Using Superelements in the Calculation of Lattice-Boom Cranes

In this paper a superelement formulation for geometric nonlinear finite element analysis is proposed. The element formulation is based on matrices generated by the static condensation algorithm. After defining the element characteristics, a method for the calculation of the element forces in a large displacement and rotation analysis is developed. In order to use the element in the solution of stability problems, the formulation of the geometric stiffness matrix is derived. An example shows the benefits of the element for the calculation of lattice-boom cranes.

A General Solution Framework for Component-Commonality Problems

Component commonality - the use of the same version of a component across multiple products - is being increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As components influence to a greater or lesser extent nearly every process step along the supply chain, it is not surprising that a multitude of diverging commonality problems is being investigated in literature, each of which are developing a specific algorithm designed for the respective commonality problem being considered. The paper on hand aims at a general framework which is flexible and efficient enough to be applied to a wide range of commonality problems. Such a procedure based on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.