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EN
A novel approach is employed to a general solution for one-dimensional steady-state thermal and mechanical stresses in a hollow thick cylinder made of a functionally graded material (FGM). The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the cylinder. The material properties, except Poisson’s ratio, are assumed to be exponentially-varying through the thickness. Forcing functions applied to the inner boundary are internal pressures which may be in form of steps. These conditions result in governing differential equations with variable coefficients. Analytical solutions to such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem in hand. The novelty of the present study lies in the fact that the Complementary Functions Method (CFM) is employed in the analysis. The Complementary Functions method (CFM) will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be readily applied to cylinders. It is also well suited for problems in which mechanical properties are graded.
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Content available remote Numerical analysis of thermal stresses in a new design of microtubular stack
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EN
Microtubular Solid Oxide Fuel Cells (mSOFCs) are one of the most promising and efficient devices that convert chemical energy of fuels into electrical energy. However, mSOFC stacks work at high operating temperature over 650°C, which leads to thermally induced mechanical stresses and in consequence may cause failure of stack components. In order to reduce the local thermal gradients and prevent high stresses in the stack components, it is desirable to study the effect of stack design on its performance. For this purpose a 3D numerical approach was developed to estimate thermal expansion of fuel cell inside an mSOFC stack and to reduce the associated experimental efforts and costs. Initially, a Computational Fluid Dynamics (CFD) model was used to calculate the temperature and species concentration profiles. During the second modeling step temperature profiles were used in the thermo-mechanical model to calculate the thermal stress distribution in the mSOFC stack. The results maximum thermal axial elongation that equals 1.4 mm for the mSOFC stack. The modelled maximum radial elongation was equal to 0.5 mm in the contact areas of the cylindrical housing and manifolds on the fuel inlet side.
EN
The preceding to this study was a finite element analysis (FEA) of transient temperature fields in a disk brake. In this paper, a FE model to determine corresponding quasi-static stresses in a such tribosystem is proposed. Numerical simulation of a single braking process for the 2D axisymmetric model of the brake disk is carried out. It is assumed that the contact pressure on the friction surfaces is constant, and the angular speed decreases linearly. Evolutions and spatial distributions of the components of the stress tensor and the equivalent Huber-Mises stress in the disk are analyzed.
EN
This paper presents the methodology for determining thermal strains and stresses during heating the charge in a rotary furnace. The calculations were made with the original software, which uses the finite element method. The heat transfer boundary conditions used for computing were verified on the basis of industrial tests. Good compatibility between the experimental data and numerical calculations was obtained. The possibility of the material cracking occurrence was checked for a set exhaust gas temperature distribution on the furnace length. As a result, it was possible to develop steel heating curves characterized by short process times.
PL
W eksploatacji samolotów napędzanych silnikami turboodrzutowymi obserwowane jest częste zjawisko przypadkowego rozrzutu czasu pełnej akceleracji silnika. Przyjęto koncepcję, że jedną z przyczyn tego zjawiska mogą być termiczne deformacje tzw. gorących części jego struktury. W pracy przedstawiono potwierdzające tę koncepcję wyniki eksperymentów, przeprowadzonych na modelu symulacyjnym oraz na rzeczywistym silniku, podczas jego badań na hamowni. W kolejnym etapie postanowiono oszacować, za pomocą obliczeń MES, zmianę wymiarów uproszczonych konstrukcji zastępczych silnika, obejmujących korpus, dyszę oraz połączony z nią stożek wewnętrzny, obciążonych polami temperatury i ciśnieniem wewnętrznym. Wyniki obliczeń wykazały, że deformacje i naprężenia termiczne w analizowanych konstrukcjach są znaczące i powinny być brane pod uwagę zarówno w pracach projektowych, jak i w eksploatacji.
EN
In the maintenance of airplanes powered by jet engines a frequently occuring phenomenon, which consists of variation of engine full acceleration time is observed. The authors make the assumption that one reason for this phenomenon may be thermal deformations of hot parts of the engine structure. Presented in this article are the results from experiments performed on a model simulation, which are also verified by tests on the actual engine while on the test bench. In the next stage an analysis of dimensional variation of simplified engine structures including casting, exhaust nozzle joined with the inner cone loaded with temperature fields and inner pressure was performed using the FEM. The results of the analysis proved that the deformations and thermal stresses in the analyzed structures are significant and should be taken into consideration both the design works and the maintenance.
EN
In this paper influence of temporal profile of the specific friction power (i.e. the product of the coefficient of friction, sliding velocity and contact pressure) on thermal stresses in a friction element during braking was investigated. Spatio-temporal distributions of thermal stresses were analytically determined for a subsurface layer of the friction element, based on the model of thermal bending of a thick plate with unfixed edges (Timoshenko and Goodier, 1970). To conduct calculations, the fields of dimensionless temperature were used. These fields were received in the article (Topczewska, 2017) as solutions to a one-dimensional boundary-value problem of heat conduction for a semi-space heated on its outer surface by fictional heat flux with three, different time profiles of the friction power.
7
Content available remote Thermal fracture of a model of ceramic catalysator
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EN
Grains in form of circles are connected by elastic joints. Grains expand thermally, but do not deform elastically. The joints deform elastically, but do not expand thermally. The special situation is considered when the composite consists of only two kinds of grains, first kind with larger and the second kind with smaller expansion coefficient. The grains are randomly distributed in the specimen. All joints are equal. The specimen is free of external load. The uniform temperature increases from zero and leads to internal stresses. If the stress exceeds some fixed limits the joint breaks down and for all later instants the stress equals zero. The number of damaged joints and thermal stresses is calculated as a function of the proportion of the two kinds of grains.
9
Content available remote Mathematical modelling of induction hardening on view of thermal stresses
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EN
Mathematical modelling of regimes of induction hardening of details in view of phase transformations, non-stationary thermal and thermostress state, residual stresses and fatigue has been carried out.
PL
W pracy omówiono modelowanie matematyczne układów hartowania indukcyjnego elementów z punktu widzenia przemian fazowych, staniu niestacjonarnych naprężeń cieplnych, naprężeń szczątkowych i zmęczenia materiału.
EN
An approximate analytical solution is presented for thermal stresses in an annular convectiveconductive fin of a hyperbolic profile with temperature dependent thermal conductivity. The classical thermo-elasticity theory coupled with the ADM based polynomial form of temperature field is employed for an approximate analytical solution of thermal stresses. The influence of thermal parameters, i.e. variable thermal conductivity, the thermo-geometric parameter and the non-dimensional coefficient of thermal expansion on temperature and sttress fields are investigated. The results for the stress field obtained from the ADM based solution are compared with those available in literature and found to be in close agreement.
EN
We discuss the problem of a contact of two parallel elastic cylinders heated to different temperatures. The purpose of our investigation is to derive the conditions which have to be satisfied so that the solution to the thermoelastic problem is physically meaningfull (i.e. the paradox of "the cooled cylinder" can be avoided). Pertinent formulae have been derived for relations between the contact pressure, geometrical characteristics of the solids and distributions of heat flux over the contacting region. The paper has been ilustrated by an example diagrams.
PL
Kiedy można uniknąć paradoksów w zagadnieniu termosprężystego kontaktu dwóch walców Rozpatrujemy zagadnienie kontaktu ściskanych sprężystych walców o równoległych tworzących w polu temperatury. Głównym celem pracy jest wyprowadzenie odpowiednich warunków gwarantujących fizyczny sens rozwiązań odpowiednich zagadnień termosprężystości (tzn. uniknięcie paradoksu "chłodnego walca"). W tym celu wyprowadzone zotały wzory na związki łączące ciśnienie na powierzchni kontaktu, geometryczne charakterystyki cylindrów i rozkład strumienia ciepła poprzez powierzchnię kontaktu. Pracę zilustrowano przykładem liczbowym i wynikającymi stąd wykresami.
EN
In this paper the comparison of material eort models: the classic Huber-Mises-Hencky approach and the Burzynski condition was presented. Burzynski yield condition is pressure sensitive and naturally takes into account the strength dierential eect, which has been observed in nickel-base super alloys such as Inconel 718. Investigation was performed during thermal-uidstructure interaction analysis of a power turbine guide vane of turbine helicopter engine PZL- 10W. Firstly, computational uid dynamics conjugate heat transfer analysis was carried out, then stress analysis was performed with boundary conditions obtained via computational uid dynamics analysis. During stress analysis, two mentioned above equivalent stress denitions were applied and dierence in material eort modelling by them was shown.
EN
This paper is concerned with the problem of an interface insulated plane crack obstructing a uniform heat flux in a two-layer microperiodic space. An approximate analysis is performed within the framework of linear stationary thermoelasticity with microlocal parameters. A general method of solving the resulting boundary-value problem is presented. It is based on the use of potential functions and an analogy between the thermal crack problem and the skew-symmetric mechanical loading problem. The thermal stress singularities are discussed.
PL
Problem stałego przepływu ciepła zakłóconego istnieniem izolowanej termicznie szczeliny międzywarstwowej w periodycznie dwuwarstwowej przestrzeni jest przedmiotem pracy. Przybliżoną analizę przeprowadzono w ramach liniowej stacjonarnej termosprężystości z parametrami mikrolokalnymi. Podano i zilustrowano metodę rozwiązania wynikającego zagadnienia brzegowego, polegającą na zastosowaniu potencjałów harmonicznych i ustaleniu analogii z odpowiadającym mechanicznym, niesymetrycznym problemem szczeliny. Zbadano osobliwości naprężeń cieplnych wokół szczeliny.
EN
The influence of the change with time of friction power on thermal stresses in a friction element of a brake system is investigated. For this purpose, a list of ten different temporal profiles of specific friction power is used, which has been experimentally established for a single braking process. The corresponding profiles of transient temperature fields in the considered element are applied as input parameters to find quasi-static thermal stresses. Numerical analysis concerned with spatio-temporal distributions of the stresses and their evolutions on the heated surface is presented.
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tom Vol. 54 nr 1
205--218
EN
The quasi-static thermal stress state within the linear uncoupled elasticity is studied. The calculations were performed using the finite element method (MSC.Patran/MSC.Nastran). In order to examine smooth stress changes in a brake disk during braking, based on the temperature fields at particular time steps, additionally the script using Python programming language was developed. The numerical three-dimensional FE model of the brake disk for calculation of the transient temperature field was adopted from the previous author’s study. A single braking process at linear deceleration and constant contact pressure was simulated. The evolutions and the contours of the components of the stress tensor as well as the equivalent Huber-Mises stress were examined. The most important aspects of the stress state during braking were discussed.
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