The reliability mathematical model of load-sharing parallel systems based on fatigue cumulative damage

Conventional reliability models for parallel systems are not applicable for the analysis of parallel systems with load transfer and sharing. In this short communication, firstly, the dependent failures of parallel systems are analyzed, and the reliability model of load-sharing parallel system is presented based on Miner cumulative damage theory and the full probability formula. Secondly, the parallel system reliability is calculated by Monte Carlo simulation when the component life follows the Weibull distribution. The research result shows that the proposed reliability mathematical model could analyze and evaluate the reliability of parallel systems in the presence of load transfer.

Investigating practitioner self-efficacy in an era of mathematical reform

The purpose of this study is to explore teacher self-efficacy at a time of radical mathematical reform. Project Maths – the new initiative which was rolled out nationwide in 2010 differs from previous attempts at innovation in that it targets a much closer connection between curriculum and pedagogy. Gone are the days of well-rehearsed routines where the role of the mathematician was essentially that of demonstrator. Teaching for understanding is now the main ‘official’ pedagogical focus, with emphasis on the practitioner playing the part of mediator between subject-matter and student. Mathematical instruction is not merely concerned with the transmission of knowledge and skills which is a particular pedagogical position to take. It is also an emotional practice (Hargreaves, 1998) that colours and expresses the feelings and actions of practitioners. While emotion plays a key role in teachers’ commitment to curricular reform, it is also shaped by the social and cultural contexts of mathematical change, alongside with the attitudes and beliefs of the mathematical teaching community. Inspired by Bandura’s theory of learning (1986), this investigation aims to shed light on the complex interplay between so-called mastery and vicarious experiences, social persuasion and physiological states. Vygotsky’s view of learning (1978) as a socio-cultural process is also drawn upon, as it provides a useful structure against which teacher self-efficacy and professional development can be examined. Finally, Hiebert’s theory (1986) is used to examine mathematics teaching self-efficacy and mathematics self-efficacy.

Fundamental studies of the application of wheat for malting and brewing

Wheat (Triticum aestivum L.) has a long tradition as a raw material for the production of malt and beer. While breeding and cultivation efforts for barley have been highly successful in creating agronomically and brew- technical optimal specialty cultivars that have become well established as brewing barley varieties, the picture is completely different for brewing wheat. An increasing wheat beer demand results in a rising amount of raw material. Wheat has been - and still is – grown almost exclusively for the baking industry. It is this high demand that defines most of the wheat breeding objectives; and these objectives are generally not favourable in brewing industry. It is of major interest to screen wheat varieties for brewing processability and to give more focus to wheat as a brewing cereal. To obtain fast and reliable predications about the suitability of wheat cultivars a new mathematical method was developed in this work. The method allows a selection based on generally accepted quality characteristics. As selection criteria the parameters raw protein, soluble nitrogen, Kolbach index, extract and viscosity were chosen. During a triannual cultivation series, wheat varieties were evaluated on their suitability for brewing as well as stability to environmental conditions. To gain a fundamental understanding of the complex malting process, microstructural changes were evaluated and visualized by confocal laser scanning and scanning electron microscopy. Furthermore, changes observed in the micrographs were verified and endorsed by metabolic changes using established malt attributes. The degradation and formation of proteins during malting is essential for the final beer quality. To visualise fundamental protein changes taking place during malting, samples of each single process step were analysed and fractioned according their solubility. Protein fractions were analysed using a Lab-on-a-chip technique as well as OFFgel analysis. In general, a different protein distribution of wheat compared to barley or oat could be confirmed. During the malting process a degradation of proteins to small peptides and amino acids could be observed in all four Osborn fractions. Furthermore, in this study a protein profiling was performed to evaluate changes during the mashing process as well as the influence of grist composition. Differences in specific protein peaks and profile were detected for all samples during mashing. This study investigated the suitability of wheat for malting and brewing industry and closed the scientifical gap of amylolytic, cytolytic and proteolytic changes during malting and mashing.

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.