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EN
This paper analyzes the effect of additional masses for lattice structures on the nature of changes in the natural frequencies of the structure. An attempt to mathematically describe this nature and the scale of the effect with a known thickness of the icing layer was also made. The discussion concerns a structure with a sacred purpose - the Gate of the Third Millennium, located in the Lednickie Fields, in the Kiszkowo Municipality, Gniezno Poviat. The icing of structural bars (frost, rime) is treated as a source of additional masses, although the origin of non-structural mass is of secondary importance for the analysis in question. The analysis was carried out by Finite Element Method (FEM) modeling of the structure, assuming a single-parameter variation of its mass (that is, the additional mass of all elements of the test object varies proportionally to a single parameter, which is the outer surface of the element on which the ice layer is deposited). By solving the vibration eigenproblem for successive models, representing different intensities of icing of the object, the values of successive frequencies and descriptions of the corresponding eigenmodes were determined. The results obtained allow us to formulate a postulate that the possibility of a change in the mass of the analyzed object resulting from icing or other causes should be taken into account in strength analyses, wherein the dynamic properties of the structure play an important role, such as in assessing the susceptibility of the structure to dynamic loads.
PL
W pracy dokonano analizy wpływu dodatkowych mas dla konstrukcji typu kratownicowego na charakter zmian częstotliwości drgań własnych tej konstrukcji. Przeprowadzono też próbę matematycznego opisu tego charakteru oraz skali wpływu przy znanej grubości warstwy oblodzenia. Rozważania dotyczą budowli o przeznaczeniu sakralnym - Bramy Trzeciego Tysiąclecia, zlokalizowanej na Polach Lednickich w gminie Kiszkowo w powiecie gnieźnieńskim. Jako źródło dodatkowych mas traktowane jest oblodzenie prętów konstrukcyjnych (szron, szadź), jakkolwiek pochodzenie masy niekonstrukcyjnej ma dla przedmiotowej analizy znaczenie drugorzędne. Analizy dokonano w drodze modelowania Metodą Elementów Skończonych (MES) konstrukcji, przyjmując założenie o jednoparametrycznej zmienności jej masy (to znaczy, że dodatkowa masa wszystkich elementów badanego obiektu zmienia się proporcjonalnie do jednego parametru, którym jest powierzchnia zewnętrzna elementu, na której odkłada się warstwa lodu). Rozwiązując zagadnienie własne drgań dla kolejnych modeli, reprezentujących różne intensywności oblodzenia obiektu, wyznaczono wartości kolejnych częstotliwości i opisy odpowiadających im postaci drgań własnych. I tak, przyrost grubości warstwy lodu na powierzchniach, od 0 do 1 cm spowodował redukcję wszystkich wyznaczonych (dziesięciu podstawowych) częstotliwości drgań własnych o co najmniej 11%. Grubość oblodzenia 2 cm wpływa na redukcję częstotliwości, jak wyżej, o ok. 22% zaś 4 cm warstwa oblodzenia oznacza redukcję przedmiotowych częstotliwości powyżej 39%. Są to istotne wartości, z punktu widzenia zastosowań technicznych. Uzyskane wyniki pozwalają na sformułowanie postulatu, aby w analizach wytrzymałościowych, w których istotną rolę odgrywają właściwości dynamiczne konstrukcji, np. w ocenie podatności konstrukcji na obciążenia dynamiczne, uwzględniana była możliwość zmiany masy analizowanego obiektu wynikająca z oblodzenia lub z innych przyczyn.
EN
Parallel realizations of discrete transforms (DTs) computation algorithms (DTCAs) performed on graphics processing units (GPUs) play a significant role in many modern data processing methods utilized in numerous areas of human activity. In this paper the authors propose a novel execution time prediction model, which allows for accurate and rapid estimation of execution times of various kinds of structurally different DTCAs performed on GPUs of distinct architectures, without the necessity of conducting the actual experiments on physical hardware. The model can serve as a guide for the system analyst in making the optimal choice of the GPU hardware solution for a given computational task involving particular DT calculation, or can help in choosing the best appropriate parallel implementation of the selected DT, given the limitations imposed by available hardware. Restricting the model to exhaustively adhere only to the key common features of DTCAs enables the authors to significantly simplify its structure, leading consequently to its design as a hybrid, analytically–simulational method, exploiting jointly the main advantages of both of the mentioned techniques, namely: time-effectiveness and high prediction accuracy, while, at the same time, causing mutual elimination of the major weaknesses of both of the specified approaches within the proposed solution. The model is validated experimentally on two structurally different parallel methods of discrete wavelet transform (DWT) computation, i.e. the direct convolutionbased and lattice structure-based schemes, by comparing its prediction results with the actual measurements taken for 6 different graphics cards, representing a fairly broad spectrum of GPUs compute architectures. Experimental results reveal the overall average execution time and prediction accuracy of the model to be at a level of 97.2%, with global maximum prediction error of 14.5%, recorded throughout all the conducted experiments, maintaining at the same time high average evaluation speed of 3.5 ms for single simulation duration. The results facilitate inferring the model generality and possibility of extrapolation to other DTCAs and different GPU architectures, which along with the proposed model straightforwardness, time-effectiveness and ease of practical application, makes it, in the authors’ opinion, a very interesting alternative to the related existing solutions.
3
Content available remote Mathematical approach to design 3D scaffolds for the 3D printable bone implant
EN
This work demonstrates that an artificial scaffold structure can be designed to exhibit mechanical properties close to the ones of real bone tissue, thus highly reducing the stress-shielding phenomenon. In this study the scan of lumbar vertebra fragment was reproduced to create a numerical 3D model (this model was called the reference bone sample). New nine 3D scaffold samples were designed and their numerical models were created. Using the finite element analysis, a static compression test was performed to assess the effective Young modulus of each tested sample. Also, two important metrics of each sample were assessed: relative density and surface area. Each new designed 3D scaffold sample was analyzed by considering two types of material properties: metal alloy properties (Ti-6Al-4V) and ABS polymer properties. Numerical analysis results of this study confirm that 3D scaffold used to design a periodic structure, either based on interconnected beams (A, B, C, D, E and F units) or made by removing regular shapes from base solid cubes (G, H, I units), can be refined to obtain mechanical properties similar to the ones of trabecular bone tissue. Experimental validation was performed on seven scaffolds (A, B, C, D, E, F and H units) printed from ABS material without any support materials by using Fused Deposition Modeling (FMD) technology. Results of experimental Young modulus of each printed scaffold are also presented and discussed.
EN
In this study, we propose a cooling structure manufactured using a specialized three-dimensional (3D) printing design method. A cooling performance test system with complex geometry that used a thermoelectric module was manufactured using metal 3D printing. A test model was constructed by applying additive manufacturing simulation and computational fluid analysis techniques, and the correlation between each element and cooling efficiency was examined. in this study, the evaluation was conducted using a thermoelectric module base cooling efficiency measurement system. The contents were compared and analyzed by predicting the manufacturing possibility and cooling efficiency, through additive manufacturing simulation and computational fluid analysis techniques, respectively.
EN
Closed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.
PL
Ważnym problemem w ochronie środowiska są kompensacje przyrodnicze związane z zapewnieniem utrzymania tras przelotu nietoperzy. Te małe ssaki odgrywają bardzo ważną rolę w zwalczaniu szkodników i owadów, jak również w zapylaniu, rozproszeniu nasion. Uwzględniając powyższe, w wielu krajach stosuje się różne rozwiązania zrównoważonego projektowania dróg i obiektów, związanych z zapewnieniem utrzymania tras przelotu nietoperzy nad budowanymi lub przebudowanymi ciągami komunikacyjnymi. W artykule przedstawiono hipotezy prawdopodobieństwa przyczyn mniejszej i większej skuteczności wybudowanych trzech konstrukcji bramowych na trasach przelotu nietoperzy do miejsc zimowej hibernacji.
EN
Environmental compensation aimed at keeping bat flight paths open is a major environmental protection issue. The mammals play a very important role in eliminating pests and insects, pollination and seed dispersal. Given the above, many countries use different solutions of sustainable civil engineering, geared towards maintaining tree passage for bats over currently constructed or rebuilt traffic routes. The paper hypothesises on the reasons for better or worse performance of the three gantries on bat migration routes to their winter habitats.
7
Content available remote Wpływ rodzaju skratowania wież na ich nośność i mechanizm zniszczenia
PL
W artykule porównano eksperymentalne wyniki sił niszczących oraz mechanizmy zniszczenia dwóch wież tej samej wysokości 42 m (badania obiektów w skali naturalnej), ale o dwóch różnych typach skratowania ścian (typ pojedynczy i typ X). Na podstawie uzyskanych wyników sił niszczących i obserwacji mechanizmów zniszczenia stwierdzono, że mniejsze zużycie stali w wieży z pojedynczym skratowaniem powoduje znaczny spadek nośności w porównaniu z wieżą mającą skratowanie typu X.
EN
The main issue presented in the article is a comparison of the experimental failure loads for two steel lattice towers (two different bracing systems – K and X) with the height equal to 42 m. Paper presents experimental data obtained in full-scale pushover tests, where the mechanism of failure plays extremely important role. Experimental results allow to draw the conclusion that lower material consumption for the tower with K bracing system causes significant decrease of the overall carrying capacity comparing to the tower with the X bracing system.
EN
In this paper, we present a novel approach to calculation of discrete wavelet transform (DWT) on modern Graphics Processing Units (GPUs) with CUDA architecture which takes advantage of highly parallel lattice structure. The experimental results obtained for model signals show that the proposed approach allows to obtain several times acceleration compared with sequential calculations carried out on the CPU while taking into account not only time of calculations but also time required for data transfers.
XX
W artykule zaproponowano nowe podejście do obliczania dyskretnego przekształcenia falkowego (DWT) na nowoczesnych procesorach graficznych (GPUs) o architekturze CUDA oparte o wysoce równoległe struktury kratowe. Wyniki badań eksperymentalnych przeprowadzonych na sygnałach modelowych pokazują, że zaproponowane podejście daje możliwość uzyskania kilkukrotnego przyśpieszenia obliczeń w porównaniu do obliczeń sekwencyjnych na CPU, biorąc pod uwagę nie tylko czas obliczeń , ale również czasy przesyłu danych.
EN
Diagnostics of electric power lines is an important component of their operation and consists in determination which components of the support structures need repairs or maintenance. The paper presents the method for semi-automatic diagnostics of support structures for high voltage lines with use of metrical photographs.
10
Content available remote Completion in a common supercategory of Met, UAP, wsAP and Near
EN
This paper investigates the notion of approach nearness spaces. Using clusters, completion of an approach nearness space is constructed, which is a unified study of completion in the context of metric spaces, uniform approach spaces, weakly symmetric approach spaces and nearness spaces. Another generalization of completeness, called ultrafilter completeness is introduced to prove the Niemytzki–Tychonoff theorem for approach nearness spaces. Both definitions of completions are shown to be equivalent in a limit-regular approach space. Various examples are given to support the present study.
11
Content available remote L-approach merotopies and their categorical perspective
EN
In the present paper, we have made a category theoretic and lattice theoretic study of some nearness-like structures in the L-approach theory. Using L-grills, the notion of L-approach grill structure is introduced as a characterization of L-approach grill merotopy on X; their categorical perspectives and implications are also investigated. A number of illustrative examples are included.
12
EN
This paper continues discussion of a lattice structure for parametrization and implementation of a Discrete Wavelet Transform. Based on an algorithm for converting the lattice structure to a wavelet filter bank coefficients, developed in the first part of this paper, second part of the proof demonstrating that filters implemented by the lattice structure fulfil conditions imposed on an orthogonal wavelet filter bank is carried out.
13
EN
This paper presents concept of a lattice structure for parametrization and implementation of a Discrete Wavelet Transform. Theoretical properties of the lattice structure are discussed in detail. An algorithm for converting the lattice structure to a wavelet filter bank coeffcients is constructed. A theoretical proof demonstrating that filters implemented by the lattice structure fulfil conditions imposed on an orthogonal wavelet filter bank is conducted.
EN
In this paper a new method for adaptive synthesis of a smooth orthogonal wavelet, using fast neural network and genetic algorithm, is introduced. Orthogonal lattice structure is presented. A new method of supervised training of fast neural network is introduced to synthesize a wavelet with desired energy distribution between output signals from low–pass and high–pass filters on subsequent levels of a Discrete Wavelet Transform. Genetic algorithm is proposed as a global optimization method for defined objective function, while neural network is used as a local optimization method to further improve the result. Proposed approach is tested by synthesizing wavelets with expected energy distribution between low– and high–pass filters. Energy compaction of proposed method and Daubechies wavelets is compared. Tests are performed using image signals.
15
Content available remote Lattice Structures for Synthesis and Implementation of Wavelet Transforms
EN
In this paper the novel lattice structure composed of homogeneous invertible two-point operations which are connected in regular and simple structure is proposed. Further on the pipeline scheme for implementation of such a structure is presented. It is proved with the orthogonal variant of the presented scheme that with respect to the computational complexity it is equivalent to the lifting technique. It means that the proposed scheme belongs to the class of the most effective algorithms for calculation of orthogonal wavelet transforms. The variant of the lattice structure with simplified two-point operations is also proposed. Finally the fundamentals of the synthesis of lattice structure coefficients with the aid of artificial neural networks and some aspects of lattice structures implementation on basic computational architectures are discussed.
PL
Badania dotyczą przestrzennej struktury prętowej o powierzchni środkowej w kształcie konoidy parabolicznej. Przeprowadzenie badań modelowych w tunelu aerodynamicznym wymagało zastosowania modelu ciągłego spełniającego geometryczne kryteria podobieństwa modelowego. Analizy numeryczne oraz badania modelowe uzasadniły stosowanie modelu ciągłego do badań struktury prętowej. Przeprowadzone badania potwierdziły zasadność zastosowania takiej struktury w przekryciach znacznej rozpiętości.
EN
Results of an investigation concerning a lattice space structure in the form of a parabolic conoidal shell are presented. Numerical analyses and model tests were carried out. The continuous model used for the wind-tunnel tests fulfilled criteria of model similarity and therefore was accepted as a proper substitution of a lattice space structure in wind-tunnel tests. The investigation confirms that a parabolic conoidal lattice space structure can be used to cover large span area.
EN
A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.
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