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Domain-Modeling Techniques
Published in Alexandru Telea, Data Visualization, 2014
Area-constrained triangulations enforce a maximum triangle area and are useful in creating a sampling of a given domain with a user-specified density, which is in turn useful for representing signals with nonuniform variation with a minimal number of sample points, as explained in Chapter 3. Figure 8.3(d) shows the area-constrained triangulation of the same point set as discussed previously. Similar to the angle constraint, the minimal area constraint forces the creation of 1272 extra (Steiner) points. The original point set is colored in red, while the extra points are colored in yellow. In addition to angle and area constraints, geometric constraints can be used too. For example, the triangulation can be forced to cover the inside area of a specified convex or concave polygon whose vertices are part of the input point set, instead of covering the entire convex hull of the input point set. This triangulation variant is useful in automatically creating unstructured grids for domains with complex shapes and boundaries.
Crashworthiness analysis and multi-objective optimisation of a novel circular tube under three-point bending
Published in International Journal of Crashworthiness, 2022
Yonghui Wang, Qiang He, Xiaona Shi, Jianlin Zhong
Nowadays, people pay more and more attention to the safety and protection performance of automobile and owing to the light weight and amazing energy absorption potential of thin-walled structure, thin-walled structure has become a research hotspot of scholars. More than 10 years ago, scholars have done relevant work on thin-walled structures, and thin-walled structures with different cross-sections (such as square [1,2], circle [3–6], triangle [7], hexagon [8,9], concave polygon [10], convex polygon [11]) were studied by numerical, analytical and experimental methods.
Energy absorption characteristics of multi-cell tubes with different cross-sectional shapes under quasi-static axial crushing
Published in International Journal of Crashworthiness, 2022
Ming-Zhu Jin, Guan-Sheng Yin, Wen-Qian Hao, Hong-Liang Tuo, Ru-Yang Yao
The deformation processes of polygonal single-cell tubes and square multi-cell tubes were investigated by experiments and numerical simulations, and the basic folding mechanism was proposed by many researchers [28–39]. An ideal folding mechanism was put forward by Wierzbicki and Abramowicz [28] firstly, which shows a deforming stage for one quarter of a square section. Subsequently, a method was proposed by Abramowicz and Wierzbicki [30] to investigate the mean crushing force and kinematic parameters of arbitrary corner elements of multi-corner prismatic tubes. A simplified super folding element (SSFE) theory that predicts the mean crushing force of tube was proposed by Chen and Wierzbicki [31]. It divided the cross-sectional of tube into a variety of constitutive elements (CEs) and assumed that each flange contributed to a similar role in the tube. Several novel square multi-cell tubes with four square elements at the corner were designed by Kim [32], and it can be obtained that the SEA of novel square multi-cell tube has dramatic improvements than that of square single-cell tube. The energy absorption characteristics of square multi-cell tubes with different cross-sectional shapes under the quasi-static axial crushing were compared by Zhang and Zhang [34–38]. They had a conclusion that the energy absorption efficiency of multi-cell tubes was higher than that of single-cell tubes significantly, and the increase percentages in SEA was up to approximately 220% for square profiles. The triangular and square multi-cell tubes were investigated by theoretical prediction and crashworthiness optimisation design under impact loading by Tran et al. [39,40], and it can be noticed that multi-cell tubes with right angle-type, T-type and cross-type elements produce the highest SEA [41]. The crashworthiness of hexagonal thin-walled tubes with single-cell and multi-cell configurations were studied by Hou [42], and it was identified that hexagon multi-cell tubes provided higher SEA than that of single-cell tubes. In order to maximise SEA of tubes under axial crushing, an investigation was carried out by Faruque and Saha [43] to determine the optimal cross-sectional shapes by numerical simulation. They came to the conclusion that hexagonal and octagonal tubes exhibited higher energy absorption characteristics than that of square tubes. A method for improving crashworthiness performance under quasi-static axial crushing was to vary the cross-sectional shape with only convex polygon, thus it was also necessary to develop tubes with concave polygon cross-sectional shape [44,45]. The simulation results showed that all of the tubes developed stable and progressive folding deformation modes [43–48]. Therefore, the previous studies showed that multi-cell tubes were preferable than that of single-cell tubes as energy absorbing structures and they were widely used to be crashworthiness structures in all walks of life.