menger sponge
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2021 ◽  
Vol 11 (22) ◽  
pp. 10554
Author(s):  
Pablo Pavón-Domínguez ◽  
Guillermo Portillo-García ◽  
Alejandro Rincón-Casado ◽  
Lucía Rodríguez-Parada

In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (FD). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity of the optimized solutions to be efficiently distributed in the design space. Furthermore, the possible relationships between the fractal dimension and beams’ mechanical properties are explored. First, a set of theoretical beams are studied based on their well-known fractal dimension. A 3D fractal called Menger sponge is reproduced on a Michell’s beam (cantilever with a single force applied at the end). The programming codes that generate those beams are created in Matlab software, as are the algorithms for estimating the fractal dimension (box-counting method). Subsequently, identical beams are modelled in the software Inspire in order to apply the topology optimization and determine the mechanical parameters from the static analysis. Results indicate that the fractal dimension is affected by the design geometry and proposed optimized solutions. In addition, several relationships among fractal dimension and some mechanical resistance parameters could be established. The obtained relations depended on the objectives that were initially defined in the topology optimization.


2021 ◽  
Author(s):  
Subhash Kak

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.


2021 ◽  
Author(s):  
Subhash Kak

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.


2021 ◽  
Author(s):  
Subhash Kak

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.


Crystals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 468
Author(s):  
Serena Cicalò

In 2015, the author developed a new origami technique, called PJS technique (where PJS stands for “pleat and join strips”), by which we can construct polycubes, that are polyhedrons composed of elementary cubes, called units, connected face to face. Each strip, pleated in squares, has to cover four faces of a tower of stacked units, called a segment, having as length the number of units that form the tower. Each unit is composed by weaving together three paper strips in the three spatial directions and the length of each strip depends on the length of the segment in each respective direction. The PJS technique allowed the author to build, at the end of 2016, the first specimen of a level-4 origami Menger sponge and three yeas later, the first level-3 complement model. In this paper, we give a formula to compute the number of segments that make up a level-n Menger sponge complement in all directions and consequently, the number of modules needed for each length to build this polycube with the PJS technique.


2021 ◽  
pp. 2001471
Author(s):  
Brijesh Kushwaha ◽  
Kush Dwivedi ◽  
Rushikesh S. Ambekar ◽  
Varinder Pal ◽  
Dibya Prakash Jena ◽  
...  

2021 ◽  
Vol 21 (1) ◽  
pp. 343-353
Author(s):  
Wei-Dong Xie ◽  
Meng Wang ◽  
Xiao-Qi Wang ◽  
Yan-Di Wang ◽  
Chang-Qing Hu

Pore structure and fractal dimensions can characterize the adsorption, desorption and seepage characteristics of shale gas reservoirs. In this study, pore structure, fractal characteristics and influencing factors were studied of the Longmaxi formation shale gas reservoir in southeastern Chongqing, China. Scanning electron microscopy was used to describe the characteristics of various reservoirs. High pressure mercury intrusion and low temperature liquid N2 and CO2 adsorption experiments were used to obtain pore structure parameters. V–S model, FHH model and Menger sponge model were selected to calculate the micropore, mesopore and macropore fractal dimensions, respectively. The results show that organic matter pores, inter-granular pores, intra-granular pores and micro-fractures are developed within the shale, and the pore morphology is mostly ink pores and parallel plate pores with aperture essentially in the 1–2 nm and 2–50 nm ranges. Moreover, macropores are the most complex in these samples, with mesopores being less complex than macropores, and the micropores being the simplest. D1 (micropore fractal dimension) ranges from 2.31 to 2.50, D2 (mesopore fractal dimension) ranges from 2.74 to 2.83, D3 (macropore fractal dimension) ranges from 2.87 to 2.95, and Dt (comprehensive fractal dimension) ranges from 2.69 to 2.83 of fractal characteristics. D1 and D2 are mainly controlled by TOC content, while D3 and Dt are mainly controlled by brittle and clay mineral content. These results may be helpful for exploration and the development of shale gas in southeastern Chongqing, China.


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