Explicit methods are widely used in finite element analysis as efficient ways to solve differential equations. The efficiency of explicit methods relies on the economical evaluation of internal forces at each time step. The greatest efficiency can be provided by one-point quadrature. However, instability arises because of the shortcomings in the use of one-point quadrature. The instability is called hourglass mode, or spurious singular mode. An effective method to control the instability is to add “hourglass stiffness” to an element integrated by one-point quadrature. Explicit methods often require a very small time step to ensure stability. Thus, for complex problem with refined meshes, a very large number of timesteps will be required to complete the analysis. Minimizing the number of operations per time step can provide significant improvement on efficiency of the methods. Since hourglass terms typically require more computational operations than one-point quadrature terms, we are very interested in reducing the number of operations on hourglass control. In addition, considerable approximation is involved with hourglass control, and hence overall accuracy may not be seriously affected by relaxing the precision of the temporal integration of the hourglass force. Consequently, there is a possibility of trading some accuracy of the hourglass control for computational efficiency. A subcycling approach is applied to the hourglass portion of explicit methods. Namely, instead of updating hourglass forces every time step, we update hourglass forces every two steps. The proposed approach is examined with the use of mass-spring models. The applicability to more complex models is demonstrated on a 3-D model with the subcycling approach implemented into an explicit finite element code. Efficiency, stability and accuracy are discussed as important issues of the proposed approach. The mass-spring models and finite element implementation show that a beating instability can be introduced by the subcycling approach, and additional restriction is placed on the stable time step for the central difference operator. However, sufficient damping can restore the usual stability conditions. Thus, the proposed subcycling approach is seen to be highly advantageous where damping can be used, and it can cut computation time by 30% or more without significantly affecting the overall accuracy of the solution. / Thesis / Master of Applied Science (MASc)

Indiana University-Purdue University Indianapolis (IUPUI) / In this project, a chassis concept has been developed for a small electric vehicle ’minibus’. The vehicle is intended to be used as a transport between agricultural locations in Ethiopia to cities where the products can be sold. The objective is to develop a chassis that can house several different modular structures for the purposes of transporting refrigerated goods, a mobile power grid, or people. Literature studies have been conducted on current electric vehicle markets, battery markets, chassis materials, and optimal cross-sections. The battery housings have also been analyzed from an environmental perspective to account for conditions in Ethiopia. Based on this, it was found that a four-wheeled ’minibus’ design including space for approximately fourteen custom batteries is optimal. It is essential to keep in mind that this project has been carried out both on a conceptual level within the framework of a degree project as well as a production project for use in Ethiopian rural areas. This master thesis project aims to provide a solid benchmark for further development and research within the subject.

This thesis discusses the analysis of surface cracked configurations in order to develop a fracture prediction criterion suitable for ductile materials. A similar criteria has been successfully developed for brittle materials. However, the criteria has not been applied to ductile materials. Finite element analysis results are presented as well as laboratory test data. The validity of the proposed criterion is addressed and future work is proposed.

This thesis discusses the analysis of fatigue crack growth in the presence of residual stresses to determine a suitable method for fatigue life predictions. In the research discussed herein, the prediction methodologies are compared to determine the most accurate prediction technique. Finite element analysis results are presented as well as laboratory test data. The validity of each methodology is addressed and future work is proposed.

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