Relevant bibliographies by topics / Structures lattices

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Structures lattices'

Author: Grafiati
Published: 15 March 2025

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Journal articles on the topic "Structures lattices"

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Majari, Parisa, Daniel Olvera-Trejo, Jorge A. Estrada-Díaz, Alex Elías-Zúñiga, Oscar Martinez-Romero, Claudia A. Ramírez-Herrera, and Imperio Anel Perales-Martínez. "Enhanced Lightweight Structures Through Brachistochrone-Inspired Lattice Design." Polymers 17, no. 5 (February 28, 2025): 654. https://doi.org/10.3390/polym17050654.

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Lattice structures offer unique mechanical properties and versatility in engineering applications, yet existing designs often struggle to balance performance and material efficiency. This study introduces the brachistochrone curve as a novel framework for optimizing lattice geometries, enhancing mechanical behavior while minimizing material usage. Using finite element simulations and compressive testing of 3D-printed samples, we analyzed the mechanical response of brachistochrone-based (B-) and standard lattice structures (diamond, IWP, gyroid, and BCC). We investigated the scaling behavior of the volume-to-surface area ratio, incorporated fractal dimension analysis, and compared experimental and numerical results to evaluate the performance of B-lattices versus standard designs (S-). Our findings indicate that brachistochrone-inspired lattices enhance mechanical efficiency, enabling the design of lightweight, high-strength components with sustainable material use. Experimental results suggest that B-gyroid lattices exhibit lower stiffness than S-gyroid lattices under small displacements, highlighting their potential for energy absorption applications.
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Maskery, Ian, Alexandra Hussey, Ajit Panesar, Adedeji Aremu, Christopher Tuck, Ian Ashcroft, and Richard Hague. "An investigation into reinforced and functionally graded lattice structures." Journal of Cellular Plastics 53, no. 2 (July 28, 2016): 151–65. http://dx.doi.org/10.1177/0021955x16639035.

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Lattice structures are regarded as excellent candidates for use in lightweight energy-absorbing applications, such as crash protection. In this paper we investigate the crushing behaviour, mechanical properties and energy absorption of lattices made by an additive manufacturing process. Two types of lattice were examined: body-centred-cubic (BCC) and a reinforced variant called BCC z. The lattices were subject to compressive loads in two orthogonal directions, allowing an assessment of their mechanical anisotropy to be made. We also examined functionally graded versions of these lattices, which featured a density gradient along one direction. The graded structures exhibited distinct crushing behaviour, with a sequential collapse of cellular layers preceding full densification. For the BCC z lattice, the graded structures were able to absorb around 114% more energy per unit volume than their non-graded counterparts before full densification, 1371 ± 9 kJ/m3 versus 640 ± 10 kJ/m3. This highlights the strong potential for functionally graded lattices to be used in energy-absorbing applications. Finally, we determined several of the Gibson–Ashby coefficients relating the mechanical properties of lattice structures to their density; these are crucial in establishing the constitutive models required for effective lattice design. These results improve the current understanding of additively manufactured lattices and will enable the design of sophisticated, functional, lightweight components in the future.
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Horváth, Eszter K., Sándor Radeleczki, Branimir Šešelja, and Andreja Tepavčević. "A Note on Cuts of Lattice-Valued Functions and Concept Lattices." Mathematica Slovaca 73, no. 3 (June 1, 2023): 583–94. http://dx.doi.org/10.1515/ms-2023-0043.

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ABSTRACT Motivated by applications of lattice-valued functions (lattice-valued fuzzy sets) in the theory of ordered structures, we investigate a special kind of posets and lattices induced by these mappings. As a framework, we use the Formal Concept Analysis in which these ordered structures can be naturally observed. We characterize the lattice of cut sets and the Dedekind-MacNeille completion of the set of images of a lattice valued function by suitable concept lattices and we give necessary and sufficient conditions under which these lattices coincide. In addition, we give conditions under which the lattice of cuts is completely distributive.
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El-Gayar, Mostafa A., and Radwan Abu-Gdairi. "Extension of topological structures using lattices and rough sets." AIMS Mathematics 9, no. 3 (2024): 7552–69. http://dx.doi.org/10.3934/math.2024366.

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<abstract><p>This paper explores the application of rough set theory in analyzing ambiguous data within complete information systems. The study extends topological structures using equivalence relations, establishing an extension of topological lattice within lattices. Various relations on topological spaces generate different forms of exact and rough lattices. Building on Zhou's work, the research investigates rough sets within the extension topological lattice and explores the isomorphism between topology and its extension. Additionally, the paper investigates the integration of lattices and rough sets, essential mathematical tools widely used in problem-solving. Focusing on computer science's prominent lattices and Pawlak's rough sets, the study introduces extension lattices, emphasizing lower and upper extension approximations' adaptability for practical applications. These approximations enhance pattern recognition and model uncertain data with finer granularity. While acknowledging the benefits, the paper stresses the importance of empirical validations for domain-specific efficacy. It also highlights the isomorphism between topology and its extension, revealing implications for data representation, decision-making, and computational efficiency. This isomorphism facilitates accurate data representations and streamlines computations, contributing to improved efficiency. The study enhances the understanding of integrating lattices and rough sets, offering potential applications in data analysis, decision support systems, and computational modeling.</p></abstract>
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Shatabda, Swakkhar, M. A. Hakim Newton, Mahmood A. Rashid, Duc Nghia Pham, and Abdul Sattar. "How Good Are Simplified Models for Protein Structure Prediction?" Advances in Bioinformatics 2014 (April 29, 2014): 1–9. http://dx.doi.org/10.1155/2014/867179.

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Protein structure prediction (PSP) has been one of the most challenging problems in computational biology for several decades. The challenge is largely due to the complexity of the all-atomic details and the unknown nature of the energy function. Researchers have therefore used simplified energy models that consider interaction potentials only between the amino acid monomers in contact on discrete lattices. The restricted nature of the lattices and the energy models poses a twofold concern regarding the assessment of the models. Can a native or a very close structure be obtained when structures are mapped to lattices? Can the contact based energy models on discrete lattices guide the search towards the native structures? In this paper, we use the protein chain lattice fitting (PCLF) problem to address the first concern; we developed a constraint-based local search algorithm for the PCLF problem for cubic and face-centered cubic lattices and found very close lattice fits for the native structures. For the second concern, we use a number of techniques to sample the conformation space and find correlations between energy functions and root mean square deviation (RMSD) distance of the lattice-based structures with the native structures. Our analysis reveals weakness of several contact based energy models used that are popular in PSP.
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Grabowski, Adam. "Stone Lattices." Formalized Mathematics 23, no. 4 (December 1, 2015): 387–96. http://dx.doi.org/10.1515/forma-2015-0031.

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Summary The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the other which is dense. The core of the paper is of course the idea of Stone identity $$a^* \sqcup a^{**} = {\rm{T}},$$ which is fundamental for us: Stone lattices are those lattices L, which are distributive, bounded, and satisfy Stone identity for all elements a ∈ L. Stone algebras were introduced by Grätzer and Schmidt in [18]. Of course, the pseudocomplement is unique (if exists), so in a pseudcomplemented lattice we defined a * as the Mizar functor (unary operation mapping every element to its pseudocomplement). In Section 2 we prove formally a collection of ordinary properties of pseudocomplemented lattices. All Boolean lattices are Stone, and a natural example of the lattice which is Stone, but not Boolean, is the lattice of all natural divisors of p 2 for arbitrary prime number p (Section 6). At the end we formalize the notion of the Stone lattice B [2] (of pairs of elements a, b of B such that a ⩽ b) constructed as a sublattice of B 2, where B is arbitrary Boolean algebra (and we describe skeleton and the set of dense elements in such lattices). In a natural way, we deal with Cartesian product of pseudocomplemented lattices. Our formalization was inspired by [17], and is an important step in formalizing Jouni Järvinen Lattice theory for rough sets [19], so it follows rather the latter paper. We deal essentially with Section 4.3, pages 423–426. The description of handling complemented structures in Mizar [6] can be found in [12]. The current article together with [15] establishes the formal background for algebraic structures which are important for [10], [16] by means of mechanisms of merging theories as described in [11].
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Pan, Chen, Yafeng Han, and Jiping Lu. "Design and Optimization of Lattice Structures: A Review." Applied Sciences 10, no. 18 (September 13, 2020): 6374. http://dx.doi.org/10.3390/app10186374.

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Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.
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Lan, Tian, Chenxi Peng, Kate Fox, Truong Do, and Phuong Tran. "Triply periodic minimal surfaces lattice structures: Functional graded and hybrid designs for engineering applications." Materials Science in Additive Manufacturing 2, no. 3 (September 27, 2023): 1753. http://dx.doi.org/10.36922/msam.1753.

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In this work, we propose the strategies for designing radial graded sheet-based gyroid lattice and the approach to hybridizing solid-network-based gyroid lattice and primitive lattice. The elastic property of triply periodic minimal surfaces (TPMS) sheet-based gyroid lattice structures was explored. We also conducted numerical analysis to investigate the effect of functionally graded sheet-based gyroid lattices on the implant application, and explored the elastic properties of the uniform gyroid lattice parametrically with different relative densities based on the representative volume element model. Analytical equations based on the Gibson-Ashby model were generated to predict the elastic properties. Compressive tests on the samples fabricated by the Stratasys J750 were conducted to validate the feasibility of applying hybridization of different types of lattices. A comparison between radial hybrid primitive-gyroid and gyroid-primitive lattices revealed that the compressive behavior of gyroid-primitive was strengthened. We also found that the gyroid-primitive lattice could achieve auxetic compressive behavior. In conclusion, the numerical analysis illustrates that the application of the functional graded gyroid lattices can relieve the stress shielding effect as well as protects the bone from damage. The hybridization of different lattices can not only strengthen the mechanical properties of TPMS structures but also create a counter-intuitive deformation response.
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Liu, Tinghao, and Guangbo Hao. "Design of Deployable Structures by Using Bistable Compliant Mechanisms." Micromachines 13, no. 5 (April 19, 2022): 651. http://dx.doi.org/10.3390/mi13050651.

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A deployable structure can significantly change its geometric shape by switching lattice configurations. Using compliant mechanisms as the lattice units can prevent wear and friction among multi-part mechanisms. This work presents two distinctive deployable structures based on a programmable compliant bistable lattice. Several novel parameters are introduced into the bistable mechanism to better control the behaviour of bistable mechanisms. By adjusting the defined geometry parameters, the programmable bistable lattices can be optimized for specific targets such as a larger deformation range or higher stability. The first structure is designed to perform 1D deployable movement. This structure consists of multi-series-connected bistable lattices. In order to explore the 3D bistable characteristic, a cylindrical deployable mechanism is designed based on the curved double tensural bistable lattice. The investigation of bistable lattices mainly involves four types of bistable mechanisms. These bistable mechanisms are obtained by dividing the long segment of traditional compliant bistable mechanisms into two equal parts and setting a series of angle data to them, respectively. The experiment and FEA simulation results confirm the feasibility of the compliant deployable structures.
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Flaut, Cristina, Dana Piciu, and Bianca Liana Bercea. "Some Applications of Fuzzy Sets in Residuated Lattices." Axioms 13, no. 4 (April 18, 2024): 267. http://dx.doi.org/10.3390/axioms13040267.

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Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory.
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Dissertations / Theses on the topic "Structures lattices"

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Galvin, Brian Russell. "Numerical studies of localized vibrating structures in nonlinear lattices." Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/28408.

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Zhang, Botao. "Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535374427634743.

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Brown, Stephen A. "The response of polyhedra in close packed structures to temperature and pressure." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-11102009-020124/.

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Damon, François. "Sonder des structures complexes avec des ondes de matière." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30342/document.

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Ce manuscrit présente les travaux que j'ai effectués au Laboratoire de Physique Théorique durant ma thèse. Ils portent sur l'interaction d'ondes de matière avec des réseaux optiques modulables en temps et en espace. L'utilisation de ces réseaux a permis de contrôler de manière cohérente les propriétés dynamiques d'un gaz d 'atomes ultra-froids. Cette étude théorique a été réalisée en collaboration avec le groupe Atomes Froids du Laboratoire LCAR. Les variations spatiales de l'enveloppe d u réseau créent, localement, des gaps spatiaux créant une cavité de Bragg pour onde de matière, dont nous avons étudié en détail les propriétés et qui a fait l'objet d'une réalisation expérimentale impliquant la propagation d'un condensat de Bose-Einstein de rubidium 85 dans un guide d'onde. Nous avons également étudié la propagation d'un nuage d 'atomes dans un réseau bichromatique qui permet de réaliser un simulateur quantique du modèle de Harper. Le spectre du hamiltonien de ce système a une dimension fractale pouvant être caractérisée nu­ mériquement. Nous avons montré, par ailleurs, qu'il est possible d'exploiter les interactions inter-atomiques répulsives d'un condensat de Bose-Einstein afin d'amplifier les corrélations position-vitesse lors de sa pro­ pagation dans un guide. Notre étude montre qu'une mesure des grandeurs dynamiques locales du nuage atomique permet de sonder expérimentalement les résonances d'un potentiel optique jusqu'à l'échelle du picoKelvin. Enfin, un nuage d'atomes en interaction attractive admet une solution d'équilibre : le soliton. Nous avons démontré, numériquement, que celui-ci peut être utilisé pour sonder des états liés d'un poten­ tiel de taille finie, en peuplant ces états lors d'une expérience de diffusion comme, par exemple, des états de surface
This thesis presents the studies that I did at the Laboratoire de Physique Théorique. It concerns the interaction between matter waves and time and space depandant optical lattices. Using such lattices allows one to manipulate coherently the dynamical properties of ultra cold atoms. This theoretical study has been done in collaboration with the Cold Atoms group at the LCAR laboratory. The spatial variations of the lattice envelope locally create spatial gaps which create a Bragg cavity for matter waves. We have st udied in detail their properties and the cavity has been realized experimentally by using a Ru bid ium 85 Bose-Einstein condensate in a wave guide. We have also studied the propagation of an atomic cloud in a bichromatic optical lattice which allows us to make a quantum simulator of the Harper madel. The spectrum of the system Hamiltonian· posseses a fractal dimension which can be numerically characterized. We have also shawn that it is possible to use the repulsive interatomic interaction of a Bose-Einstein condensate in arder to amplify the momentum-position correlation during propagation in a guide. Our st udy shows that a mesure of local dynamical quantities of the atomic cloud enables one to experimentally probe resonances of an optical potential down to the picoKelvin scale. At last, an atomic cloud with attractive interactions admit a stable solution, the soliton. We have numerically demonstrated that this soliton can be used to probe bound states of a potential by populating those states through a scattering experiment, for example surface states
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Reid, Robert. "Propagation and period-doubling of coherent structures in coupled lattice maps." Thesis, University of Warwick, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369417.

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Leo, James Lewis. "The transport properties of semiconductor super-lattices and multiple quantum well structures." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47153.

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Holder, Jonathan Paul. "Resonant tunnelling spectroscopy of vertical GaAs/AlGaAs structures." Thesis, University of Exeter, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312281.

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Stay, Justin L. "Multi-beam-interference-based methodology for the fabrication of photonic crystal structures." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31783.

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Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Thomas K. Gaylord; Committee Member: Donald D. Davis; Committee Member: Gee-Kung Chang; Committee Member: Muhannad S. Bakir; Committee Member: Phillip N. First. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Refai, Khalil. "Effet de la méso-architecture sur le comportement en fatigue des structures lattices optimisées obtenues par fabrication additive." Thesis, Paris, HESAM, 2020. http://www.theses.fr/2020HESAE028.

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Une approche numérique est proposée pour évaluer la résistance en fatigue à grand nombre de cycles des structures cellulaires périodiques produites par SLM sous des chargements multiaxiaux. Le modèle est basé sur un schéma général d'homogénéisation numérique et une description explicite de la cellule élémentaire combinée à une analyse des valeurs extrêmes utilisant un paramètre indicateur de fatigue basé sur le critère de Crossland. De plus, l'écart géométrique et la rugosité de surface sont caractérisés expérimentalement et prisent en compte dans le modèle numérique en utilisant trois méthodes qui sont comparées à la résistance en fatigue expérimentale. L'optimisation topologique (OT) repousse encore plus loin les limites de la liberté de conception. Dans notre étude, l'OT a été développée pour prévenir les défaillances dues à la fatigue en utilisant la méthode SIMP reformulée dans le cadre mathématique des fonctions NURBS (Non-Uniform Rational BSpline)
A numerical approach is proposed to assess the high cycle fatigue strength of periodic cellular structures produced by SLM under multiaxial loads. The model is based on a general numerical homogenisation scheme and an explicit description of the Elementary Cell combined to an extreme values analysis making use of a fatigue indicator parameter based on Crossland’s criterion. Also, geometric discrepancy and surface roughness are experimentally characterised and considered in the numerical model using three methods which are compared to the experimental fatigue strength. Topology optimisation (TO) pushes the boundaries of design freedom even further. In our study, Topology Optimisation was developed to prevent fatigue failure using SIMP method revisited and reformulated within the mathematical framework of Non-Uniform Rational BSpline functions
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Chen, Li. "A quasicontinuum approach towards mechanical simulations of periodic lattice structures." Doctoral thesis, Universite Libre de Bruxelles, 2020. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/314314.

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Thanks to the advancement of additive manufacturing, periodic metallic lattice structures are gaining more and more attention. A major attraction of them is that their design can be tailored to specific applications by changing the basic repetitive pattern of the lattice, called the unit cell. This may involve the selection of optimal strut diameters and orientations, as well as the connectivity and strut lengths. Numerical simulation plays a vital role in understanding the mechanical behavior of metallic lattices and it enables the optimization of design parameters. However, conventional numerical modeling strategies in which each strut is represented by one or more beam finite elements yield prohibitively time­ consuming simulations for metallic lattices in engineering­ scale applications. The reasons are that millions of struts are involved, as well as that geometrical and material nonlinearities at the strut level need to be incorporated. The aim of this thesis is the development of multi­scale quasicontinuum (QC) frameworks to substantially reduce the simulation time of nonlinear mechanical models of metallic lattices. For this purpose, this thesis generalizes the QC method by a multi­-field interpolation enabling amongst others the representation of varying diameters in the struts’ axial directions (as a consequence of the manufacturing process). The efficiency is further increased by a new adaptive scheme that automatically adjusts the model reduction whilst controlling the (elastic or elastoplastic) model’s accuracy. The capabilities of the proposed methodology are demonstrated using numerical examples, such as indentation tests and scratch tests, in which the lattice is modeled using geometrically nonlinear elastic and elastoplastic beam finite elements. They show that the multi­scale framework combines a high accuracy with substantial model reduction that are out of reach of direct numerical simulations.
Doctorat en Sciences de l'ingénieur et technologie
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Books on the topic "Structures lattices"

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Müller-Hoissen, Folkert, Jean Marcel Pallo, and Jim Stasheff, eds. Associahedra, Tamari Lattices and Related Structures. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0405-9.

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Fuentes, Benjamin J. Optical lattices: Structures, atoms, and solitons. Hauppauge, N.Y: Nova Science Publishers, 2012.

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Galvin, Brian Russell. Numerical studies of localized vibrating structures in nonlinear lattices. Monterey, Calif: Naval Postgraduate School, 1991.

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International Conference on Modulated Semiconductor Structures (3rd 1987 Montpellier, France). 3rd International Conference on Modulated Semiconductor Structures, 6-10 July 1987, Montpellier, France. Cedex: Editions de Physique, 1987.

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1956-, Strien Sebastian van, Verduyn Lunel S. M, and Koninklijke Nederlandse Akademie van Wetenschappen. Afdeling Natuurkunde., eds. Stochastic and spatial structures of dynamical systems: Proceedings of the colloquium, Amsterdam, 26-27 January 1995. Amsterdam: North-Holland, 1996.

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C, McGill T. Device Physics of Superlattices and Small Structures. Ft. Belvoir: Defense Technical Information Center, 1987.

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H, Sowa, ed. Cubic structure types described in their space groups with the aid of frameworks. Karlsruhe, [West Germany]: Fachinformationszentrum Energie, Physik, Mathematik, 1985.

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Leung, Henry Hon Hung. Trellis structure and decoding of lattices. Ottawa: National Library of Canada, 1994.

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American Society of Civil Engineers., ed. Design of latticed steel transmission structures. Reston, Va: American Society of Civil Engineers, 2000.

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American Society of Civil Engineers. Design of latticed steel transmission structures. Reston, Virginia: American Society of Civil Engineers, 2015.

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Book chapters on the topic "Structures lattices"

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Loeb, Arthur L. "Lattices and Lattice Complexes." In Space Structures, 123–25. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0437-4_15.

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Meyer-Nieberg, Peter. "Structures in Banach Lattices." In Banach Lattices, 321–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76724-1_5.

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Loeb, Arthur L. "Orthorhombic and Tetragonal Lattices." In Space Structures, 139–46. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0437-4_18.

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Senthil Kumar, B. V., and Hemen Dutta. "Lattices and Boolean Algebra." In Discrete Mathematical Structures, 223–56. Boca Raton, FL : CRC Press/Taylor & Francis Group, 2020. | Series: Mathematics and its applications : modelling, engineering, and social sciences: CRC Press, 2019. http://dx.doi.org/10.1201/9780429053689-5.

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Eilbeck, J. C., and A. C. Scott. "Quantum Lattices." In Nonlinear Coherent Structures in Physics and Biology, 1–14. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-1343-2_1.

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Suryanarayana, C., and M. Grant Norton. "Lattices and Crystal Structures." In X-Ray Diffraction, 21–62. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0148-4_2.

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Cole, James A. "Non-distributive Cancellative Residuated Lattices." In Ordered Algebraic Structures, 205–12. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3627-4_10.

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Jipsen, P., and C. Tsinakis. "A Survey of Residuated Lattices." In Ordered Algebraic Structures, 19–56. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3627-4_3.

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Conrad, P. F., S. M. Lin, and D. G. Nelson. "Torsion Classes of Vector Lattices." In Ordered Algebraic Structures, 11–30. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1723-4_2.

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Trubin, Alexander. "Antenna Structures on Lattices of." In Lattices of Dielectric Resonators, 97–116. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25148-6_5.

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Conference papers on the topic "Structures lattices"

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Cheng, Dali, Eran Lustig, Kai Wang, and Shanhui Fan. "Band structure measurements in multi-dimensional synthetic frequency lattices." In CLEO: Fundamental Science, FTh4D.6. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.fth4d.6.

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We experimentally demonstrate a method to fully measure multi-dimensional band structures in synthetic frequency dimensions by introducing a gauge potential into the lattice Hamiltonian. We use this method to study non-Hermitian topology in high dimensions.
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Chen, Jiangce, Martha Baldwin, Sneha Narra, and Christopher McComb. "Multi-Lattice Topology Optimization With Lattice Representation Learned by Generative Models." In ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/detc2024-145592.

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Abstract Additive manufacturing (AM) technologies are often capable of fabricating geometries that are more complex than traditional manufacturing methods. A notable innovation enabled by AM is the fabrication of multi-lattice structures, an advanced design concept featuring an array of heterogeneous lattices in the mesoscale that are arranged to achieve a diverse distribution of material properties at the macroscale. Compared to uniform lattice structures, multi-lattice structures permit greater design freedom and a larger design space, which makes it possible to achieve superior structure performance. However, the expanded design space introduces a substantial increase in the complexity of multi-lattice structure design. There is still lack of an optimization framework that can maximize the physical properties of the macro-structures through fully exploiting lattice diversity while ensuring lattice connectivity. To solve these challenges, this paper introduces a multi-scale topology optimization (TO) framework for multi-lattice structures which simultaneously optimizes the structure topology at macroscale and the lattice heterogeneity at mesoscale. The distribution of the pseudo-densities and lattice parameters are represented by neural networks (NNs) whose weights and biases are the design variables. The spatial gradients of NN over the physical domain reflect the dissimilarity of adjacent lattices. So, the connection between the lattices can be implicitly constrained by restricting the spatial gradients of NNs. The diversity of the lattices is guaranteed through a generative lattice model which is trained over a large lattice dataset and is embedded into the optimization framework. The performances of various NN types are compared, and we found that Fourier Neural Operators (FNOs) have the best flexibility in balancing the lattice diversity and local connectivity. In the design problems of structural compliance minimization under complex loading conditions, our results show that the multi-lattice TO structures achieve a higher stiffness-to-weight ratio than normal TO structures.
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Toropova, Marina M., and Craig A. Steeves. "Thermal Actuation Through Bimaterial Lattices." In ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/smasis2015-8855.

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The goal of this study is to examine the theoretical capability of bimaterial lattices as thermally driven actuators. The lattices are composed of planar non-identical cells. Each cell consists of a skewed hexagon surrounding an irregular triangle; the skew angles of the hexagon and the ratio of the coefficients of thermal expansion (CTEs) of the two component materials determine the overall performance of the actuator. Such a cell has three tailorable CTEs along the lines connecting the points where adjoining cells are connected. Each individual cell and a lattice consisting of such cells can be strongly anisotropic in terms of thermal expansion. While these lattice cells have been used as stress-free connectors for components with differing CTEs, they have not been explored for their actuation capacity. This paper develops models for bimaterial lattices that can be used as mechanical actuators for valves, switches and differential motion. A general procedure for lattice design includes drawing of its skeleton, which identifies the points at which a lattice cell is connected to other cells or substrates; calculation of three CTEs in each cell depending upon the functionality desired; choosing lattice materials; and finding of the skew angles for each cell as solutions of three nonlinear algebraic equations. By changing materials and geometry, we can determine the change of their configuration when the temperature changes. This paper illustrates the concepts with several examples: a two-cell lattice that is connected to a substrate that functions as a lever in a switch; a three-cell lattice that serves as a valve; and a lattice that controls the maximum total deflection of two adjoining parts of a structure.
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Ayaz Uddin, Mohammed, Imad Barsoum, Shanmugam Kumar, and Andreas Schiffer. "Enhancing Energy Absorption Capacity of Pyramidal Lattice Structures via Geometrical Tailoring and 3D Printing." In ASME 2024 Aerospace Structures, Structural Dynamics, and Materials Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/ssdm2024-121512.

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Abstract Pyramidal lattice structures have frequently been employed as the core material in the design of sandwich panels due to their impressive weight-specific strength. However, the struts in pyramidal lattice structures bend when subjected to axial, shear, or bending loads, leading to non-uniform stress distributions, especially at low relative densities. The current work introduces a geometrical tailoring scheme that provides the designer with additional parameters that can be adjusted to tune the cross-sectional properties of the lattice struts with the goal of obtaining more uniform stress distributions across their thickness. Specifically, the conventional square and circular pyramidal lattice struts are reshaped into I-beam-like cross-sections, forming a tailored pyramidal lattice. These geometrically tailored pyramidal lattices are 3D printed via the Digital Light Processing (DLP) technique. The quasi-static compressive responses of the lattices are experimentally evaluated in terms of elastic modulus, collapse strength, and energy absorption capacity. Additionally, the collapse mechanisms of the geometrically tailored structures were assessed via a non-linear finite element analysis which was validated against the experimental evidence. The results substantiate the validity of the geometrical tailoring strategy as the reported energy absorption capacity of the tailored pyramidal lattice structure exhibits a significant enhancement up to 64% and 15% respectively. The latter enhancements were attributed to the lateral buckling of struts, prompting the tailored struts to bend sideways during the collapse phase.
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Venugopal, Vysakh, Matthew McConaha, and Sam Anand. "Topology Optimization for Multi-Material Lattice Structures With Tailorable Material Properties for Additive Manufacturing." In ASME 2019 14th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/msec2019-2989.

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Abstract Structurally optimized lattices have gained significant attention since the commercialization of additive manufacturing (AM). These lattices, which can be categorized as metamaterials, are used in aviation and aerospace industries due to their capacity to perform well under extreme structural, thermal, or acoustic loading conditions. This research focuses on the design of a unit cell of a multi-material lattice structure using topology optimization to be manufactured using multi-material additive manufacturing processes. The algorithm combined with octant symmetry and support elimination filters yields optimized unit cells with overall reduction in effective coefficient of thermal expansion and thermal conductivity with high mechanical strength. Such unit cells can be used in multi-material additive manufacturing to generate lattice structures with optimized structural and thermal properties.
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Hathcock, Megan, Bogdan Popa, and Kon-Well Wang. "Continuous Dirac Cone Evolution in Modulated Phononic Crystal." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-95839.

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Abstract Dirac cones in the band structures of highly symmetric phononic crystal lattices have been extensively studied to produce unique acoustic phenomena. Traditionally, these interesting phenomena produced by Dirac cones occur at fixed frequencies, which cannot be adapted unless significant lattice material or geometric changes occur. To create tunable phononic structures, researchers have successfully utilized Miura-origami to modulate phononic inclusions between discrete high symmetry Bravais lattice configurations. However, the origami transformation between Bravais lattices is a continuous process, meaning that between the high symmetry Bravais lattices, the structure will transform into low symmetry lattices, which are largely unexplored. In this work, we study the perturbation of a hexagonal phononic lattice away from high symmetry. Interestingly, we see the Dirac cone at the K point of the Brillouin zone for the hexagonal lattice persist through the lattice modulation, despite loss of symmetry. Using this insight, we propose an origami phononic structure capable of continuous adjustment and refinement of Dirac cone frequency. Ultimately, we demonstrate continuous Dirac cone modulation for beam forming with the proposed origami phononic structure.
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Zhang, Botao, Kunal Mhapsekar, and Sam Anand. "Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68047.

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Additive manufacturing (AM) processes enable the creation of lattice structures having complex geometry which offer great potential for designing light weight parts. The combination of AM and cellular lattice structures provide promising design solutions in terms of material usage, cost and part weight. However, the geometric complexity of the structures calls for a robust methodology to incorporate the lattices in parts designs and create optimum light weight designs. This paper proposes a novel method for designing light weight variable-density lattice structures using gyroids. The parametric 3D implicit function of gyroids has been used to control the shape and volume fraction of the lattice. The proposed method is then combined with the density distribution information from topology optimization algorithm. A density mapping and interpolation approach is proposed to map the output of topology optimization into the parametric gyroids structures which results in an optimum lightweight lattice structure with uniformly varying densities across the design space. The proposed methodology has been validated with two test cases.
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Kapral, Raymond. "Discrete Dynamics of Spatio-Temporal Structures." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.is9.

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A heirarchy of discrete models for the description of spatio-temporal structures will be presented and applied to the study of specific physical systems. These models include classical cellular automata, coupled map lattices and lattice gas cellular automata.
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McConaha, Matthew, and Sam Anand. "Design of Stochastic Lattice Structures for Additive Manufacturing." In ASME 2020 15th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/msec2020-8439.

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Abstract With recent development of additive manufacturing methods, topology optimization, an increased focus on the generation of designs which maximize material efficiency by lightweighting has gained considerable interest. Lattice structures are one of the popular methods chosen by design engineers for constructing highly complex, functional geometries which are only manufacturable by additive processes. Stochastic lattices have been finding their way into additively manufactured geometries due to their strength at low volume fraction, as well as the ease of implementation with various generative design tools on the market. However, optimization of these stochastic lattices for maximizing part strength and stiffness is a research topic that has been largely overlooked. By tweaking stochastic lattice generation procedures, non-isotropic structures can be generated and these directional strength properties can be exploited. This paper describes a method for homogenizing the effective properties of non-isotropic stochastic lattices generated using stretched Voronoi tessellations, optimization of the stretching aspect ratio and angle within a part design space, and generation of the non-isotropic and smoothly graded Voronoi-based stochastic lattice structures for that design space. The method was applied to a case study of a cantilever beam with nine different Voronoi lattice configurations. Stiffness of parts designed using this procedure was found to be significantly higher than parts designed using an isotropic design.
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Lishi Zhang, Yi Su, and Xiaodong Liu. "AFS Structures and Concept Lattices." In 2006 6th World Congress on Intelligent Control and Automation. IEEE, 2006. http://dx.doi.org/10.1109/wcica.2006.1712820.

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Reports on the topic "Structures lattices"

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Fry, A. T., L. E. Crocker, M. J. Lodeiro, M. Poole, P. Woolliams, A. Koko, N. Leung, D. England, and C. Breheny. Tensile property measurement of lattice structures. National Physical Laboratory, July 2023. http://dx.doi.org/10.47120/npl.mat119.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190037.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190611.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada170316.

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Liu, Keh-Fei, and Terrence Draper. Lattice QCD Calculation of Nucleon Structure. Office of Scientific and Technical Information (OSTI), August 2016. http://dx.doi.org/10.2172/1323029.

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Skowronski, Marek, and D. W. Greve. Growth of Lattice Matched Nitride Alloys and Structures. Fort Belvoir, VA: Defense Technical Information Center, September 1998. http://dx.doi.org/10.21236/ada354115.

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Braun, D. W., G. W. Crabtree, H. G. Kaper, G. K. Leaf, D. M. Levine, V. M. Vinokur, and A. E. Koshelev. The structure of a moving vortex lattice. Office of Scientific and Technical Information (OSTI), November 1995. http://dx.doi.org/10.2172/179299.

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Parsa, Z., and S. Tepikian. Overview of the structure resonances in the AGS-Booster lattices. Office of Scientific and Technical Information (OSTI), June 1986. http://dx.doi.org/10.2172/1150423.

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Hughes, Nathan. Computed Tomography (CT) Analysis of 3D Printed Lattice Structures. Office of Scientific and Technical Information (OSTI), May 2023. http://dx.doi.org/10.2172/1975633.

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Williams, James H., Nagem Jr., and Raymond J. Computation of Natural Frequencies of Planar Lattice Structure. Fort Belvoir, VA: Defense Technical Information Center, March 1987. http://dx.doi.org/10.21236/ada185387.

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