development of home appliances.

Emmy Noether, German female mathematician, published in 1918 an important paper, entitled "On Invariant Functionals", in which two theorems are proved. The first theorem is about the symmetries and the invariants in classical mechanics; the second theorem is about the general relativity. Noether's first theorem is now a basis not only for classical mechanics and classical field theory, but also for the studies of symmetries and invariants in quantum mechanics and quantum field theory. This paper gives an introduction to her paper and the development her ideas, as well as the Noether's theorem in classical mechanics.

In order to popularize the nonlinear dynamics and to improve the general education by integrating the new scientific achievements, the paper summarizes and analyzes the design and the practice of the course "Chaos and Nonlinear Thinking". Nonlinear dynamics nowadays becomes a part of the general human knowledge. The course "Chaos and Nonlinear Thinking" is intended for all three categories of students, namely, those majored in science and technology, economics and management, as well as humanities, in Shanghai University. The course involves the scientific concepts of chaos and its cultural impacts. Nonlinearity is treated not only as a mathematical model but also a thinking mode. The course encourages the students to observe, analyze, and understand unpredictable and uncertain phenomena in nature or society via the nonlinear thinking. The teaching practice demonstrates that the nonlinear dynamics can be appropriately popularized for undergraduates in all fields to form a substantial part of a general education course.

With the developments of science and technology, the main modes of experimental teaching have become diversified. Experimental courses play indispensable roles in higher education. Experimental courses are not only the basis of students' practice, but also the transformations from knowledge understanding to scientific research. The outbreak of the Corona Virus Dissease 2019 (COVID-2019) was accidental, which caused unprecedented difficulties to the experimental teaching. A series of emergency methods, such as video or online teaching, the use of digital resources, the transformation of teaching modes, and the adjustment of evaluation system, achieved good effects on the experimental teaching, including well cooperation with the related theoretical courses, the improvement of students' self-learning ability. The epidemic situation of COVID-2019 has raised some thoughts on the development of experimental teaching in the universities. The experimental teaching should be devoted to the talent cultivation and persistent innovation.

The catenary problem is a very classical mechanical problem. There are many methods to derive the catenary equation from static equilibrium methods to variational principles. This paper establishes and solves the catenary equation based on the discrete static equilibrium model. Furthermore, this paper establishes a discrete static equilibrium model with torsion spring, then derives and solves the beam displacement equation. In the end, the beam displacement equations with different parameters are solved to obtain the gradual solution, and the existence of various equilibrium states is analyzed.

In order to better popularize kites in the aviation education among youngsters, the design principles for the kite, such as its structure and the force and stability analyses, are discussed, and a design software Kite Modeler of NASA, as well as our education practice, is introduced in the present paper. It is shown that the design, the making and the flying of the kite is a practical activity, which integrates the simple aircraft design, the handcrafting, the physical exercise, the leisure and the entertainment, and has practical significance in the aviation education in primary and secondary schools.

In view of the education under the background of "Emerging Engineering", the "Micro-course Participating Teaching Mode" is proposed in this paper to further develop students' comprehensive qualities. The exploration and the practices of this new mode are conducted in Engineering Fluid Mechanics course. To achieve good teaching effects, the teaching contents are optimized, the teaching pattern is re-designed, accompanied with the teaching practice throughout the course. The assessment method is also improved to reasonably evaluate the performance of each student by increasing the number of regular evaluations. At the end of the semester, the teaching effect of the "Micro-course Participating Teaching Mode" is compared with that based on the old teaching mode and evaluated by questionnaire survey. Results show that the "Micro-course Participating Teaching Mode" has stimulated the student's interest and improved the participation of the class. This new mode helps students to better master the basic knowledge. Moreover, students' comprehensive qualities are enhanced, such as the innovation ability, the self-study ability, the expression ability and the team cooperation, for bringing up all-round talents under the background of the "Emerging Engineering".

In view of the characteristics of teaching naval architecture and ocean engineering fluid mechanics, this paper puts forward a kind of heuristic teaching mode: "interests-research-exploration". In this teaching mode, the "interests" are taken as the drive, the "research and application" are taken as the support, and "exploring the unknown" is taken as the guidance, to maximize the active learning abilities and divergent thinking potentials of the students. With the cavitation phenomenon as an example, the mode is combined with relevant knowledge points of the naval architecture and the ocean engineering fluid mechanics, to stimulate curiosity and interest of the students for the knowledge points, to for them to master and apply the knowledge points, and the understanding and the imagination of the students are inspired round the knowledge points.

Over 40 years ago, the author once faced with several strength and vibration problems related to the structural mechanics and solid mechanics in the design, manufacturing and operating of machines and tried to solve these failure problems and to improve the working of machines. It was found that three aspects are important, that is, the configuration and constraint, the nature of external loading and the properties of structural materials. They are actually based on three elements in the Newtonian mechanics: the loading $F$, the mass of matter $m$ and the acceleration of motion $a$, and the linking between them. This framework can be extended to describe the analysis of solid mechanics. The research framework is further extended in the 1970s, the 1990s and the early 21st century, as shown in Figures 1,2,3. In recent years, the analytical methodology has already extended to more extensive scientific and technological territory and the coupling between the different disciplines asks people to discover new development directions. Smaller and larger scales in space-time will be considered, as well as the process of information and data production and transformation, and the motion of living matters under conventional or extreme loading environment. These new fields can be expected to open for future solid mechanics.

The realization of an unmanned self-stabilizing bicycle is discussed. A stability analysis is made for a mathematical model of a bicycle controlled by the rotation of the front set. It is shown that the self- running bicycle can be asymptotically stabilized only when the damping factor in the rotation axis of the front set is considered, and the input signals of the control system should contain the angular velocity of the side-leaning of the bicycle.

The biomechanics is the science of applying the mechanical principles and methods to quantitatively study mechanical problems in organisms. This paper points out that the constitutive relationship and the stress-growth relationship are the two core issues in the biomechanics. The meaning of the constitutive relationship can be explained by using three examples: the "blood is thicker than water", the "artery hardening" and the "bone under loading"; and the meaning of the stress-growth relationship can be explained by using other three examples: the "bone growth", the "hard Qigong" and the "hypertension and cardiovascular diseases".

This paper presents the design scheme and the operational process of the competition team from Jiangsu University of Science and Technology in the "Theoretical Design and Operation" competition of the 12th Zhou Peiyuan Mechanics Competition for College Students of China.