Triangular Cells Research Articles

Calculation of the triangular panels’ orthotropic covers for the retained domes

The experience of design and construction of single-mesh spherical dome coverings based on meshes with triangular cells was studied. Constructive solutions of wooden domes made of triangular panels with orthotropic plywood covers are considered. The method analysis for constructing a bar model of an orthotropic plate in the form of an oblique triangle has been carried out. It is proposed to reduce the calculation of the triangular dome panel’s rod-sheet structure to the calculation of the hinge-bar system. The stiffness matrices of the contour and intra-contour rods of the super cell are obtained.

Simple homotopy theory and nerve theorem for categories

We study a combinatorial homotopy theory for small categories without a loop (loopfree categories) which is closely related to Whitehead's simple homotopy theory for regular CW-complexes with triangular cells. Quillen's theorem A and the nerve theorem for loopfree categories are considered from the viewpoint of the simple homotopy theory. Moreover, we extend the classical nerve theorem and discuss an application to the topological data analysis for data-sets lying in a non-convex field.

About Calculation the Resistance of Two-dimensional Infinite Grid Systems

The paper considers the problem of calculating the resistance between nodes of infinite grid resistor systems with square and triangular cells. There has long been a question about the resistance between the nearest nodes of an infinite grid of resistances with square cells with the same resistance <i>r</i>. Here, earlier, by the method of symmetry and superposition, a result was obtained <i>r</i>/2 that is striking in its simplicity. However, this result is only approximate, although many physicists consider this result to be accurate. New examples are presented proving what the results obtained earlier by the superposition and symmetry method is only approximate. The result <i>r</i>/2 gives only the lower limit of the correct resistance value. In our work, the correctness of using the equivalent resistance method to calculate the resistance between nearest nodes of infinite grid systems is proved. Using this method, for the resistance between the nearest nodes of an infinite grid of resistances with square cells, a result is obtained about 0.5216 <i>r</i> that only slightly differs from <i>r</i>/2. The results differ from the previously obtained values by about 10%. The resistance between the diagonal points of an infinite grid of identical resistors <i>r</i> with square cells is calculated. For the value of this resistance, a value founded about 0.7071 <i>r</i> that differs from the value 2<i>r</i>/<i>π</i> obtained previously by the superposition and symmetry method.

Emergence of uniform tilt and π-stacking in triangular liquid crystalline honeycombs.

The synclinic tilted organization of specifically designed polyphilic oligo(p-phenylene ethynylene) rods in cylindrical shells around triangular prismatic cells on the <5 nm scale leads to a new kind of liquid crystalline honeycomb composed of helical shells with alternating helix sense. Core fluorination at the outer ring modifies the core-core interactions, thus resulting in triangular arrays with face-to-face π-stacking along the honeycomb.

On energy-absorbing mechanisms and structural crashworthiness of laterally crushed thin-walled structures filled with aluminum foam and CFRP skeleton

In the present study, thin-walled tubes filled with aluminum foam and CFRP skeleton (FCFTs) are developed and manufactured based on a multiple material system. The structural crashworthiness of the proposed design is investigated under quasi-static lateral loading. Further, the aluminum tube, the foam-filled tube and the tubes filled with CFRP skeleton are also designed and tested to perform a comparative study. It is found that the FCFT-1 (the tube filled with foam and CFRP skeleton with square cells) exhibits superior SEA (specific energy absorption), which is almost five times that of the individual aluminum tube, and almost 10% higher than that of the foam-filled tube. However, FCFT-2 (the tube filled with foam and CFRP skeleton with triangular cells) provides relatively lower energy-absorbing capacity, as its aluminum tube generates several axial cracks during crushing process leading to low deformation level of the foams. Furthermore, crush simulations are conducted to better understand the energy-absorbing mechanisms of the FCFT-1. The numerical results demonstrate that the plastic deformation of the separated foams makes up the major part of the total energy absorption. Besides, the performance improvement of FCFT-1 can be partly attributed to the fact that the separated foams generate larger plastic deformation during crushing process. Apart from this, the increased interaction effects between the separated foams and the CFRP skeleton lead to a higher FE (frictional energy), which also makes a slight contribution to the performance improvement of FCFT-1. Finally, parametric studies are performed to explore the influences of design parameters on the crashworthiness characteristics of FCFT-1. It is indicated that the energy-absorbing capacity can be slightly improved by raising cell number, proportion of 45° layer or foam density. The present work is expected to provide some insights for researchers and engineers to design such structures for energy absorption applications.

Elastic buckling analysis of plate girders stiffened with triangular cell flanges under patch loading

This paper aims at developing an analytical expression for the buckling coefficient of steel plate girders stiffened with triangular cell flanges subjected to patch loading. In this study, buckling coefficients are computed numerically through linear buckling analysis (LBA) using the finite element method. Firstly, a numerical model for longitudinally stiffened girders subjected to patch loading is verified by computing buckling coefficients and comparing the results with those reported in the literature. Afterward, a numerical model is developed for plate girders stiffened with a triangular cell flange. Thereafter, an extensive parametric study is conducted to investigate the influence of various geometric parameters such as the relative position of the triangular cell with respect to the web, the ratio between the thicknesses of the plates forming the cell and the web, the relative position of the cell in the flange, and the web panel aspect ratio. The influence of these parameters is analyzed in detail. Finally, an analytical expression for the buckling coefficient is fitted through regression analysis of the results. This expression can be used in the design of steel bridge girders stiffened with triangular cell flanges.

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

The global tide is simulated with the global ocean general circulation model ICON-O using a newly developed tidal module, which computes the full tidal potential. The simulated coastal M2 amplitudes, derived by a discrete Fourier transformation of the output sea level time series, are compared with the according values derived from satellite altimetry (TPXO-8 atlas). The experiments are repeated with four uniform and sixteen irregular triangular grids. The results show that the quality of the coastal tide simulation depends primarily on the coastal resolution and that the ocean interior can be resolved up to twenty times lower without causing considerable reductions in quality. The mesh transition zones between areas of different resolutions are formed by cell bisection and subsequent local spring optimisation tolerating a triangular cell’s maximum angle up to 84°. Numerical problems with these high-grade non-equiangular cells were not encountered. The results emphasise the numerical feasibility and potential efficiency of highly irregular computational meshes used by ICON-O.

A focused and constrained 2D inversion of potential field geophysical data through Delaunay triangulation, a case study for iron-bearing targeting at the Shavaz deposit in Iran

This work illustrates the performance of a focused algorithm for 2D inversion of potential field geophysics (gravity and magnetic) in regions with rugged topography. A non-structured model discretization mesh is performed through Delaunay triangular cells to accurately represent the rugged observation surface and recover complex-shaped sources. Several synthetic single and multi-source targets are simulated to evaluate the applicability of the focused algorithm for simultaneously preserving the edges, correct depth estimation and body distribution of the inverted models. The algorithm is written in such a way that it is able to improve the modeling result per iteration by imposing physical properties constraining (magnetic susceptibility or density contrast), depth weighting and focused term in the central system of linear equation. Whereby a preconditioned conjugate gradient scheme is used iteratively to solve efficiently the L2-norm cost function comprising of a data misfit norm and a model stabilizer. Potential field data pertaining to a real case study for iron-bearing targeting are also inverted along two profiles to investigate the geometry of the sought targets at the Shavaz deposit in Iran. Iron-oxide ore occurrence was approved by exploratory drilling indicating a shallow hematite target with minor compounds of magnetite. Of note is that the significant point of this study lies in accurate recovering of causative sources responsible for potential field anomaly when a severe undulating topography occurs.

Development of passive protection devices for a power head of a high-speed multiple unit train at its collisions

Ukrainian passenger multiple-unit train upgrading supposes on creation of new power heads with passive safety systems (PSS) to save passengers lives, to reduce rolling stock damage and to minimize consequences at collisions. The purpose of this research is to develop energy absorption devices (EADs) for power head PSS according to DSTU EN 15227. EAD 1, EAD 2, EAD 3 designs have been developed with using successful experience of EP20 locomotive EADs creation and EAD prototype crash test results. EAD 1 design includes two elements which are located sequentially. Element 1 is a box with a single-layer package of hexagonal honeycombs inside. Element 2 is a truncated pyramid of honeycombs with triangular cells. EAD 2 design has three steps in element 2 form. EAD 3 design has been developed on the basis of element 1. It has been recommended to install two EAD 1 in a power head frontal part at the coupling level, two EAD 2 in power head window-sill part and two EAD 3 in the inter-car connection at the coupling level. Finite element simulation of EAD plastic deformation at an impact has been carried out for determination of design parameters.

Triangular Quantum-Dot Cellular Automata Wire for Standard Ternary Logic

Quantum-dot cellular automata (QCA) is a computational paradigm that is based on encoding information in terms of the configuration of charge among quantum dots without requiring current switches. Mostly, QCA cells have been realized by employing the electron switching in square quantum-dot cells. In this paper, a triangular metal-dot cell with a single electron is proposed to represent ternary information. Then, an inverter chain of the proposed triangle cells is suggested through juxtaposing the cells. Additionally, wire crossing and wire fan-out are the two inseparable subjects of QCA wire. A wire-crossing method is presented for the proposed ternary wire. Wire fan-out is also dealt with in this paper by an innovative approach. The correctness of operation of proposed cells and wires are thoroughly verified by applying the physical relations.

Different Modes of Deformation of Soft Triangular Honeycombs at the Sub-5nm Scale.

Patterning on the sub-5nm length scale is a contemporary challenge for further miniaturization of microelectronic circuits. Here, the first soft self-assembled triangular patterns are reported showing transitions between regular and two different kinds of isosceles (acute and obtuse angled) triangles on this length scale, formed by liquid crystalline honeycombs of polyphilic block molecules involving a fluorinated oligo(para-phenylene ethynylene) core. The type of formed triangular pattern depends on the degree and position of fluorination and on temperature. They are the first soft honeycombs combining tilted and nontilted organizations in a uniform nanostructure, where the tilted molecules in only one or two sides of the triangular prismatic cells dominate the shape and the size of the morphology.

Research on Flood Propagation for Different Dam Failure Modes: A Case Study in Shenzhen, China

Dam-break flood simulation can evaluate the impact of a dam-break, and is significant in conducting risk analyses, creating emergency plans, and mitigating calamities. This study investigates the dam-break flood propagation in the downstream urban areas of the Minzhi Reservoir in Shenzhen, China, based on a two-dimension shallow-water model (SWM-2D). The SWM-2D solves two-dimensional shallow water equations for free surface flow using the finite-volume method. A refined grid with an unstructured mesh of triangular cells, constrained by building walls, is constructed to represent urban structures in this model. The flood hydrographs of dam-break and the flood propagation under different failure modes are calculated by adopting two breach mechanisms, namely instantaneous dam-break and gradual dam-break. The results indicate that the peak flow of the instantaneous dam-break is relatively large at the beginning of the dam-break. The gradual dam-break peak flow is relatively small when seepage failure deformation develops towards the upper part of the dam. The inundation information during the evolution of the dam-break flood, including the regularity of the flood propagation, distribution of maximum water depth, and variation of depth and velocity with time are also analysed.

Topological and morphological design of additively-manufacturable spatially-varying periodic cellular solids

The focus of this research is to create a methodology to systematically generate spatially-varying, periodic, cellular microstructures that are tailored to attain optimized performance of the macrostructure. The unit cell lattice is represented by Fourier series expansions, and the corresponding amplitudes and phase spectrum are obtained. Then, the material distribution (topology) and orientation of each cell (morphology) are optimized for multiple load cases. The phase of the spatial harmonics is updated based on the optimized orientation, and the analog response is thresholded with the optimized material distribution to find the binary lattices. The framework is tested for three types of lattices with various periodicities. The square cell with a rectangular hole shows the exploitation of the cell's orthotropic properties for structures subjected to a single load case; the triangular cell with the triangular lattice depicts the applicability of other types of cells and lattices to transfer shear for the structures subjected to multiple load cases; and the square cell with pentagonal lattices shows the versatility of the framework. An optimized triangular cellular solid is additively manufactured, and it is validated experimentally that 12% higher stiffness and 57% higher strength can be achieved compared to the conventional topology optimization design.

Damping in cellular structures made from composite struts and walls with elastic and viscoelastic phases

Emerging three-dimensional printing approaches enable cellular structures with composite walls or struts, creating new opportunities for architected materials with high specific stiffness and damping. This paper describes the damped dynamic response of composite walls comprising elastic and viscoelastic phases, and quantifies the scaling between material and structural loss factors. These descriptions are embedded in a highly efficient finite element framework to predict the steady-state frequency-dependent dynamic response of cellular structures, with an emphasis on structural loss factors arising from viscoelasticity. The framework is then used to compare the response of prismatic structures comprising hexagonal, triangular, rhombic and Kagome cells, and to quantify the scaling relationships between cell properties, structural loss factors and material loss factors. Case studies of structures with heterogeneous cell shapes and composite walls illustrate that significant damping gains are possible through architecture. Increases of a factor of two are possible using simple lattice distortions in a monolithic material, while increases of a factor of ten can be achieved with composite walls when the damping material has a loss factor of ∼0.2−1 and a modulus of at least 1% of the elastic phase. The results strongly suggest that future topology and materials optimization will enable dramatic gains in damping.

Form-Finding of Spine Inspired Biotensegrity Model

This paper presents a study on form-finding of four-stage class one self-equilibrated spine biotensegrity models. Advantageous features such as slenderness and natural curvature of the human spine, as well as the stabilizing network that consists of the spinal column and muscles, were modeled and incorporated in the mathematical formulation of the spine biotensegrity models. Form-finding analysis, which involved determination of independent self-equilibrium stress modes using generalized inverse and their linear combination, was carried out. Form-finding strategy for searching the self-equilibrated models was studied through two approaches: application of various combinations of (1) twist angles and (2) nodal coordinates. A total of three configurations of the spine biotensegrity models with different sizes of triangular cell were successfully established for the first time in this study. All members in the spine biotensegrity models satisfied the assumption of linear elastic material behavior. With the established spine biotensegrity model, the advantageous characteristics of flexibility and versatility of movement can be further studied for potential application in deployable structures and flexible arm in the robotic industry.

Crushing characteristic of polygonal tubes with hierarchical triangular cells

This paper proposes N-sided polygonal tubes with hierarchical triangular cells (PHTNs) for use as energy-absorbing devices. Different cross sections of the PHTNs are obtained by changing the number of sides and cells of the sandwich wall. Quasi-static compression experiments and finite element (FE) simulations are used to analyse the axial crushing behaviour and energy absorption performance of the PHTNs. The results show that the PHTNs has two deformation modes: when N ≤ 24, the deformation mode is progressive folding, whereas when N > 24, the deformation mode is sandwich folding. The 24-sided PHTN (PHT24) exhibits the best energy absorption performance, and the specific energy absorption (SEA) of PHT24 is 110.37% greater than the minimum SEA, which is exhibit by PHT06. The results also reveal that the energy absorption is improved mainly by shortening the wavelength or increasing the plastic bending moment of the sandwich wall. Finally, theoretical models are established for predicting the mean crushing force in the PHTNs under both deformation modes. The predictions from these models are in good agreement with the FE simulation results, thereby indicating that the predictions are highly accurate.

Study of tunable locally resonant metamaterials: Effects of spider-web and snowflake hierarchies

The present research is an effort to enhance and control locally resonant bandgaps in periodic metamaterials of hexagonal and triangular topologies by introducing spider-web and snowflake-inspired hierarchies to the conventional geometries. Due to their low connectivity number, hexagonal lattice structures are unable to exhibit locally resonant bandgaps. By introducing the spider-web hierarchy, the connectivity number of the structure is increased, and the constituting beams act as local resonators. Thus, the hexagonal lattice structure can attenuate propagating waves in desirable frequency ranges by localizing the wave energy in the constituent beams. As a result, better wave-filtering performance is achieved by introducing hierarchy to hexagonal lattices. Furthermore, the snowflake hierarchical triangular lattice structures exhibit new tunable attenuation zones for which the locations depend on the mechanical and geometrical parameters. The finite element method and Bloch’s theorem are applied to analyze the wave propagation in the considered architected structures. Moreover, theoretical formulations are presented to predict the locations of each locally resonant bandgaps. It is shown that by changing the mechanical and geometrical parameters of the added hierarchical structures, the locally resonant bandgaps can be perfectly tuned to the desired frequencies in the long-wavelength region. Finally, two theoretical diagrams are proposed to represent initial design concepts of tunable acoustic/elastic metamaterials of hexagonal and triangular unit cells with maximum bandgap widths in low frequencies. To present a more comprehensive analysis of the wave propagation in hierarchical structures, the effects of imaginary wave-vector components on the dispersion curves and attenuation behavior of each topology are also investigated. The results of the current study enable the engineers to design architected periodic structures with the ability to present bandgaps in desired frequencies, which has been the goal of structural engineers for years.

Coupled numerical analysis for in-plane elastic T-stress evaluation in isotropic FG solids

This contribution establishes a coupled numerical method to show its effectiveness in the simulation of LEFM problems. The semi-meshless method uses the MLPG1 meshfree theory to discrete governing equations while geometry is modeled by simple CPS3 triangular cells. The cells help to propose an efficient neighboring method for meshfree interpolations. Three benchmark homogeneous cases are considered whose analytical solutions are available to carefully examine the accuracy of this method and validate the numerical implementation by comparing relative errors in terms of error norms, crack onset angle and also fracture parameters, i.e. KI, KII and T-stress that characterize the crack tip condition. Good computational accuracy is observed in this article. Three FG structures by simple linear, exponential and complex hyperbolic-tangent gradations are taken from the literature and investigated under thermo-mechanical conditions. A thermal barrier coating with an FG structure is also modeled. Then, fracture parameters and crack growth angles with and without considering T-stress are compared with FE solutions. Generalized maximum tangential stress (GMTS) criterion and interaction integral method are used to respectively compute crack growth angle and capture T.

A 3-D-Printed Multibeam Dual Circularly Polarized Luneburg Lens Antenna Based on Quasi-Icosahedron Models forKa-Band Wireless Applications

This article presents a multibeam dual circularly polarized (CP) Luneburg lens (LL) antenna based on quasi-icosahedron (QICO) models. The lens is sliced into multiple shells and each shell comprises of several triangular unit cells, and then the permittivity variation is achieved by manipulating the wall thickness of each triangular unit cells after the QICO discretization. Such a QICO model is firstly proposed to be used in LL design, which not only makes the lens mechanically robust and manufacturing-friendly (no support is needed in the processing) but also enables the antenna to be polarization insensitive and thus can sustain CP beams very well. A wideband ridged waveguide feed is selected to initiate left-handed CP (LHCP) and right-handed CP (RHCP) beams simultaneously. To prove the concept, a prototype was fabricated using 3-D-printing (3DP) technologies. The measurement results reveal an overlapped bandwidth of 33.1% (26.5-37 GHz) in terms of reflection coefficients lower than -10 dB and axial ratios smaller than 3 dB. Five LHCP and five RHCP beams with gains of 19-21.2 dBic and couplings lower than -20 dB are also demonstrated.

Fase gametofítica de tres taxones de Anemia (Anemiaceae)

Antecedentes y Objetivos: Anemiaceae presenta un único género, Anemia, con 115 especies que se distribuyen en el Neotrópico, África, India e islas en el Océano Índico. El objetivo de este trabajo es caracterizar las esporas vivas y la fase gametofítica de tres taxones de Anemia sudamericanas, poco estudiadas o con estudios fragmentados, A. herzogii, A. tomentosa var. anthriscifolia y A. tomentosa var. tomentosa.Métodos: Los gametofitos de los tres taxones han sido obtenidos a través de cultivos in vitro de las esporas. Las esporas y los gametofitos fueron estudiados a través del microscopio de luz y electrónico de barrido. Se describió el patrón de germinación de las esporas, evolución del desarrollo gametofítico y expresión sexual.Resultados clave: Los gametofitos filamentosos estaban formados por 4-20 células, los adultos fueron cordados simétricos o asimétricos, bisexuales y protándricos, en sus superficies y márgenes se observaron tricomas clavados. Los gametangios corresponden al tipo leptosporangiado. La dehiscencia de los anteridios se produjo mediante una perforación en la célula opercular. Los arquegonios tenían cuellos con cuatro a siete células y cuatro células triangulares en el extremo distal del cuello. Anemia herzogii mostró tricomas ramificados sobre los gametofitos y más tarde desarrolló esporofitos.Conclusiones: La germinación en todos los taxones corresponde al tipo Anemia y el desarrollo gametofítico al tipo Ceratopteris. Anemia herzogii se distingue de las dos variedades por la presencia de tricomas ramificados exclusivos de la fase gametofítica. Los taxones estudiados se caracterizan por la morfología del gametofito, tipo de tricomas y sexualidad.