Search results for: dodecagonal

Authors: Rima A. Ajlouni

Abstract:

The discovery of quasi-periodic structures in material science is revealing an exciting new class of symmetries, which has never been explored before. Due to their unique structural and visual properties, these symmetries are drawing interest from many scientific and design disciplines. Especially, in art and architecture, these symmetries can provide a rich source of geometry for exploring new patterns, forms, systems, and structures. However, the structural systems of these complicated symmetries are still posing a perplexing challenge. While much of their local order has been explored, the global governing system is still unresolved. Understanding their unique global long-range order is essential to their generation and application. The recent discovery of dodecagonal quasi-periodic patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. Astonishingly, many centuries before its description in the modern science, ancient artists, by using the most primitive tools (a compass and a straight edge), were able to construct patterns with quasi-periodic formations. These ancient patterns can be found all over the ancient Islamic world, many of which exhibit formations with 5, 8, 10 and 12 quasi-periodic symmetries. Based on the examination of these historical patterns and derived from the generating principles of Islamic geometry, a global multi-level structural model is presented that is able to describe the global long-range order of dodecagonal quasi-periodic formations in Islamic Architecture. Furthermore, this method is used to construct new quasi-periodic tiling systems as well as generating their deflation and inflation rules. This method can be used as a general guiding principle for constructing infinite patches of dodecagon-based quasi-periodic formations, without the need for local strategies (tiling, matching, grid, substitution, etc.) or complicated mathematics; providing an easy tool for scientists, mathematicians, teachers, designers and artists, to generate and study a wide range of dodecagonal quasi-periodic formations.

Keywords: dodecagonal, Islamic architecture, long-range order, quasi-periodi

Procedia PDF Downloads 369

Authors: Tomasz Dubiel, Tadeusz Balawender, Miroslaw Osetek

Abstract:

The paper presents the influence of non-metallic inclusions on the multi-stage forging process and the mechanical properties of the dodecagon socket bolt used in the automotive industry. The detected metallurgical defect was so large that it directly influenced the mechanical properties of the bolt and resulted in failure to meet the requirements of the mechanical property class. In order to assess the defect, an X-ray examination and metallographic examination of the defective bolt were performed, showing exogenous non-metallic inclusion. The size of the defect on the cross-section was 0.531 [mm] in width and 1.523 [mm] in length; the defect was continuous along the entire axis of the bolt. In analysis, a FEM simulation of the multi-stage forging process was designed, taking into account a non-metallic inclusion parallel to the sample axis, reflecting the studied case. The process of defect propagation due to material upset in the head area was analyzed. The final forging stage in shaping the dodecagonal socket and filling the flange area was particularly studied. The effect of the defect was observed to significantly reduce the effective cross-section as a result of the expansion of the defect perpendicular to the axis of the bolt. The mechanical properties of products with and without the defect were analyzed. In the first step, the hardness test confirmed that the required value for the mechanical class 8.8 of both bolt types was obtained. In the second step, the bolts were subjected to a static tensile test. The bolts without the defect gave a positive result, while all 10 bolts with the defect gave a negative result, achieving a tensile strength below the requirements. Tensile strength tests were confirmed by metallographic tests and FEM simulation with perpendicular inclusion spread in the area of the head. The bolts were damaged directly under the bolt head, which is inconsistent with the requirements of ISO 898-1. It has been shown that non-metallic inclusions with orientation in accordance with the axis of the bolt can directly cause loss of functionality and these defects should be detected even before assembling in the machine element.

Keywords: continuous casting, multi-stage forging, non-metallic inclusion, upset bolt head

Procedia PDF Downloads 127