Academic literature on the topic 'Structured lattices'

<p> Data structures are vital entities that strongly impact the efficiency of several software applications. Compactness, predictable memory access patterns, and good temporal and spacial locality of the structure's operations are increasingly becoming essential factors in the selection of a data structure for a specific application. In general, the less data we store and move the better for efficiency and power consumption, especially in infrastructure software and applications for hand-held devices like smartphones. In this dissertation, we extensively study a data structure named lattice data structure (LDS) that is as compact and suitable for memory hierarchies as the array, yet with a rich structure that enables devising procedures with better time bounds. </p><p> To achieve performance similar to the performance of the optimal O(log(N)) time complexity of the searching operations of other structures, we provide a hybrid searching algorithm that can be implemented by searching the lattice using the basic searching algorithm when the degree of the sortedness of the lattice is less than or equal to 0.9h, and the jump searching algorithm when the degree of the sortedness of the lattice is greater than 0.9h. A sorting procedure that can be used, during the system idle time, to incrementally increase the degree of sortedness of the lattice is given. We also provide randomized and parallel searching algorithms that can be used instead of the usual jump-and-walk searching algorithms. </p><p> A lattice can be represented by a one-dimensional array, where each cell is represented by one array element. The worst case time complexity of the basic LDS operations and the average time complexity of some of the order-statistic operations are better than the corresponding time complexities of most of other data structures operations. This makes the LDS a good choice for memory-constrained systems, for systems where power consumption is a critical issue, and for real-time systems. A potential application of the LDS is to use it as an index structure for in-memory databases.</p>

The application of lattice structures have become increasingly popular as additive manufacturing (AM) opens up the possibility to manufacture complex configurations. However, modelling such structures can be computationally expensive. The following thesis has been conducted in order for the department of Structural Analysis, at SAAB in Järfälla, to converge with the future use of AM and lattice structures. An approach to model lattice structures using homogenization is presented where three similar methods involving representative volume element (RVE) have been developed and evaluated. The stiffness matrices, of the RVEs, for different sizes of lattice structures, comprising of BCC strut-based units, have been obtained. The stiffness matrices were compared and analysed on a larger solid structure in order to see the deformational predictability of a lattice-based structure of the same size. The results showed that all methods were good approximations with slight differences in terms of boundary conditions (BCs) at the outer edge. The comparative analyses showed that two of the three methods matches the deformational predictability. The BCs in all methods have different influences which makes it pivotal to establish the BCs of the structure before using the approach presented in this thesis.<br>Ökad implementering av gitterstrukturer i komponenter är ett resultat av utvecklingen inom additiv tillverkning. Metoden öppnar upp för tillverkning av komplexa strukturer med färre delmoment. Dock så uppkommer det svårigheter vid simulering av dessa komplexa strukturer då beräkningar snabbt tyngs ner med ökad komplexitet. Följande examensarbete har utförts hos avdelningen Strukturanalys, på SAAB i Järfälla, för att de ska kunna möta upp det framtida behovet av beräkningar på additivt tillverkade gitterstrukturer. I det här arbetet presenteras ett tillvägagångsätt för modellering av gitterstrukturer med hjälp av represantiva volymselement. Styvhetsmatriser har räknats fram, för en vald gitterkonfiguration, som sedan viktats mot tre snarlika representativa volymselement. En jämförelseanalys mellan de olika styvhetsmatriserna har sedan gjorts på en större och solid modell för att se hur väl metoderna förutsett deformationen av en gitterstruktur i samma storlek. Resultaten har visat att samtliga metoder är bra approximationer med tämligen små skillnader från randeffekterna. Vid jämförelseanalysen simulerades gitterstrukturen bäst med två av de tre metoder. En av slutsatserna är att det är viktigt att förstå inverkan av randvillkoren hos gitterstrukturer innan implementering görs med det tillvägagångssätt som presenterats i det här examensarbetet.