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EN
The objective of the paper is to look at the propagation and reflection of plane waves in a thermo-diffusion isotropic medium. The reflection of plane waves in a thermo-diffusion medium was investigated in this study with reference to triple phase lag thermo-elasticity. The memory dependent derivative (MDD) is applied for this investigation. The fundamental equations are framed and solved for a particular plane. The four plane waves that are propagating across the medium are, shown namely: longitudinal displacement, P-wave, thermal diffusion T-wave, mass diffusion MD-wave and shear vertical SV-wave. These four plane wave velocities are listed for a specific medium, illustrating the impact of the diffusion coefficient and are graphically represented. Expressions for the reflection coefficient for the incidence plane wave are produced from research on the reflection of plane waves from the stress-free surface. It should be noted that these ratios are graphically represented and shown when diffusion and memory dependent derivative (MDD) factors are in play. The new model is relevant to many different fields, including semiconductors, earth- engineering, and electronics, among others, where thermo-diffusion elasticity is significant. Diffusion is a technique that can be applied to the production of integrated circuits, MOS transistors, doped polysilicon gates for the base and emitter in transistors, as well as for efficient oil extraction from oil reserves. Wave propagation in a thermos-diffusion elastic media provides crucial information about the presence of fresh and enhanced waves in a variety of technical and geophysical contexts. For experimental seismologists, developers of new materials, and researchers, this model might be useful in revising earthquake estimates.
EN
We have studied the problem of homogenous, isotropic non-local couple stress micropolar thermoelastic solid in the absence of body forces, couple density and heat resources. The reflection and transmission of waves at the interface of two distinct media have been investigated. It is observed that amplitude ratios of various reflected and transmitted waves are functions of wave number of incident waves and are affected by the non-local parameter of thermoelastic solid.
EN
The propagation of plane waves in a rotating homogeneous, isotropic, thermoelastic solid with double porosity following Lord-Shulman’s theory of thermoelasticity has been investigated. It is assumed that the medium rotates about an axis normal to the surface with a uniform angular velocity. There may exist five coupled waves that evolved due to the longitudinal, transverse disturbance, voids of type-I and type-II, and temperature change in the medium. The secular equation for the model under consideration has been derived with the help of formal solutions and boundary conditions. The amplitude of displacements, temperature change and volume fraction fields for voids of type-I and type-II have also been computed analytically. Finally, numerical computations have been carried out for magnesium crystal material to understand the behavior of amplitude of phase velocity, penetration depth, specific loss, displacement components, temperature change, and volume fraction field due to type-I and type-II voids corresponding to the different rotation rates. Various graphs have been plotted to support the analytical findings. The study may be used in the development of rotation sensors, material design and thermal efficiency.
EN
Thermo-elasto-plastic analysis of a rotating disc made of Functionally Graded Materials (FGMs) is studied in this paper using Successive Approximation Method (SAM). The plane stress condition is assumed for formulation of the problem. After computation of effective material properties based on modified mixture rule, the governing equations are derived analytically and then is solved using the Differential Quadratic Method (DQM). After obtaining the displacements and stresses, the yield conditions are calculated by von-Mises failure criteria. The rotating disc is made of an Aluminum–Silicon Carbide functionally graded material. The plastic behavior of Aluminum is considered as strain hardening one. The effects of angular speed, percentage of ceramic particles, particle reinforcement power, and boundary conditions such as temperature gradient on the radial and tangential thermo-elasto-plastic strains, stresses, and equivalent stresses is investigated. The results show that the radial stresses through the disc are significantly less than tangential stresses, therefor the tangential stresses has a significant effect on the equivalent stress and yield conditions.
EN
The presented paper is focused on the comparison of the Continuous and Discontinuous Galerkin Methods in terms of thermoelasticity for a cubic element. For this purpose, a numerical model of the phenomenon was built using both methods together with the Finite Element Method (FEM). The comparison of the results of numerical simulation obtained with the use of an original computer program based on the derived final set of FEM equations for both methods is presented.
PL
Stałe lub zmienne w czasie (stacjonarne lub niestacjonarne) obciążenia cieplne wywołują w konstrukcji ustalone lub nieustalone pola temperatury. Te z kolei są źródłem naprężeń, które mają szczególne znaczenie w przypadkach urządzeń pracujących w warunkach dużych zakresów temperatur i ich częstej zmienności w czasie. W niniejszym opracowaniu przedstawiono przykłady zastosowania programów MSC.Patran (budowa modeli i analiza wyników obliczeń) i MSC.Nastran (obliczenia) w zakresie termosprężystości niesprzężonej, czyli z pominięciem ciepła wytwarzanego na skutek odkształcania materiału.
EN
Fixed or time-varying (fixed or non-fixed) heat loads cause in the structure fixed or transient temperature fields. These, in turn, are a source of stresses which are particularly important for equipment operating in large temperature ranges and their frequent variability over time. The paper presents examples of application of MSC.Patran (construction of models and analysis of calculation results) and MSC.Nastran (calculations) in the range of uncoupled thermal resilience, i.e. excluding the heat produced by material deformation.
PL
Stałe lub zmienne w czasie (stacjonarne lub niestacjonarne) obciążenia cieplne wywołują w konstrukcji ustalone lub nieustalone pola temperatury. Te z kolei są źródłem naprężeń, które mają szczególne znaczenie w przypadkach urządzeń pracujących w warunkach dużych zakresów temperatur i ich częstej zmienności w czasie. W niniejszym opracowaniu przedstawiono przykłady zastosowania programów MSC.Patran (budowa modeli i analiza wyników obliczeń) i MSC.Nastran (obliczenia) w zakresie termosprężystości niesprzężonej, czyli z pominięciem ciepła wytwarzanego na skutek odkształcania materiału. W tej części artykułu zamieszczono przykładowe zadania modelowania naprężeń termomechanicznych.
EN
Fixed or time-varying (fixed or non-fixed) heat loads cause in the structure fixed or transient temperature fields. These, in turn, are a source of stresses which are particularly important for equipment operating in large temperature ranges and their frequent variability over time. The paper presents examples of application of MSC.Patran (construction of models and analysis of calculation results) and MSC.Nastran (calculations) in the range of uncoupled thermal resilience, i.e. excluding the heat produced by material deformation. This part of the paper provides examples of tasks for modelling thermomechanical stresses.
EN
The paper focuses on the mathematical and numerical modelling of the thermoelasticity problem in the three-dimensional region. The governing equations of the mathematical model are a set of equilibrium equations. The numerical model uses continuous Galerkin formulation together with the Finite Element Method (FEM). Both models are discussed in detail. The final set of FEM equations is derived. The example of numerical calculations obtained with the use of an original computer program is presented. The main goal of presented paper is to develop the alternative model to the one based on the Discontinuous Galerkin Method (DGM).
EN
In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.
10
Content available A study on fractional order thermoelastic half space
EN
In this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.
EN
The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.
EN
The present investigation is concerned with vibration phenomenon of a homogeneous, isotropic thermoelastic microbeam with double porosity (TDP) structure induced by pulsed laser heating, in the context of Lord-Shulman theory of thermoelasticity with one relaxation time. Laplace transform technique has been applied to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field, and temperature distribution. The resulting quantities are recovered in the physical domain by a numerical inversion technique. Variations of axial displacement, axial stress, lateral deflection, volume fraction field, and temperature distribution with axial distance are depicted graphically to show the effect of porosity and laser intensity parameter. Some particular cases are also deduced.
EN
The present investigation deals with the twodimensional deformation because of laser pulse heating in a thermoelastic microelongated layer with a thickness of 2d, which is immersed in an infinite nonviscous fluid. Normal mode analysis technique is applied to obtain the analytic expressions for displacement component, force stress, temperature distribution, and microelongation. The effect of elongation and laser pulse rise time on the derived components have been depicted graphically.
EN
In the present discussion, the plane strain deformation due to laser pulse heating in a thermoelastic microelongated solid has been discussed. The analytic expressions for displacement component, force stress, temperature distribution and micro-elongation have been derived. The effect of pulse rise time and micro-elongation on the derived components have been depicted graphically.
PL
Praca dotyczy problematyki zakrzywionej powłoki wykonanej z anizotropowego materiału o funkcyjnej gradacji. W rachunku wykorzystano koncepcję tensora krzywizny Riemanna-Christoffela wzbogaconą o wpływ pola temperatury przez obecność tensora właściwości termicznych. W ramach wykonanych obliczeń różnica wektora poddanego koneksji afinicznej wzdłuż infinitezymalnego czworokąta wyraża się, zależnie od drogi przejścia, sumą zarówno efektu geometrycznego, reprezentowanego tensorem krzywizny Riemanna-Christoffela, jak również efektu termicznego wyrażonego przez symbol krzywizny termicznej.
EN
This work concerns the problem of a curvilinear shell made of anisotropic material with functional gradation. The calculus is based on the concept of the Riemann-Christoffel curvature tensor enhanced by the influence of temperature field through the presence of a thermal tensor. Calculations comprise estimation of the difference of a vector subjected to the affine connection along the infinitesimal quadrangle expressed, correspondingly to the shifting path, by a sum of both the geometric effect, represented by the Riemann-Christoffel curvature tensor, as well as certain symbol of the thermal curvature.
16
EN
In this note the influence of temperature on vibrations of laminated layer made of two different materials is presented. The macroscopic properties of this layer are changing continuously along one direction x1, perpendicular to the laminas. To obtain the equations describing this problem, the tolerance averaging technique is used [1]. In this work, three models are proposed: the tolerance and the asymptotic-tolerance model, taking into account the effect of the microstructure size on the overall behaviour of this type of structures, and the asymptotic model, which equations omit this effect. To solve the equations of these three models the finite difference method is used.
EN
The present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.
18
Content available remote On thermoelasticity in FGL - tolerance averaging technique
EN
In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented - the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.
EN
In this work the possibility to characterize mechanical components combining thermoelastic measurement technique (TSA) and digital image correlation (DIC) is studied. The combination of these two different methodologies allows to analyze thermo-mechanical characteristics of materials such as plastic and rubber, which are difficult to study with the only thermoelastic methodology. The digital image correlation allows to determinate the first invariant of deformation ε1, using a differential thermocamera. Lack of adiabatic conditions, essential for methodology use, makes analysis not simple. Digital image correlation allows to obtain the same information by correlating digital images acquired during static or dynamic deformationof an object, but with limitations linked to acquisition system. An accurate analysis is dedicated to the study of first invariant of deformation related to Young’s module variation, performed by load cycles with variable amplitude and displacement. Comparative analysis between the two measurement methodologies has been performed on rubber samples loaded by dynamic compression.
EN
The sliding period is considered a critical period in the lifetime of friction clutches, because most failures occur during this period. High temperatures due to sliding velocity will appear on the contacting surfaces of the friction clutch system (e.g., in single -disc clutch are pressure plate, clutch discs and flywheel). The finite element technique has been developed to investigate the effect of the type of friction material (material properties) on the transient thermoelastic behaviour of a single-disc dry clutch. Two types of friction materials are used in this work: organic and sintered friction materials. Axisymmetric models are developed to simulate a friction clutch system (single disc with two effective sides). The results represent the comparisons between organic and sintered friction discs, behaviours during slipping periods in clutches.
PL
Stan poślizgu tarciowego ze względu na występowanie największej ilości uszkodzeń jest krytycznym stanem pracy sprzęgieł tarciowych. Wysoka temperatura pracy występująca na powierzchniach trących elementów sprzęgieł spowodowana jest poślizgiem (np. w sprzęgłach jednotarczowych na klockach, tarczach i kole zamachowym). Metoda elementów skończonych została wykorzystana do zbadania wpływu rodzaju materiału (właściwości materiału) na zagadnienie termosprężystości w suchych sprzęgłach tarciowych. W pracy wykorzystano dwa rodzaje materiałów tarciowych: organiczny i spiekany. Opracowano osiowosymetryczne modele symulujące sprzęgło tarciowe (pojedyncza tarcza z dwoma okładzinami). Wynikiem pracy jest porównanie cyklów poślizgu pomiędzy dyskami wykonanymi z materiału organicznego oraz spiekanego.
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