Thermal Axial Force Research Articles

Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model

The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si3N4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size.

A comparison study on the long-term thermomechanical performance of energy piles under three climatic conditions

Energy piles provide a profitable solution for both structural support and space cooling and heating of residential and commercial buildings. Nevertheless, very few details have been reported on the long-term thermomechanical performance of energy piles concerning the influence of climatic conditions. In this paper, a numerical study is performed to elucidate the long-term thermomechanical behaviour of energy piles under three typical climatic conditions by considering thermal demands of a reference office building. Pile and soil temperature fluctuations, thermal pile axial force, and thermally induced pile head displacement are determined and compared. The results show that the surrounding soil thermal imbalance under climatic conditions with nonsymmetrical thermal demands is more significant than that under climatic conditions with balanced thermal demands. Moreover, notably lower thermal axial forces are induced at the end of thermal cycles under climatic conditions with nonsymmetrical thermal demands. However, the thermally induced pile head displacements are much larger under such climatic conditions, and longer thermal operations are needed to reach the steady state. The study suggests that the use of the unified design method of energy piles subjected to different climatic conditions may adversely affect the design effect. Besides, compared with the thermal forces, energy pile design should pay more attention to the adverse effects of thermally-induced pile head displacement on normal service.

Dynamics and stability analysis of a flexible liquid-filled rotor in a constant thermal environment

In this study, the dynamics and stability of a flexible rotor containing liquid in a constant thermal environment are investigated. According to thermoelastic theory, the thermal axial force exerted on the rotor is calculated by using the analytical method. A spinning Rayleigh beam is used as a simplified model of the rotor. Applying the Hamilton principle, the governing equation of motion for the flexible liquid-filled rotor system is derived. Using the obtained model, the stability prediction model and the critical spinning speed for the rotor system are formulated. To demonstrate the validity of the developed model, the present analysis is compared with the results reported in the previous study, and good agreement is observed from the comparison results. Finally, numerical results based on the obtained model are performed for a better understanding of the parameters including filling parameters, mode number, rotatory inertia and thermal effect on the stability, and critical spinning speed of the rotor system.

Stability and critical spinning speed of a flexible liquid-filled rotor in thermal environment with nonlinear variable-temperature

This paper deals with the stability and critical spinning speed of a liquid-filled rotor in thermal environment with nonlinear variable-temperature. The nonlinear temperature field model of the rotor is developed by using Laplace transform. The thermal axial force exerted on the rotor as a result of the thermal effect is calculated as functions of temperature rise rate and rotor thickness ratio. Spinning Timoshenko beam model is employed to establish the structural dynamics equations of the rotor system. The governing equation of the motion is derived by using the Hamilton principle. The validity of the developed model is confirmed by comparing with the numerical solutions available in the literature. The numerical results based on the obtained analytical solutions are given for a better understanding of the effects of the shear deformation, rotary inertia, filling parameters and thermal effect on the system stability and critical spinning speed. The results show that the system stability is dependent on the thermal axial force and cavity ratio. Moreover, the results also highlight the role of thermal effect, rotary inertia, cavity ratio and mass ratio on the critical spinning speed.

Whirl characteristics of a flexible liquid-filled rotor under thermal shock

In this paper, the whirl characteristics of a flexible liquid-filled rotor subjected to thermal shock are investigated. On the basis of the Hamilton principle, the whirl frequency equation of the rotor system is derived. Using Laplace transform, the analytical model of the temperature field of the rotor is obtained. The validity of the developed temperature model is demonstrated by comparing with the finite element results. Then, the thermal axial force exerted on the rotor is calculated and the influence factors are studied. The system stability is analyzed in terms of the whirl frequency equation. The reasonability of the predict model for system stability is verified, and a good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data. Finally, the critical spinning speed of the rotor system is analyzed, and the effects of some main parameters on system critical speed are investigated.

Shear tab connection with composite beam subjected to transient-state fire temperatures

Purpose This study aims to develop a rational model to predict the thermal axial forces developed in shear tab connections with composite beams when subjected to transient-state fire temperatures. Design/methodology/approach Finite element (FE) models are first developed in ABAQUS and validated against experimental data available in the literature. Second, a parametric study is conducted to identify the major parameters that affect the behavior of shear tab connections with composite beams in the fire. This includes beam length, shear tab thickness, shear tab location, concrete slab thickness, setback distance and partial composite action. A design-oriented model is developed to predict the thermal induced axial forces during the heating and cooling phases of a fire event. The model consists of multi-linear springs that can predict the stiffness and strength of each component of the connection with the composite beam. Findings The FE results show that significant thermal axial forces are generated in the composite beam in the fire. This is prominent when the beam bottom flange comes in contact with the column. Fracture at the toe of the welds governs the behavior during the cooling phase in most FE simulations. Also, the rational model is validated against the FE results and is capable of predicting the thermal axial forces developed in shear tab connections with composite beams under different geometrical properties. Originality/value The proposed model can predict the thermal axial force demand and can be used in performance-based approaches in future structural fire engineering applications.

Elastoplastic thermal buckling of functionally graded material beams

Elastoplastic thermal buckling characteristics of ceramic-metal functionally graded material (FGM) beams subjected to transversely non-uniform temperature rise are investigated by symplectic method in Hamiltonian system. Based on TTO model, the linear hybrid hardening elastoplastic model is used to simulate the elastoplastic material properties and establish thermal elastoplastic constitutive equations of FGM beams. Then, the canonical equations are established to transform critical loads and buckling modes into symplectic eigenvalues and eigensolutions in symplectic space. The main contributions of this study are that complete buckling mode space and critical thermal axial forces for elastoplastic thermal buckling of the FGM beams are obtained by analytical solutions; meanwhile, buckling temperatures and elastoplastic interfaces of the bucked FGM beams are obtained by inverse solutions. Numerical examples of buckling behaviors varying with thermal load, slenderness ratio and power law index are presented. The effects of elastoplastic material properties on critical temperatures and plastic zone are analyzed and discussed.

Structural performance of steel beams and frames with slant end-plate connections at elevated temperature

Thermal expansion remains as one of the most hazardous conditions a restrained steel beam could experience throughout its service life. In this regard, the design of connections plays an important role in dissipating the thermal axial force resulted from such deformation. In this paper, the finite element method (FEM) has been employed to investigate the thermal performance of the steel beam with slant connections under gravity and thermal loads. The numerical outcomes agree very well with the analytical and experimental approaches, thus demonstrating a good reliability of the model to assess the thermal performance of the steel frames with slant end-plate connections. In addition, the proposed and conventional end-plate connections are modelled separately in two 7-storey steel frames to examine their comparative thermal performance. The numerical results conclude that the thermal behaviour of steel frame with the slant end-plate connection is superior to that using conventional since it is capable to dissipate considerably the experienced additional thermal axial forces.

Numerical study on thermal deformation behaviors of the single subassembly in sodium-cooled fast reactors based on Euler-Bernoulli beam theory

Due to the special geometry and compact arrangement of subassemblies in the sodium-cooled fast reactor, thermal deformation of the assemblies are easily triggered by uneven temperature distribution in the reactor core, which is negative for reactor safety. Therefore, it is necessary for researchers and engineers to conduct quantitative analysis towards thermal deformation behaviors of subassemblies, and furthermore, give reliable evaluation results on aftermath of the assembly thermal deformation. In the present study, thermal deformation analysis code FADAC, which was developed based on Euler-Bernoulli beam theory, was applied to make numerical investigation for thermal deformation behaviors of a single subassembly in sodium-cooled fast reactor. In order to preliminarily assess the capacity for thermal deformation, different temperature gradient conditions were considered and analyzed in detail for free bowing of the subassembly, furthermore, with the aid of numerical analysis for thermal axial forces and thermal bending moments, axial displacements and deflections were calculated finally. Besides, in order to predict the comprehensive results of the assembly deformation under both thermal load and mechanical load, restrained bowing were also analyzed for different temperature conditions. All of the simulation results were in good accordance with the experimental data. The present numerical research is of great significance to assembly deformation research in the sodium-cooled fast reactor, and will surely lay a solid foundation for deformation analysis towards multi-subassemblies.

Thermal vertical buckling of surface-laid submarine pipelines on a sunken seabed

Submarine pipelines are the most viable way for transporting offshore oil and gas worldwide. However, it is easy to cause the vertical buckling in the process of work under the high temperature and high pressure. In this paper, the energy method was used to analyze and derive the relationship between the temperature and the buckling height during the thermal vertical buckling of the third-order mode of pipeline. Additionally, the finite element method was utilized to model and simulate the pipeline on submarine pit and trench respectively. From this investigation, it is found that the maximum circumferential stress and strain in mid-section of pipelines are larger than in left-section on submarine pit. On submarine trench, the maximum circumferential stress in mid-section is larger than in left-section but the maximum circumferential strain in mid-section is smaller than in left-section. The buckling height and length sharply increases with the increase of temperature or pressure whether on submarine pit or trench. With the increase of temperature, the stress of pipelines increases first and then decreases on pit but always enlarges on trench. With the increase of pressure, the stress of pipelines increases on trench, and the stress of pipelines in left-section increases but in the mid-section decreases. The length and depth of submarine pit and trench directly affect the shape of pipelines and size of the initial sunken imperfection. The friction coefficient has little effect on the buckling length, height and stress and the buckling deformation changes from third-order mode to fifth-order because the axial friction cannot balance the thermal axial force if the friction coefficient is too small. The buckling height, length and stress enlarges accompanied by the increase of diameter-thick ratio of pipelines and reducing the diameter-thick ratio in practice can effectively strengthen the ability of pipeline to resist buckling.

A Numerical Investigation on Restrained High Strength Q460 Steel Beams Including Creep Effect

Most of previous studies on fire resistance of restrained steel beams neglected creep effect due to lack of suitable creep model. This paper presents a finite element model (FEM) for accessing the fire resistance of restrained high strength Q460 steel beams by taking high temperature Norton creep model of steel into consideration. The validation of the established model is verified by comparing the axial force and deflection of restrained beams obtained by finite element analysis with test results. In order to explore the creep effect on fire response of restrained Q460 steel beams, the thermal axial force and deflection of the beams are also analyzed excluding creep effect. Results from comparison infer that creep plays a crucial role in fire response of restrained steel beam and neglecting the effect of creep may lead to unsafe design. A set of parametric studies are accomplished by using the calibrated FEM to evaluate the governed factors influencing fire response of restrained Q460 steel beams. The parametric studies indicate that load level, rotational restraint stiffness, span–depth ratio, heating rate and temperature distribution pattern are key factors in determining fire resistance of restrained Q460 steel beam. A simplified design approach to determine the moment capacity of restrained Q460 steel beams is proposed based on the parametric studies by considering creep effect.

Development of a Reinforced Bend with Shear Control Ring for District Heating

As a fitting to changing the direction of district heating pipes, bends are subjected to a transverse loading by the soil reaction. Generally the foam cushion are buried together to absorb the expansions. However foam cushions are often squeezed by the repetitive thermal axial forces and the soil reactions, it loses its function to secure the expansion space of pipes. It can be a cause of pipe fracture and decreasing the lifetime. In this study, the new reinforced bend was developed without foam cushion but satisfying the structural safety level of current bends with foam cushion. Shear control ring (SCR) was suggested and determined to deconcentrate the shear stresses in the polyurethane insulation based on the finite element analysis [1]. The Taguchi method which is one of design of experiment (DOE) method was introduced to optimize the specification of the SCR [2]. In situ test was also performed to validate the performance of SCR bend without foam cushion by comparing to current bend with foam cushion. Shear stresses of two bends were measured and analysed under the same burying and operating conditions. As a result, it was confirmed that the SCR band without foam cushion has a similar safety level itself with the current bend with foam cushion.

An approach for evaluating fire resistance of steel beams considering creep effect

Most of previous studies on fire resistance of restrained steel beams neglected creep effect due to lack of suitable creep model. This paper presents a finite element model (FEM) for accessing the fire resistance of restrained high strength Q460 steel beams by taking high temperature Norton creep model of steel into consideration. The validation of the established model is verified by comparing the axial force and deflection of restrained beams obtained by finite element analysis with test results. In order to explore the creep effect on fire response of restrained Q460 steel beams, the thermal axial force and deflection of the beams are also analyzed excluding creep effect. Results from comparison infer that creep plays a crucial role in fire response of restrained steel beam and neglecting the effect of creep may leads to unsafe design. A simplified design approach to determine the moment capacity of restrained Q460 steel beams is proposed based on the results of parametric studies by considering creep effect.

Dynamic Analysis of Space Structure Deployment with Transient Thermal Load

Thermal load is non-ignorable in the design and analysis of high precision and reliable space deployable structures. A new approach based on flexible multibody system is presented in order to investigate the thermoelastic effect on the deployment of space structure. Dynamic equations of an Euler Bernoulli beam element with transient thermal load are derived in Absolute Nodal Coordinate Formulation. The temperature distribution in the beam section is assumed as linear, which is reasonable for slender beams. The resulting generalized thermoelastic forces can be decomposed into thermal axial force and thermal bending moments, which can cause tension/compression and bending of the beam respectively. The dynamic equations of the beam element are then assembled into a flexible multibody system. Deployment analysis of a space mechanism with transient thermal load is studied with the new approach. Simulation result shows that thermoelasticity could cause static deformation of the final configuration as well as affect the external driving forces.

Thermally-induced bending-torsion coupling vibration of large scale space structures

In this paper, a finite element scheme is developed to solve the problem of thermally-induced bending-torsion coupling vibration of large scale space structures, which are usually composed of thin-walled beams with open and closed cross-section. A two-noded finite element is proposed to analyze the transient temperature field over the longitudinal and circumferential direction of a beam. Since this temperature element can share the same mesh with the two-noded beam element of Euler–Bernoulli type, a unified finite element scheme is easily formulated to solve the thermal-structural coupling problem. This scheme is characterized with very strong nonlinear formulation, due to the consideration of the thermal radiation and the coupling effect between structural deformations and the incident normal heat flux. Moreover, because the warping is taken into account, not only the thermal axial force and thermal bending moments but also the thermal bi-moment are presented in the formulation. Consequently, the thermally-induced bending-torsion coupling vibration can be simulated. The performance of the proposed computational scheme is illustrated by the analysis of the well-known failure of Hubble space telescope solar arrays. The results reveal that the thermally-induced bending-torsion coupling vibration is obviously presented in that case and could be regarded as a cause of failure.