Linear Temperature Field Research Articles

Coupled thermomechanical analysis using isoparametric curved shell elements

This study focuses on the coupled thermo-mechanical formulation in isoparametric shell elements and its implementation in curved laminar structures. The formulation is based on the direct isoparametric formulation, specifically designed for flat and curved shell elements, and relies on the theory of degenerated solids. The research provides a comprehensive description of the coupled thermo-mechanical analysis, including the mechanical equilibrium equations, the interrelations between stress, temperature, displacement, deformation, and the conservation of thermal energy. It adopts a simultaneous approach to addressing the impacts of temperature and mechanical loads. The paper elaborates on various numerical examples that substantiate the formulation. These examples include simulations that encompass linear scenarios, which are then compared to analytical solutions and results derived from other numerical software. The examples highlighted include one-dimensional temperature diffusion, radial diffusion, and the thermal behavior of a cylindrical cover and a pipe under a linear temperature gradient. These simulations demonstrate the formulation's capacity to accurately capture the interactions between temperature variations and structural displacements. They also confirm the alignment of the proposed model with existing analytical and numerical solutions. In conclusion, the research provides a good framework for coupled thermo-mechanical analysis. The flexibility of the formulation is evidenced across different configurations and scenarios, accommodating various types of boundary conditions such as constant and linear temperature fields, distributed loads, and constraints on displacements and rotations. It effectively manages temperature flows across one, two, and three dimensions, highlighting its extensive applicability in the realm of structural analysis. This versatility underscores its broad applicability in the field of structural analysis.

Deciphering non-Gaussianity of diffusion based on the evolution of diffusivity

Non-Gaussian diffusion of nanoparticles in complex media disrupts Einstein's picture of Brownian motion, and non-Gaussianity is thought to be closely related to diffusing diffusivity generated by spatiotemporal heterogeneities. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired by a recent study by Alexandre [], we demonstrate that non-Gaussianity can be deciphered through the spatiotemporal evolution of heterogeneity-dependent diffusivity distribution. Using diffusion experiments in a linear temperature field and Brownian dynamics simulations, we found that short-time non-Gaussianity can be predicted based on the boundary ratio of the diffusivity distribution; the long-time non-Gaussianity either approaches an asymptotic value of −2 or scales with 1/t, depending on the dominance of particle migration. The temporal variation of non-Gaussianity is determined by an effective Péclet number, which represents a competition between the varying rate of diffusivity and the diffusivity of diffusivity and reveals whether the tail distribution expands or contracts. The tail is more Gaussian than exponential over long times, with exceptions significantly dependent on the diffusivity distribution. Our findings provide a versatile framework for understanding non-Gaussian diffusion in probability space, and shed light on establishing a diffusion spectrum in cells and characterizing nanomedicine transport in biological microenvironment using non-Gaussian statistics. Published by the American Physical Society 2024

Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields.

Self-oscillating coupled systems possess the ability to actively absorb external environmental energy to sustain their motion. This quality endows them with autonomy and sustainability, making them have application value in the fields of synchronization and clustering, thereby furthering research and exploration in these domains. Building upon the foundation of thermal responsive liquid crystal elastomer-based (LCE-based) spring oscillators, a synchronous system comprising three LCE-based spring oscillators interconnected by springs is established. In this paper, the synchronization phenomenon is described, and the self-oscillation mechanism is revealed. The results indicate that by varying system parameters and initial conditions, three synchronization patterns emerge, namely, full synchronous mode, partial synchronous mode, and asynchronous mode. For strongly interacting systems, full synchronous mode always prevails, while for weak interactions, the adjustment of initial velocities in magnitude and direction yields the three synchronization patterns. Additionally, this study explores the impact of several system parameters, including LCE elasticity coefficient and spring elasticity coefficient, on the amplitude, frequency, and synchronous mode of the system. The findings in this paper can enhance our understanding of the synchronization behavior of multiple mutually coupled LCE-based spring oscillators, with promising applications in energy harvesting, soft robotics, signal monitoring, and various other fields.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Heat-Driven Synchronization in Coupled Liquid Crystal Elastomer Spring Self-Oscillators.

Self-oscillating coupled machines are capable of absorbing energy from the external environment to maintain their own motion and have the advantages of autonomy and portability, which also contribute to the exploration of the field of synchronization and clustering. Based on a thermally responsive liquid crystal elastomer (LCE) spring self-oscillator in a linear temperature field, this paper constructs a coupling and synchronization model of two self-oscillators connected by springs. Based on the existing dynamic LCE model, this paper theoretically reveals the self-oscillation mechanism and synchronization mechanism of two self-oscillators. The results show that adjusting the initial conditions and system parameters causes the coupled system to exhibit two synchronization modes: in-phase mode and anti-phase mode. The work conducted by the driving force compensates for the damping dissipation of the system, thus maintaining self-oscillation. The phase diagrams of different system parameters are drawn to illuminate the self-oscillation and synchronization mechanism. For weak interaction, changing the initial conditions may obtain the modes of in-phase and anti-phase. Under conditions of strong interactions, the system consistently exhibits an in-phase mode. Furthermore, an investigation is conducted on the influence of system parameters, such as the LCE elastic coefficient and spring elastic coefficient, on the amplitudes and frequencies of the two synchronization modes. This study aims to enhance the understanding of self-oscillator synchronization and its potential applications in areas such as energy harvesting, power generation, detection, soft robotics, medical devices and micro/nanodevices.

Free vibration analysis of carbon-fiber plain woven reinforced composite conical-cylindrical shell under thermal environment with general boundary conditions

In this paper, the free vibration analysis of carbon fiber/epoxy resin and carbon/carbon plain woven conical-cylindrical shell under thermal environment with general boundary conditions using generalized differential quadrature (GDQ) is conducted. A two-step homogenization approach, in which 3D finite element method (3D FEM) based on 3D representative volume elements (3D RVE) are applied, is used to get the mechanical properties of the plain woven composites. According to first order shear deformation theory (FSDT) and Hamilton’s principle, considering a thermal environment, the governing equations of both the two shells are obtained. GDQ is applied during the solving procedure and general boundary conditions are considered through artificial springs. After several comparison studies focused on convergence, mechanical properties and thermal environment, the effects of boundary conditions, geometry, total fiber volume fraction and uniform, linear temperature field are studied comprehensively.

Thermotactic navigation of an artificial microswimmer near a plane wall

Despite significant advances in the field of man-made micro- and nanomotors, it remains a challenge to precisely control their motion in bounded environments. Here, we present a theoretical analysis of a thermally activated micromotor near a plane wall under the action of a background linear temperature field. The coupling between the autonomous and field-directed motions has been resolved using a combined analytical–numerical framework comprising general solutions in bispherical coordinates and the reciprocal theorem for creeping flows. Results reveal giant augmentation in swimming speeds, the controlling parameter zones for positive and negative thermotaxes and the flexibility of steering perpendicular to the field gradient for an isolated micromotor. Boundary-instigated thermo-fluidic modulations at different levels of confinements and preferential orientations cause directional switching of both the vertical translation and rotation parallel to the wall, thereby drastically altering the phase portraits of the swimmer dynamics. Contrasting trajectory characteristics, e.g. escape, attraction, are partitioned by unstable separatrices in the phase portraits, while competitive repulsion (attraction) after attraction (repulsion) characteristics emerge for different relative field strengths$\mathcal {S}$and gradient orientations$\theta _T$. Below$\mathcal {S}=0.25$, highly counter-intuitive trajectories result when the micromotor is initially launched from an overlapping escape zone. Moreover, external-field-assisted microswimming can uniquely tune the directionality of wall-parallel translation, broadening the scope of dynamic regulation of self-propulsion. Thus, providing insights into a precisely controlled fuel-free actuation of micromotors near a physical obstacle, the present study stands as a step toward addressing the increasing demand for successful implementation of micromotors in futuristic clinical and environmental applications.

Dynamical Behaviors of a Translating Liquid Crystal Elastomer Fiber in a Linear Temperature Field.

Liquid crystal elastomer (LCE) fiber with a fixed end in an inhomogeneous temperature field is capable of self-oscillating because of coupling between heat transfer and deformation, and the dynamics of a translating LCE fiber in an inhomogeneous temperature field are worth investigating to widen its applications. In this paper, we propose a theoretic constitutive model and the asymptotic relationship of a LCE fiber translating in a linear temperature field and investigate the dynamical behaviors of a corresponding fiber-mass system. In the three cases of the frame at rest, uniform, and accelerating translation, the fiber-mass system can still self-oscillate, which is determined by the combination of the heat-transfer characteristic time, the temperature gradient, and the thermal expansion coefficient. The self-oscillation is maintained by the energy input from the ambient linear temperature field to compensate for damping dissipation. Meanwhile, the amplitude and frequency of the self-oscillation are not affected by the translating frame for the three cases. Compared with the cases of the frame at rest, the translating frame can change the equilibrium position of the self-oscillation. The results are expected to provide some useful recommendations for the design and motion control in the fields of micro-robots, energy harvesters, and clinical surgical scenarios.

A thermally-responsive fiber engine in a linear temperature field

Recently, many intriguing phenomena of the thermally responsive fiber-mass system in the inhomogeneous temperature field such as harvesting energy directly from the environment to maintain its self-oscillation have been observed, and have various potential applications. Challenges remain in the study of this complex thermodynamic coupled nonlinear dynamics problem. This paper abstractly presents a fiber engine module, establishes its constitutive model and asymptotic relationship, and demonstrates their conveniences in several cases of the fiber-mass systems. The asymptotic relationship is similar to the Kelvin-Voigt viscoelastic model consisting of a dashpot and a spring. Through several typical cases with different characteristic times of heat transfer, the fiber in a linear temperature field has three kinds of behaviors: damper, spring and engine. The fiber engine module can absorb energy from the environment and vibrate spontaneously, and even has the potential to drive a machine jumping on a hot surface. Furthermore, a stirrer driven by the fiber engine module is explored and the optimal characteristic time for maximum power density is found to be 0.5. The fiber engine module proposed can advance the understanding of the fiber-mass system and provide convenience for its applications in the fields of soft robotics, micro/nano devices, and biomedical instruments.

Vibration Characteristics of Hybrid Honeycomb Core Sandwich Structure with FG-CNT Reinforced Polymer Composite Faces under Various Thermal Fields

This paper presents the free and forced vibration characteristics of a hybrid honeycomb core sandwich structure consisting of a top and bottom FG-CNT reinforced polymer composite face sheet in a thermal environment. Different thermal fields like the uniform, linear and nonlinear temperature fields in the thermal environment along the thickness direction are considered to study the dynamic characteristics of the hybrid honeycomb core sandwich structure. The mathematical model is developed using Hamilton’s principle along with the third-order shear deformation theory. Five unknown modal coefficients are found using the modal superposition principle to calculate the forced vibration response. From the free and forced vibration results, it is observed that the FG-V[Formula: see text] grading pattern face sheets with lower cell size honeycomb core and with higher cell wall thickness honeycomb core show better vibration characteristics. It is noticed that the sandwich structure with honeycomb core and FG-V[Formula: see text] CNT reinforced polymer composite face has a higher critical buckling temperature in the thermal environment. Furthermore, for different percentages of critical buckling temperature, the natural frequencies and vibrating patterns for uniform, linear and nonlinear temperature fields are the same for the sandwich structure with UD, FG-V[Formula: see text] and FG-[Formula: see text]V CNT reinforced polymer composite faces. In addition, the resonant peak of the sandwich structure with FG-V[Formula: see text] CNT reinforced polymer composite face in nonlinear temperature field shifts more toward the right, while that of the uniform temperature field shifts more toward the left in the velocity response.

Similarity Criterion of Freezing Model Test considering Nonlinear Variation of Thermal Parameters with Temperature

The significant differences in specific heat and thermal conductivity of ice and water lead to the changes of specific heat and thermal conductivity of soil during the freezing process. This makes it hard for the temperature field similarity criterion based on constant thermal parameters to accurately reflect the temperature field evolution of soil mass caused by nonlinearity of thermal parameters in the process. Based on heat conduction differential equation considering nonlinear changes of thermal parameters, this paper uses similarity transformation method to derive the similarity criterion of the temperature field in the frozen soil model test and arrives at the conclusion that the prototype soil and model soil should meet when the original soil is used for the model test. At the same time, given the impact of the third boundary condition on the similarity criterion, the thermal physical similarity conditions for the model soil are derived. On this basis, ABAQUS finite element software is used to numerically simulate the linear and nonlinear prototype and model temperature fields. The third boundary condition considered the temperature evolution of the characteristic points during the freezing process is analyzed. The calculation results indicate that the nonlinear thermal conductivity similarity criterion established herein can correctly reflect the evolution process of the prototype frozen soil temperature field. It is also suggested that the model soil thermal parameters are reasonably calculated. At the same time, it shows that the nonlinear freezing similarity criterion of the soil, when the third boundary condition is satisfied, has clear physical meaning and higher practical value. The research results provide a practical and reasonable parameter calculation method for the model soil preparation in the frozen soil model test and a theoretical basis and technical support for the design and implementation of the water-heat-force coupling model test on frozen soil.

Temperature Variation Effect on the Active Vibration Control of Smart Composite Beam

Abstract Due to their impressive capacity of sensing and actuating, piezoelectric materials have been widely merged in different industrial fields, especially aeronautic and aerospace area. However, in the aeronautic industry, the structures are operating under critical environmental loads such as high and very low temperature, which made the investigation of the effect of thermal forces on the piezoelectric structures indispensable to reach the high functionality and performance. The present paper focuses on the effect of thermal loads on the active vibration control (AVC) of structures like beams. For this purpose, a finite element model of composite beam with fully covered piezoelectric sensor and actuator based on the well-known high order shear deformation theory is proposed by taking into account the electrical potential field and a linear temperature field. Hamilton’s principle is used to formulate the electro-thermo-mechanical governing equations. The negative velocity feedback controller is implemented to provide the necessary gain for the actuator. Different analyses are effectuated to present the effect of the temperature ranging from -70°C to 70°C on the active vibration control of the composite beam.

Концентрація нормальних напружень у включенні за дії лінійного температурного поля

Концентрація нормальних напружень у включенні за дії лінійного температурного поля

Onset of thermal convection in a rectangular parallelepiped cavity of small aspect ratios

Onset of thermal convection of a fluid in a rectangular parallelepiped cavity of small aspect ratios is examined both numerically and analytically under the assumption that all walls are rigid and of perfect thermal conductance exposed to a vertically linear temperature field. Critical Rayleigh number Rc and the steady velocity and temperature fields of most unstable modes are computed by a Galerkin spectral method of high accuracy for aspect ratios Ax and Ay either or both of which are small. We find that if Ax is decreased to 0 with Ay being kept constant, Rc increases proportionally to , the convection rolls of most unstable mode whose axes are parallel to the shorter side walls become narrower, and their number increases proportionally to . Moreover, as Ax is decreased, we observe the changes of the symmetry of most unstable mode that occur more frequently for smaller Ax. However, if is decreased to 0, although we again observe the increase in Rc proportional to , we obtain only one narrow convection roll as the velocity field of most unstable mode for all A. The expressions of Rc and velocity fields in the limit of or are obtained by an asymptotic analysis in which the dependences of Rc and the magnitude and length scale of velocity fields of most unstable modes on Ax and Ay in the numerical computations are used. For example, Rc is approximated by and in the limits of and , respectively. Moreover, analytical expressions of some components of velocity fields in these limits are derived. Finally, we find that for small Ax or A the agreement between the numerical and analytical results on Rc and velocity field is quite good except for the velocity field in thin wall layers near the top and bottom walls.

Closed Form Solutions for Thermal Buckling of Functionally Graded Rectangular Thin Plates

This work concerns the critical buckling temperature of functionally graded rectangular thin plates; the properties of functionally graded material vary continuously in accordance with the power law of thickness z. Closed form solutions for the critical thermal parameter are obtained for the plate with the following boundary condition combinations: simply supported, clamped and guided edges, under uniform, linear and nonlinear temperature fields via the separation-of-variable method. Furthermore, a new method is proposed to determine the critical buckling temperature from the critical thermal parameter. The present results coincide well with those in the literature, verifying the correctness of the present method. The influences of the length–thickness ratio, length–width ratio, power law index and initial temperature on critical buckling temperature are investigated.

Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading

In this study, natural frequency and dynamic stability of functionally graded (FG) viscoelastic nanobeams based on the Euler–Bernoulli theory on the visco-Pasternak foundation are predicted. The material characteristics of FG nanobeam are temperature-dependent, and vary according to power-law model along thickness. The FG viscoelastic nanobeam is located on a two-dimensional magnetic field which considers the effects of transverse and longitudinal magnetic field. The uniform, linear, and sinusoidal temperature fields are applied on the FG viscoelastic nanobeam. The governing equations are derived through Hamilton’s principle and Eringen’s nonlocal theory. The equations are solved by a Navier-type method and the Bolotin method for simply supported conditions. The effect of three different temperature fields on natural frequency and dynamic stability region of the nanobeam is analyzed. The importance of various parameters such as nonlocal parameter, gradient indexes, magnitude of magnetic field, angle of magnetic field, temperature changes, and aspect ratio on both natural frequency and dynamic stability region of the FG viscoelastic nanobeam is investigated.

Refined theories based on non-polynomial kinematics for the thermoelastic analysis of functionally graded plates

ABSTRACTThis article presents an analytical solution for the thermoelastic analysis of simply supported functionally graded sandwich plates using the Carrera unified formulation, which allows the automatic implementation of various structural theories. The governing equations for plates under thermal loads are obtained using the principal of virtual displacement and solved using the Navier method. Linear and nonlinear temperature fields through the thickness are taken into account. Particular attention is focused on plate theories with nonpolynomial refined kinematics. The results of the present displacement fields are compared with the classical polynomial ones, proposed by Carrera, for several orders of expansion.

Onset of thermal convection and its flow patterns in a rectangular cavity

The onset of thermal convection of a fluid in a rectangular cavity of aspect ratios Ax and Ay exposed to a vertically linear temperature field is examined under the assumption that all its walls are rigid, and of perfect thermal conductance. For several Ax and Ay smaller than 6, the critical Rayleigh number Rc and the steady flow patterns of most unstable modes are computed by a Galerkin spectral method of high accuracy. Characteristics of flow patterns are examined by using upper-wall flow patterns based on near-wall velocity fields, distributions of vertical velocity, and trajectories of fluid particles. We find that a symmetry mode that is not the most unstable when the difference between Ax and Ay is large is the most unstable if both Ax and Ay are around 4 or around 5.5. The flow pattern of this mode is consistent with the results in a preceding experimental study. Rc increases rapidly as Ax or Ay decreases to zero and decreases slowly as they increase. The validity of the assumption of finite roll is found to be limited, even if the difference between Ax and Ay is large. The flow pattern for becomes more complicated, and the number of convection cells increases as A increases. The motion of fluid particles in each cell is roughly the circulation along closed curves around an axis that is on the central horizontal plane but is not necessarily parallel to side walls. Moreover, the motion of fluid particles near side walls can be much different from that in the central part of the cavity.

Method of Lines to Solve the Linear Temperature Field of LENS

This article introduces a semi-analytical numerical method ——method of lines(MOLs) to solve steady temperature field of Laser Engineered Net shaping (LENS). The main idea of MOLs is to semi-discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The steady linear temperature fields of functionally graded materials were obtained using MOLs and the regularities of different temperature functions were also found. The effects of thermal conductivity coefficient under different formal functions on thermal temperature fields were analys. Numerical results showed that different material thermal conductivity function had obvious different effect on the temperature field.

High Rayleigh number convection in a three-dimensional porous medium

AbstractHigh-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers $Ra \leqslant 2 \times 10^4$. Measurements of the Nusselt number $Nu$ in the range $1750 \leqslant Ra \leqslant 2 \times 10^4$ are well fitted by a relationship of the form $Nu = \alpha _3 Ra + \beta _3$, for $\alpha _3 = 9.6 \times 10^{-3}$ and $\beta _3 = 4.6$. This fit indicates that the classical linear scaling $Nu \sim Ra$ is attained, and that $Nu$ is asymptotically approximately $40\, \%$ larger than in two dimensions. The dynamical flow structure in the range $1750 \leqslant Ra \leqslant 2\times 10^4$ is analysed, and the interior of the flow is found to be increasingly well described as $Ra \to \infty $ by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber $k$ and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by $k\sim Ra^{0.52 \pm 0.05}$, which is distinguishably stronger than the two-dimensional scaling of $k\sim Ra^{0.4}$.