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This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain.

In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering.

The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method.

The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.

Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

Due to social transformation in China, more than 100,000,000 people are migrating within the country. Many parents are forced to leave their children behind when they migrate. In 2008, 58,000,000 children were living as left‐behind children, mainly in the rural parts of China (Zhang, 2009).Migration and its accompanying stressors may affect the mental health of the left‐behind children. This unique literature review of Chinese literature summarises the present state of knowledge and reviews the influential factors. Possible approaches to intervention and system reforms are discussed.A literature review was performed of published studies between 2001 and 2008. Databases used were Fujian Medical University Library Interface, Chinese National Knowledge Infrastructure, Wanfang Data, and VIP Information. The Chinese word for ‘left‐behind’ was used as a key word. Books, book chapters, monographs and studies on caring were searched electronically and by hand. Altogether, 53 items were found, discussed and grouped together. Migration affected the mental health of the left‐behind children in a passive way, especially their emotions and social behaviour.There is still controversy over how serious mental health problems are among children who have been left behind. Life events, personality, coping strategies and social suppor t can be regarded as four main factors that are predictive of mental health, which provides theoretical guidance for intervention. Suppor t and prevention of mental health problems in schools, in families and in primary care should be developed and studied.

In this paper, a nine-dimensional chaotic system is designed and applied to secure communication.

Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences.

The proposed nine-dimensional system has a large key space and more complex dynamic characteristics

The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

This paper aims to study the boundary disturbance rejection control design for a flexible Timoshenko robot arm to diminish external disturbances and achieve desired angle tracking, with system vibration and elastic deformation considered.

This study introduces disturbance observer and disturbance rejection mechanism into the boundary control design for flexible Timoshenko robot arm systems. The uniform bounded stability of controlled systems is proved via Lyapunov analysis without any simplification of the infinite-dimensional system dynamics.

The proposed boundary disturbance rejection control scheme can effectively suppress vibrations and shear deformations, achieve the required angular positioning and reject external disturbances. Numerical simulations developed by the finite difference method are adapted to demonstrate the validity of the designed controller.

The originality of this study is to design boundary disturbance rejection control to suppress vibrations and shear deformations for the flexible Timoshenko robot arm, thereby improving the performance and control accuracy of the system.

The paper aims to propose a method to build environmental constraint region online in complex-shaped peg-in-hole assembly tasks.

Compared with conventional way which using computer-aided design (CAD) models of assembly parts to construct the environmental constraint region offline, the paper provides an online approach that consists of three aspects: modeling assembly parts through visual recognition, decomposing complex shapes into multiple primitive convex shapes and a numerical algorithm to simulate the peg-in-hole insertion contact. Besides, a contrast experiment is performed to validate the feasibility and effectiveness of the method.

The experiment result indicates that online construction takes less time than the offline way under the same task conditions. Furthermore, due to the CAD models of the parts are not required to be known, the method proposed in the paper has a broader application in most assembly scenarios.

With the improvement of customization and complexity of manufactured parts, the assembly of complex-shaped parts has drawn greater attention of many researchers. The assembly methods based on attractive region in environment (ARIE) have shown great performance to achieve high-precision manipulation with low-precision systems. The construction of environmental constraint region serves as an essential part of ARIE-based theory, directly affect the formulation and application of assembly strategies.

Recycling and reuse of the electric vehicle (EV) batteries are ways to extend their limited lives. If batteries can be traced from production to recycling, it is beneficial for battery recycling and reuse. Using blockchain technology to build a smart EV battery reverse supply chain can solve the difficulties of lack of trust and data. The purpose of this study is to discuss the behavioural evolution of a smart EV battery reverse supply chain under government supervision.

This study adopts evolutionary game theory to examine the decision-making behaviours of the government, EV manufacturers with recycled used batteries and third-party EV battery recyclers lacking professional recycling qualification.

On the smart reverse supply chain integrated by blockchain technology, a cooperative recycling strategy of the third-party EV battery recycler is the optimal choice when the government tends to actively regulate. The probability of the EV manufacturer choosing the blockchain adoption strategy exceeds (below) the threshold, and the government prefers negative (positive) supervision. According to numerical analysis, in the mature stage in the EV battery recycling industry, when the investment cost of applying blockchain is high, EV manufacturers' willingness to apply blockchain slows down, the government accelerates adopting a negative supervision strategy and third-party EV battery recyclers prefer cooperative recycling.

The results of this study provide opinions on the strength of government supervision and the conditions under which EV manufacturers and third-party EV battery recyclers should apply blockchain and cooperate. On the other hand, this study provides theoretical analysis for promoting the application of blockchain technology in smart reverse supply chain.

Compared with previous research, this study reveals the relevance of government supervision, blockchain application and cooperation strategy in smart EV battery reverse supply chain. In the initial stage, even if the subsidy (subsidy reduction rate) and penalty are high and the penalty reduction rate is low, the EV manufacturer should rather give up the application of blockchain technology. In the middle stage in the EV battery recycling industry, the government can set a lower subsidy (subsidy reduction rate) combined with a penalty or a higher penalty (penalty reduction rate) combined with a subsidy to supervise it. The third-party EV battery recycler is advised to cooperate with the EV manufacturer when the subsidy is low or the penalty is high.

To further promote application of BIM technology in construction of prefabricated buildings, influencing factors and evolution laws of willingness to apply BIM technology are explored from the perspective of willingness of participants.

In this paper, a tripartite game model involving the design firm, component manufacturer and construction firm is constructed and a system dynamics method is used to explore the influencing factors and game evolution path of three parties' application of BIM technology, from three perspectives, cost, benefit and risk.

The government should formulate measures for promoting the application of BIM according to different BIM application willingness of the parties. When pursuing deeper BIM application, the design firm should pay attention to reducing the speculative benefits of the component manufacturer and the construction firm. The design firm and the component manufacturer should pay attention to balancing the cost and benefit of the design firm while enhancing collaborative efforts. When the component manufacturer and the construction firm cooperate closely, it is necessary to pay attention to balanced distribution of interests of both parties and lower the risk of BIM application.

This study fills a research gap by comprehensively investigating the influencing factors and game evolution paths of willingness of the three parties to apply BIM technology to prefabricated buildings. The research helps to effectively improve the building quality and construction efficiency, and is expected to contribute to the sustainability of built environment in the context of circular economy in China.

The purpose of this paper is to solve the problem that the relationship between loading forces, which were applied at different positions on a plane, and output values of load-sharing dynamometer is non-linear.

First, the analytical model of ISPM (isodynamic surface proportional mapping method) method, which is used to calibrate dynamometer, was established. Then, a series of axial force calibration tests were performed on a load-sharing dynamometer at different loading positions. Finally, according to output values, calibration forces at different loading positions were calculated by ISPM method, and corresponding distribution histogram of calibration force error was generated.

The largest error between calculated force and standard force is 2.92 per cent, and the probability of calculated force error within 1 per cent is 91.03 per cent, which verify that the ISPM method is reliable for non-linear calibration of dynamometers.

The proposed ISPM method can achieve non-linear calibration between measured force and output signal of load-sharing dynamometer at different positions. In addition, ISPM method can also solve some complex non-linear problems, such as prediction of plane cutting force under the influence of multiple parameters, the force measurement of multi-degree-of-freedom platform and so on.