Geometry Systems for Lattice-Based Reconfigurable Space Structures

Efficient exchange of nutrients and wastes required for cell proliferation and differentiation plays a pivotal role in improving the service life of porous implants. In this study, mass transport properties for porous implant with different unit cells were evaluated and predicted when the porosities are kept the same. To this end, three typical unit cells (diamond (DO), rhombic dodecahedron (RD), and octet truss (OT)) were selected, in which DO displayed diagonal-symmetrical shape, while RD and OT share midline-symmetrical structure. Then, single unit cells were designed quantitatively, and its shape parameters were measured and calculated. Moreover, corresponding porous scaffolds with same outline size were created, respectively. Furthermore, using computational fluid dynamics (CFD) methodology, flow performances with Dulbecco's Modified Eagle's Medium (DMEM) in vitro were simulated for three different porous implants, and flow trajectory, velocity, and wall shear stress which could reflect the properties of mass transfer and tissue regeneration were compared and predicted numerically. Results demonstrated that different unit cell could directly lead to different mass transport properties for porous implant, in spite of same porosity, scaffold size, and service environment. Additionally, by the results, DO displayed greater tortuosity, more appropriate areas, and smoother shear stress distribution than RD and OT, which would provide better surroundings for implant fixation and tissue regeneration. However, RD and OT showed better mass transport properties because of bigger maximum velocity (5.177 mm/s, 4.381 mm/s) than DO (3.941 mm/s). This study would provide great helps for unit cell selection and biological performance optimization for 3D printed bone implants.

Let p p be an odd prime. Let P P be a finite p p -group of class 2 2 and exponent p p , whose commutator quotient P / [ P , P ] P/[P,P] is of order p n p^n . We define two parameters for P P related to central decompositions. The first parameter, κ ( P ) \kappa (P) , is the smallest integer s s for the existence of a subgroup S S of P P satisfying (1) S ∩ [ P , P ] = [ S , S ] S\cap [P,P]=[S,S] , (2) | S / [ S , S ] | = p n − s |S/[S,S]|=p^{n-s} , and (3) S S is centrally decomposable. The second parameter, λ ( P ) \lambda (P) , is the smallest integer s s for the existence of a central subgroup N N of order p s p^s , such that P / N P/N is centrally decomposable. While defined in purely group-theoretic terms, these two parameters generalise, respectively, the vertex and edge connectivities of graphs: For a simple undirected graph G G , through the classical procedures of Baer (Trans. Amer. Math. Soc., 1938), Tutte (J. Lond. Math. Soc., 1947) and Lovász (B. Braz. Math. Soc., 1989), there is a p p -group P G P_G of class 2 2 and exponent p p that is naturally associated with G G . Our main results show that the vertex connectivity κ ( G ) \kappa (G) equals κ ( P G ) \kappa (P_G) , and the edge connectivity λ ( G ) \lambda (G) equals λ ( P G ) \lambda (P_G) . We also discuss the relation between κ ( P ) \kappa (P) and λ ( P ) \lambda (P) for a general p p -group P P of class 2 2 and exponent p p , as well as the computational aspects of these parameters. In particular, our main results imply that the p p -group central decomposition algorithm of Wilson (J. Algebra and J. of Group Theory, 2009) can be used to solve the graph connectivity problem.

Metallic lattice structures have been widely utilized in different fields such as automobile, aerospace and so on, owing to their superior mechanical properties and energy absorption characteristics. In this paper, the enhanced dynamic mechanical properties of the modified rhombic dodecahedron (RD) lattice structures were investigated systematically through numerical simulation and theoretical analysis. Results indicated that compressive modulus, initial yield strength and normalized specific energy absorption (SEA) of the modified RD lattice structures all exhibited a quadratic growth trend with the increase of relative density beyond following the traditional law. Meanwhile, the plateau stress and normalized SEA exhibited certain sensitivity to the strain rate and almost linearly increased as the loading rate increased. Finally, a modified rigid-perfectly plastic-locking shock wave model was also proposed, and the predicted results of the proposed modified shock wave model were consistent with the simulation results.

The cyclic vertex (resp., edge) connectivity of a graph [Formula: see text], denoted by [Formula: see text] (resp., [Formula: see text]), is the minimum number of vertices (resp., edges) whose removal from [Formula: see text] results in a disconnected graph and at least two remaining components contain cycles. Thus, to determine the exact values of [Formula: see text] and [Formula: see text] is important in the reliability assessment of interconnection networks. However, the study of the cyclic vertex (edge) connectivity is less involved. In this paper, we determine the cyclic vertex (edge) connectivity of the burnt pancake graphs [Formula: see text] which is the Cayley graph of the group of signed permutations using prefix reversals as generators. By exploring the combinatorial properties and fault-tolerance of [Formula: see text], we show [Formula: see text] and [Formula: see text] for [Formula: see text]. Moreover, we determine that [Formula: see text] for [Formula: see text].

Aluminium alloy cans are generally used as containers for electrochemical energy systems like capacitors and advanced batteries. Packing efficiency of batteries depends upon their configuration. Containers in prismatic, cylindrical and elliptic-cylindrical shapes are generally used for battery applications. Elliptic-cylindrical shape has the advantage of better heat dissipation and good packing efficiency in battery assembly. Safety device to be provided in the cans requires material in the minimum half hard (H14) condition. In the present work, ellipsoidal cans of Al-Mn alloy were successfully realised by impact extrusion process. Mechanical properties of the cans were analysed through to ensure the adequacy of the process and it has been demonstrated that impact extrusion is a viable process for making cans for batteries with required mechanical properties, for the can in total and for the safety device in particular.

Edge and vertex connectivity, as well as edge and vertex cuts are among the most basic and fundamental concepts in graph theory. In particular, they are naturally significant in a networking context as they are a measure for the rate at which information can be transferred across a network. While in a traditional, sequential setting, there is a rich literature (in particular on problems related to edge connectivity and edge cuts), until recently, much less was known from a distributed algorithms point of view. In my talk, I will discuss and give partial answers to some of the following basic questions. Using distributed algorithms, how fast can we compute or approximate the edge or vertex connectivity and is it possible to efficiently find small cuts in a network? Assuming, we have a network with good connectivity properties, to what extent is it possible to exploit this in order to speed up distributed computations? Where such properties can be exploited, are there network structures that allow to make use of good connectivity in a structured (and somewhat canonical) way and can we construct such structures in a distributed manner?

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells

In order to obtain a lightweight, high strength, and large design space wooden sandwich structure to meet the needs of modern wooden buildings, the mechanical properties of a fabricated 2D wooden pyramid lattice sandwich structure were studied. In this paper, the mechanical and compressive properties of the specimens with different arrangement of Lattice Sandwich unit cells are studied. The upper and lower panels and core materials are made into a single unit cell by inserting glue, and the prefabricated 2D wooden pyramid lattice truss core sandwich structure is prepared by the mortise tenon splicing method. The results show that the arrangement of the unit cells in the specimen has a significant effect on the bearing capacity, energy absorption, and failure mode of the specimen, and the flat compression performance of the panel-reinforced specimen is better than that of the specimen with unreinforced veneer. The results of finite element analysis are consistent with the test results. The main failure modes are core fracture and panel cracking. These results provide a theoretical basis for the system design of wood-based lattice sandwich structure in the future.

ABSTRACTCellular scaffolds can provide morphological and mechanical integrity with human bone. Various structural designs have been studied; however, their structural and mechanical properties have not been sufficiently compared under the same conditions. This study investigates the effect of unit cell type and size on the dimensional accuracy, porosity accuracy, pore size, and compressive properties of cellular polylactic acid (PLA) scaffolds. These scaffolds were additively manufactured using the fused deposition modeling (FDM) method. Three levels of unit cell type and unit cell sizes were investigated. Strut‐based cubic, octet, and surface‐based gyroid structures with 2.5, 3, and 4 mm unit cell sizes were designed, fabricated, and characterized. The scaffolds were created with a constant porosity of 60%. A two‐way analysis of variance (ANOVA) was performed to identify the significance of unit cell type and size on the measured characteristics. Unit cell type and size significantly impact structural and mechanical properties, as well as the printability of the scaffolds. The structures exhibit trabecular bone‐like mechanical properties, with deformation behavior more dependent on unit cell type than unit cell size. Results show preferability to gyroid structures, with recommendations for enhancing their porosity accuracy.

Mechanical properties and cytocompatibility of dense and porous Zn produced by laser powder bed fusion for biodegradable implant applications

Energy-absorbing parts are important for the landing system of space crafts on celestial bodies. Open-cell porousPorous aluminum aluminumAluminum alloysAluminum alloys for energy as an energy-absorbing material were manufactured through the powder bed fusion (PBF) process. Mechanical propertiesMechanical properties of the porous metalsMetal depend on the cell structure as well as the porosity. The authors manufactured ordered cell structures, truncated octahedron and rhombic dodecahedron, and disordered cell structure, based on Voronoi diagramsVoronoi diagram using a 3D-CAD software. CompressionCompression tests revealed the high compressive strength and low energy absorptionEnergy absorption efficiency of porousPorous aluminum aluminumAluminum alloysAluminum alloys with ordered cell structure. On the other hand, the porousPorous aluminum aluminumAluminum alloysAluminum alloys with disordered cell structure showed relatively high energy absorptionEnergy absorption efficiency. Controlling the disordered cell structure designed by a 3D-Voronoi diagramVoronoi diagram enables to develop the advanced porous metalsMetal having various mechanical propertiesMechanical properties .

This paper presents a comparative study of three algorithms that use occupancy grid map of environments to find a path for a mobile robot from the given start to the goal — the D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> , Two Way D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> (TWD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> ) and E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> . All three algorithms have ability of dynamic replanning in case of changes in the environment. The D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> algorithm produces a path consisted of line segments that have discrete transitions between cell edges — a multiple of 45°. This path is hard to follow by a mobile robot. The TWD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> and E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> algorithms produce more natural paths with continuous headings of the path line segments. The criteria for comparison were the path characteristics, the time of execution and the number of iterations of the algorithms' main while loop. The algorithms were verified both by simulation and experimentally on a Pioneer 3DX mobile robot equipped with a laser range finder.

Stiffness design of a multilayer arbitrary BCC lattice structure with face sheets

Cellular structures are promising applicants for additive manufacturing (AM), due to their best capabilities over solid ones such as high strength-to-weight ratio, having porosity, and light in weight. New vintile cellular structures and with the existing five different cellular structures namely cubic, tetrahedron, hexagon, octagon, and rhombic dodecahedron were designed and the effect of unit size, lattice topology, porosity, and optimization of cellular structures on the mechanical properties were discussed in this study. Eighty-four samples with different cell sizes, lattice topologies, and porosities were printed using VisiJet M3 Crystal material on Projet 3510 HDMax 3D printer. Then, electro-optical microscopic is used to determine the pore size. Based on predesigned cellular structures, finite element analysis (FEA) and experimental work were performed to estimate and evaluate the mechanical properties of cellular structures. Results shown that the cellular structure with vintile lattice topology performs less stress and less deformation than the other cellular structures. The experiment results were in good conformance with the result obtained from simulation. This study is not only limited to cellular structure design for biomedical applications but also compared the mechanical performance of uniform density and variable density cellular structures. Both non-optimized and optimized vintile cellular structures is finally tested with FEA and experiments have been carried out on samples fabricated by material jetting, and both results have shown that the optimized cellular structure had much less stress and lower deformation than the non-optimized cellular structure.

The Ni-Co alloy was coated with Ni-Co-TiN/CeO2 by Jet electrodeposition to enhance the properties of Nickel-Cobalt (Ni-Co) alloy. The morphologies, texture orientation, microhardness, coating adhesion, wear resistance, and corrosion resistance of Ni-Co-TiN/CeO2 composite coatings were characterized. The influences of concentration of mixed particles (micron-TiN and nano- CeO2) on microstructural, surface properties, mechanical properties and anti-corrosion performance of the composite coatings were studied. The addition of nano-mixed particles changed the morphology of Ni-Co-TiN/CeO2 composite coating from large cellular protrusion structures to fine granular structures, the mechanical properties and anti-corrosion performance of Ni-Co-TiN/CeO2 composite coatings were improved. The composite coating exhibited superior microhardness, bonding force, wear resistance and anti-corrosion performance, when the concentration of mixed particles was 4 g l−1. This work contributed to the development of a variety of micro- and nanoparticle phase-enhanced metal-based composite coatings.