Investigation and Computational Modelling of Variable TEG Leg Geometries

In this work, computational modelling and performance assessment of several different types of variable thermoelectric legs have been performed under steady-state conditions and the results reviewed. The study conducted has covered geometries, not previously analysed in the literature, such as Cone-leg and Diamond-leg, based on the corresponding thermoelectric generator leg shape structure. According to the findings, it has been demonstrated that the inclusion of a variable cross-section can have an impact on the efficiency of a thermoelectric generator. It has been concluded that the Diamond configuration generated a slightly larger voltage difference than the conventional Rectangular geometry. In addition, for two cases, Rectangular and Diamond configurations, the voltage generated by a TEG module consisting of 128 pairs of legs was analysed. As thermal stress analysis is an important factor in the selection of TEG leg geometries, it was observed based on simulations that the newly implemented Diamond-leg geometry encountered lower thermal stresses than the traditional Rectangular model, while the Cone-shape may fail structurally before the other TEG models. The proposed methodology, taking into account the results of the simulation carried out, provides guidance for the development of thermoelectric modules with different forms of variable leg geometry.

Effect of Defects Part II: Multiscale Effect of Microvoids, Orientation of Rivet Holes on the Damage Propagation, and Ultimate Failure Strength of Composites

Material properties at the vicinity of the cut-outs in composites are not entirely defect-free. The nteraction of multiple cutouts like rivet holes, the repercussion of their configuration on crack propagation, and ultimate strength were predicted using Peridynamic method and the results are reported in this article. The effect of microscale defects at the vicinity of the cutouts on macroscale damage propagation were shown to have quantifiable manifestation. This study focused on two to four holes in unidirectional composite plates with 0°, 45°, and 90° fiber directions, while the vicinity of a hole was considered degraded. Numerical results were validated using quantitative ultrasonic image correlation (QUIC) and the tensile test. Both the experimental and numerical results confirmed that the strength of the horizontal configuration is higher than the vertical in the plates with two holes. Furthermore, the square configuration was found to be stronger than the diamond configuration with four holes. When the effect of microscale defects was considered, the prediction of ultimate strength was better compared to the experimental results. The predictive model could be reliably used for progressive damage analysis.

Kempe-Locking Configurations

The 4-color theorem was proved by showing that a minimum counterexample cannot exist. Birkhoff demonstrated that a minimum counterexample must be internally 6-connected. We show that a minimum counterexample must also satisfy a coloring property that we call Kempe-locking. The novel idea explored in this article is that the connectivity and coloring properties are incompatible. We describe a methodology for analyzing whether an arbitrary planar triangulation is Kempe-locked. We provide a heuristic argument that a fundamental Kempe-locking configuration must be of low order and then perform a systematic search through isomorphism classes for such configurations. All Kempe-locked triangulations that we discovered have two features in common: (1) they are Kempe-locked with respect to only a single edge, say x y , and (2) they have a Birkhoff diamond with endpoints x and y as a subgraph. On the strength of our investigations, we formulate a plausible conjecture that the Birkhoff diamond is the only fundamental Kempe-locking configuration. If true, this would establish that the connectivity and coloring properties of a minimum counterexample are indeed incompatible. It would also imply the appealing conclusion that the Birkhoff diamond configuration alone is responsible for the 4-colorability of planar triangulations.