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PL
W pracy przedstawiono spójną, skomputeryzowaną metodykę kształtowania różnorodnych elementów konstrukcyjnych wg metody statycznie dopuszczalnych nieciągłych pól naprężeń. Przygotowano pakiet programów rozwiązujących wybrane układy linii nieciągłości naprężeń. Następnie opracowano algorytmy i przygotowano programy: SDNPN i KNPNs automatycznie składające w sposób statycznie dopuszczalny różnorodne pola naprężeń. Praca zawiera liczne przykłady automatycznego kształtowania węzłów konstrukcji stalowych. Opracowano nową interaktywną metodę rozwiązywania statycznie dopuszczalnych nieciągłych pól naprężeń, nie wymagającą budowania indywidualnych algorytmów (program RHM). Przygotowany pakiet programów pozwolił na znaczne usprawnienie procesu projektowania oraz po raz pierwszy powstała możliwość ścisłego logicznego powiązania metody SDNPN z MES i CAD. Przedstawiono przykłady kształtowania węzłów płaskich i przestrzennych. Dla węzłów przeprowadzono szeroką weryfikację obliczeniową MES oraz badania metodą elastooptycznej warstwy powierzchniowej. Szeroka weryfikacja obliczeniowa i doświadczalna potwierdziła praktyczną przydatność wstępnego kształtowania elementów wg kryterium nośności granicznej.
EN
The paper presents a compact computerized methodology of shaping diverse structural elements according to the methods of statically admissible discontinuous stress fields. A package of separate utility programs for solving the selected systems of stress discontinuity lines has been prepared. Further, an algorithm has been developed and the SDNPN and KNPNs programs have been created witch automatically combines various stress fields in a statically admissible way. The work encloses a number of examples of automatic shaping i.e. structural steel joints. The prepared software package allowed for a considerable speed-up of the design process and, for the first time, the posibility emerged to strictly and efficiently connect the statically admissible discontinuous stress fields method with the FEM and CAD programs. The examples 2D and 3D steel structural joints was presented. Numerical and experimental verification shown in this work confirms the practical applicability of the method of shaping the elements according to the limit load carrying capacity criterion.
EN
The main purpose of the work is the method of the description of the thermo-mechanical fatigue process of power plant components working under mechanical and thermal loading. The work focuses on the chosen component strain- stress characteristics. The FEM modelling has been used to describe the local stress- strain behaviour of the chosen power plant element. The calculations of stress distribution on the component surface show that the internal pressure induces considerably smaller values of stresses and strains in comparison with the same stresses specified for thermal loads. Thus, thermal impacts are responsible for cracks initiation and growth in areas of the greatest intensity of damage accumulation. The presented analysis is the part of the complex investigation method which main purpose is increasing the accuracy of the TMF process description and thermo-mechanical life assessment. In such situation the industrial investigations curried out in the work give the model approach and data for the comparison the real behaviour with the predictions.
EN
In the paper, the author introduces the sets of conditions that create the algorithms of the functions on which one defines the boundary problems met in the search for discontinuous limit fields existing around isolated nodes. Among those, there are functions describing states of stress in the component homogeneous regions, the parameters of lines that separate these regions, and, first of all, the formulae for determining the domains based on the general conditions of existence. These formulae play a key role in numerical implementations of the method. The fields satisfying the Huber-Mises yield condition are of primary choice however, the derived relationships have a general meaning. To emphasise this fact one presents not only the areas of existence valid for the Huber-Mises condition, but also the areas obtained for several other yield conditions applicable to plastically homogeneous materials. The knowledge of the areas opens the possibility of developing the method of search for the fields that obey these conditions, and for algorithmizing this method. This could be applied even for the fields that are characterised by arbitrary, admissible states of stress. One also presents, basing on a mathematically complete set of conditions, typical formulations of problems concerning the fields around the nodes. One discusses the balance between the set of conditions and the unknowns, as well as the transformations into global systems connected with complex fields. One consequently applies parametrisation of the yield conditions, which not only reduces the number of unknowns and leads to simple, recursive forms of the formulae, but, first of all, makes it possible to find the formulae for generation of domains, without which numerical solution of the fields and algorithmization of the method would not be possible at all.
EN
This paper presents results of the numerical stress and fracture analysis of the turbine disc. Using the finite element method, the stress state, J-integral and stress intensity factor were obtained for the disc rotated with the operational speed.
EN
The paper contains comparing calculations of the stress fields in an elastic plate with notch along the arc of a circle, ellipse or parabola obtained by analytic method based on complex Kolosov-Muskhelishvili potentials and by numerical variation-difference method. These fields differ by no more than 2%, which, in particular, indicates the reliability of such numerical implementation. This discrepancy can be explained by the fact that in the analytical solution domain is unbounded, while the numerical calculation was carried out, obviously, for a finite field. The given stresses at the top of the notch along the arc of an ellipse or a parabola significantly increase with increasing of the relative depth of the notch (while increasing its depth or decreasing width).
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Content available remote Numerical and experimental analysis of stress field on the crack front zones
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EN
The paper presents experimental and numerical analysis of stress field in neighbourhood crack front for different configuration of crack in tension plate. Photo - elastic method and numerical analysis were used for specimens made by epoxy resin material.
EN
Because the heat release of plutonium material, the composite structure is heated and the stress and strain of the composite structure will increase, which will affect the thermodynamic properties of the structure. The thermodynamic analysis of complex structures, which are composed of concentric structures of plutonium, beryllium, tungsten, explosives, and steel, was carried out. The results showed that when the structure is spherical, the temperature is higher than that of the ellipsoid structure. Stress of the elliptical structure is greater than the spherical structure. This study showed that the more flat the shell is, the greater the stress concentration point occurs at the long axis, and the maximum stress occurs at the beryllium layer. These conclusions provide theoretical support for the plutonium composite component testing.
PL
W artykule przedstawiona została charakterystyka pól naprężeń przed wierzchołkiem pęknięcia dla kwadratowej płyty zawierającej centralne pęknięcie, poddanej dwuosiowemu rozciąganiu. Praca prezentuje szczegóły obliczeń numerycznych, a także porównania stanów naprężeń dla płyt poddanych jednoosiowemu rozciąganiu oraz płyt poddawanych dwuosiowemu rozciąganiu. Analiza numeryczna prowadzona jest dla szeregu modeli materiałów sprężysto-plastycznych oraz różnych względnych długości pęknięcia. Dyskusja dotyczy wpływu geometrii, poziomu i rodzaju obciążenia zewnętrznego oraz charakterystyki materiałowej na pole naprężeń przed wierzchołkiem pęknięcia.
EN
In the paper the stress field near front of crack for center cracked square plate in biaxial tension was pre-sented. The paper presents the details of numerical calculations, and also the comparison of states of stress for plates subjected to uniaxial tensile and plates to be in biaxial tension. The influence of the crack length, material characteristic and the level or type of external load were discussed.
PL
W artykule przedstawiono wyniki obliczeń zmian pola temperatury i naprężeń cieplnych podczas obróbki cieplnej walca hutniczego o średnicy beczki 855 mm, wykonanego ze staliwa L200HNM. Pole temperatury wyznaczono z rozwiązania równania przewodzenia ciepła w całym cyklu nagrzewania i chłodzenia walca. Pole naprężeń wywołane zmianą pola temperatury i przemianami fazowymi wyznaczono z rozwiązania równań Prandtla-Reussa dla ciała sprężysto - plastycznego. Do określenia granicznych wartości naprężeń i odkształceń wykorzystano kryterium Rice i Tracy.
EN
The results of the evaluation of the temperature field and stress and strain field while heat treatment of the rolling mill rolls has been performed. The roll cylinder was made from the cast steel L200HM. The temperature field was calculated from the solution to the heat conduction equation in the whole heat treatment cycle. The stress field was calculated from the Prandtl - Reuss equation for the elastic - plastic body. To indicate the critical zones based on the stress and strain values, the Rice and Tracy criterion was used.
EN
In work the presented numerical models of tool steel hardening processes take into account mechanical phenomena generated by thermal phenomena and phase transformations. In the model of mechanical phenomena, apart from thermal, plastic and structural strain, also transformations plasticity was taken into account. The stress and strain fields are obtained using the solution of the Finite Elements Method of the equilibrium equation in rate form. The thermophysical constants occurring in constitutive relation depend on temperature and phase composite. For determination of plastic strain the Huber-Misses condition with isotropic strengthening was applied whereas for determination of transformation plasticity a modified Leblond model was used. In order to evaluate the quality and usefulness of the presented models a numerical analysis of stresses and strains associated hardening process of a fang lathe of cone shaped made of tool steel was carried out.
PL
W pracy przedstawiono model numeryczny procesu hartowania stali narzędziowej, w którym uwzględniono zjawiska mechaniczne generowane zjawiskami cieplnymi i przemianami fazowymi. W modelu zjawisk mechanicznych uwzględniono oprócz odkształceń termicznych, plastycznych i strukturalnych - również odkształcenia transformacyjne. Pola naprężeń i odkształceń uzyskuje się z rozwiązania metodą elementów skończonych równań równowagi w formie prędkościowej. Stałe termofizyczne występujące w związkach konstytutywnych uzależniono od temperatury i składu fazowego. Do wyznaczania odkształceń plastycznych wykorzystano warunek Hubera-Misesa ze wzmocnieniem izotropowym, natomiast do wyznaczania odkształceń transformacyjnych zastosowano zmodyfikowany model Leblonda. W celu oceny jakości i przydatności prezentowanego modelu dokonano analizy numerycznej pól temperatury, udziałów fazowych, naprężeń i odkształceń towarzyszących procesowi hartowania kła tokarki ze stali narzędziowej.
EN
Unconventional reservoirs require a new approach at every level of the operation on the object, starting from exploration of reservoir formation, through well and drilling design and ending with well completion including reservoir development. Due to the specific nature of unconventional reservoir properties, the hydrocarbons bearing formation requires stimulation treatments like hydraulic fracturing, aiming to improve the pores connectivity and enabling the free flow of the gas into the well bore, which in the end brings production rates to economic levels. In the paper a geomechanical model of the synthetic object, allowing the analysis of many processes accompanying real hydrocarbons exploitation was presented. Special attention was paid to the demonstration of changes in the state of stress in the geological formation, due to the exploitation of hydrocarbons and the influence of the initial horizontal stresses relationship (σH/σh), on the effectiveness of stimulation treatments in unconventional formations.
PL
Formacje złożowe o charakterze niekonwencjonalnym do poprawy właściwości transportowych i uzyskania eksploatacji na poziomie uzasadnionym ekonomicznie wymagają stymulacji poprzez szczelinowanie hydrauliczne, którego efektywność uzależniona jest od panujących warunków mechanicznych, m.in. właściwości sprężystych szczelinowanego ośrodka i oddziałującego pola naprężeń. W pracy przedstawiono i omówiono wyniki modelowania geomechanicznego obiektu syntetycznego, pozwalającego na analizę wielu procesów towarzyszących wydobyciu węglowodorów. Specjalną uwagę poświęcono zmianom w rozkładzie naprężeń w górotworze będących skutkiem eksploatacji oraz wpływowi początkowego układu naprężeń poziomych na efektywność zabiegów udostępnienia niekonwencjonalnej formacji złożowej.
EN
This paper is concerned with static analysis of functionally graded (FG) circular plates resting on Winkler elastic foundation. The material properties vary across the thickness direction so the power-law distribution is used to describe the constituent components. The differential transforms method (DTM) is utilized to solve the governing differential equations of bending of the thin circular plate under various boundary conditions. By employing this solution method, governing differential equations are transformed into recurrence relations and boundary/regularity conditions are changed into algebraic equations. In this study, the plate is subjected to uniform/non-uniform transverse load in two cases of boundary conditions (clamped and simply-supported). Some numerical examples are presented to show the influence of functionally graded variation, different elastic foundation modulus, and variation of the symmetrical transverse loads on the stress and displacement fields. Based on the results, the obtained out-plane displacement coincide with the available solution for a homogenous circular plate. It can be concluded that the applied method provides accurate results and it is easily used for static analysis of circular plates on an elastic foundation.
EN
The strong earthquake with magnitude 6.9 occurred ofshore at the northernmost edge of the Samos Island and was strongly felt in the north Aegean islands and İzmir metropolitan city. In this study, the effective elastic thicknesses of the lithosphere and seismogenic layer thickness were correlated with each other in order to understand the nature of the earthquakes. We determined that the upper and lower depth limits of seismogenic layer are in a range of 5–15 km, meaning that only the upper crust is mostly involved in earthquakes in the study area. The fact that seismogenic layer and effective elastic thicknesses are close to each other indicates that the earthquake potential may be within the seismogenic layer. Following that, we estimate the stress feld from the geoid undulations as a proxy of gravity potential energy in order to analyze the amplitude and orientation of the stress vectors and seismogenic behavior implications. The discrete wavelet transform has been carried out to decompose the isostatic residual gravity anomalies into horizontal, vertical and diagonal detail coefcients. The results delineated edges of gravity anomalies that reveal some previously unknown features.
14
Content available remote Neotectonic stress fields of platform structures in the Baltic region
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EN
A reconstruction of Neotectonic stress fields of the East European Craton (EEC) and the Variscan West European Platform WEP) with younger basement, performed for the first time, has demonstrated that platform basement age does not affect the orientation of regional stresses. The deformation of the northern and western parts of the EEC and the eastern part of the VWEP was possibly due to riftogenesis in the Arctics and Atlantic. Orogenic processes in the Carpathians caused deformation processes only in the narrow marginal parts adjacent surrounding platforms.
PL
Z rekonstrukcji pola naprężeń w obrębie kratonu wschodnioeuropejskiego (EEC) oraz waryscyjskiej platformy europejskiej (WEP) przeprowadzonej po raz pierwszy wynika, że wiek platformy nie ma wpływu na orientację osi naprężeń regionalnych. Deformacje w obrębie zachodniej części EEC i wschodnich części WEP są wywołane prawdopodobnie przez procesy ryftowe w Arktyce i Atlantyku. Karpacka orogeneza spowodowała deformacje na platformie i kratonie jedynie z wąskiej strefie kontaktu z orogenem.
EN
In the paper, numerical verification and catalogue of the numerical solutions based on Modify Boundary Layer Approach to determine the relationship between Q-stress and T-stress are presented. Based on the method proposed by Larsson and Carlsson, the Q-stress value are calculated for some elastic-plastic materials for different value of T-stress and external load expressed by J-integral. The influence of the external load, T-stress value and material properties on Q-stress value were tested. Such catalogue may be useful during solving the engineering problems, especially while is needed to determine real fracture toughness with including the geometric constraints, what was proposed in FITNET procedures.
EN
The Vrancea seismic zone, located in the bend region of the South-Eastern Carpathians, is a unique area with both crustal and intermediate-depth seismic activity and is known as one of the most active seismic area in Europe. Moderate crustal seismicity is recorded all over the Carpathian region, but the far more intense activity occurs in a small subcrustal seismogenic volume beneath the SE‐bend of the Carpathian arc with about 20×50 km lateral and 110 km vertical extent (70–180 km depth). A unique slab geometry, likely preserved until the present, causes stress localization due to the slab bending and subsequent stress release resulting in large mantle earthquakes in the region. The main focus of this study is to determine the focal mechanisms for events with a magnitude larger than 2.7, between 2005 and 2020 and evaluate the current stress field along the Vrancea subcrustal region, from the derived fault plane solutions. The main style of faulting for Vrancea subcrustal events presents a predominant reverse one, with two main earthquakes categories: the first one with the nodal planes, oriented NE–SW parallel with the Carpathian Arc and the second one with the nodal planes, oriented NW–SE perpendicular on the Carpathian Arc. The results of stress inversion indicate a dominant thrust faulting style, with an average stress regime index of 2.87. The stress pattern shows similar partitioning with vertical extension in the slab and no preferred orientation in the overlying crust, showing a transition regime from the extensional regime in the Moesian Platform to the compressional regime in the Vrancea subcrustal zone.
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EN
The complex potentials governing the elastic equilibrium of a finite circular disc, elliptically perforated at its center, are obtained using Muskhelishvili’s formulation. The disc is subjected to non-uniform distribution of pressure along two symmetric finite arcs of its periphery. Given the complex potentials, the stress- and displacement-fields can be determined everywhere on the disc by introducing a novel flexible interpretation of the conformal mapping, suitably adjusted to the computational process. The results of this procedure are given for various strategic loci and are critically discussed. The length of the loaded arc is considered similar to that obtained from the solution of the intact disc-circular jaw elastic contact problem assuming that the disc is compressed between the steel jaws of the device suggested by the International Society for Rock Mechanics for the implementation of the Brazilian-disc test. Concerning the distribution of the externally induced pressure along the loaded arcs, it is proven that for the general asymmetric configuration (i.e. the axes of the elliptical hole are neither parallel nor normal to the loading axis) the induced asymmetric displacement field does not permit maintenance of equilibrium of the disc as a whole in case the disc is considered exclusively under a distribution of radial pressure: Additional tractions must be exerted along the loaded arcs, obviously in the form of frictional stresses. Besides, providing full-field, analytic expressions for stresses and displacements, the main advantage of the present solution is that, by properly choosing the ratio of the ellipse’s semi-axes, the solution of three additional configurations, of major importance in engineering praxis, are obtained: These of the intact disc, the circular ring and the cracked disc.
EN
The paleo-tectonic stress field was hereby inverted by using the stereographic projection method through field and underground observations of conjugate shear joints. On the basis of analyzing and studying the characteristics of gas occurrence in mining areas, the control effect of paleo-tectonic stress field on gas occurrence was discussed from three aspects of gas generation, preservation environment and gas migration. The results show that: (1) During the Indosinian and early-middle Yanshan period, the coal seam was buried deep, and the temperature and pressure conditions were suitable for massive gas generation, especially during the Indosinian period featuring massive gas generation and weak gas migration; (2) During the late Yanshan period, the metamorphic evolution rate of coal seams accelerated, secondary hydrocarbon generation occurred in the coal seams, and a large amount of gas was generated. Meanwhile, the gas migration was enhanced. The gas generation amount was much larger than the emission amount, therefore, making it still a period of massive gas generation in general; (3) During the Himalayan period, the coal measure stratum was in the uplift stage, and a large number of geological structures were developed in the stratum. The tectonic stress field in this period caused the escape of massive coal seam gas. Multi-stage tectonic stress field acted on coal measures strata in turn, resulting in gas generation in coal seam and gas migration at the same time. Besides, gas occurrence is the superposition effect of gas generation, preservation conditions, and gas migration in coal seam.
PL
Przedstawiono wyniki modelowania numerycznego procesu wyciskania współbieżnego przez matryce o różnej geometrii ze szczególnym uwzględnieniem matryc wypukłych. Wyniki doświadczeń przeprowadzonych na rzeczywistym materiale dotyczące sposobu płynięcia metalu w okolicy otworu matrycy zostały z dużą dokładnością potwierdzone na drodze modelowania numerycznego. Stwierdzono, że użycie matryc wypukłych podczas wyciskania zmienia rozkład naprężeń i odkształceń w strefie odkształcenia głównego na bardziej jednorodny niż w przypadku użycia matryc tradycyjnych. Można wyznaczyć optymalny kąt rozwarcia matrycy wypukłej gwarantujący dobre warunki płynięcia metalu.
EN
Numerical modelling of direct aluminium extrusion through the dies of different geometry with particular focus on the convex dies is presented. Results of calculation are in good accuracy with experiment. It was found that in case of convex dies the more uniform stress and strain distribution in the deformation zone is observed. The optimal die angle can be established leading to the best flow conditions.
EN
The shrinkage and swelling of the coal matrix due to the effects of temperature were investigated through the performance by Henan Province Key Lab of Gas Geology & Gas Control of a permeability test of loaded coal under various temperature and working conditions using its own seepage equipment for thermo-fluid-solid-mechanical coupling of methane-containing coal. The variation of coal permeability under the combined effects of stress and temperature was investigated, and the gas motion law in the coal samples was tested. The variation equations of coal permeability under the combined effects of stress and temperature, as well as the motion equations describing the nonlinear gas seepage law in coal seams were established. The established equations were proved to fit well with the experimental data, which demonstrated that the motion equations and the research methods were both reasonable. Study on the seepage nonlinear motion law of gas in the coal seam is great significance to mineral gas extraction.
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