Nonlinear Thermal Stress Research Articles

The shape function method of nonlinear thermal stress of granite fracture tips in a high-temperature environment

Exposed rock masses in tunnel portals are susceptible to thermal deterioration in southern China, where temperatures are relatively high. The thermal stress field of rock masses is affected by fracture shape and distribution as fractures near the surface are channels for solar radiation energy to be converted into rock thermal energy. In this study, a function expression is developed for triangular heat sources of fractured rock masses in a tunnel portal in a high-temperature environment. By the function expression, the temperature field and thermal stress field are calculated, and the influence of fracture shape parameters and multi-fracture interaction is analyzed. The results are as follows: (1) the temperature field and thermal stress field of exposed rocks are redistributed by fractures. The internal temperature of the fractured rocks is higher than that of non-fractured rocks, and thermal stress near the fracture tip increases. (2) For triangular fractures of the same length, thermal stress increases as the apex angle increases. (3) When the spacing between parallel fractures or coplanar fractures is close, the superposition effect of thermal stress becomes significant. (4) In a high-temperature environment, temperature field and thermal stress field of a fractured rock are both nonlinear as temperature and thermal stress around fractures increase significantly. The results provide effective reference for stability evaluation of fractured rock masses in tunnel portals and offer theoretical foundation for thermal diseases analysis and protection measures of tunnel engineering in high-temperature environments of southern China.

DYNAMIC ANALYSIS OF THE VISCOELASTIC MICROTWEEZER UNDER ELECTROSTATIC FORCES AND THERMAL FIELDS

This is the first study to examine the nonlinear dynamic behavior of a microtweezer under electrostatic forces by taking into account viscoelastic effects and linear and nonlinear thermal stresses. The van der Waals (vdW) forces and Casimir intermolecular forces have been included in order to consider more realistic assumptions. Hamilton's principle is applied to derive the nonlinear equations governing the system. A nonlinear partial differential equation has been converted into an ordinary nonlinear differential equation using the Galerkin method. The equations are numerically solved and the results are analyzed at different values of the effective parameters, such as the coefficients of the Casimir force and the vdW forces. Results indicate that the increase in the small size parameter and Casimir and vdW forces results in a decrease in the equivalent stiffness and, therefore, a decrease in the pole's voltage. In addition, the viscoelastic behavior causes a significant change in the stability behavior of the microbeams, and with an increase in damping, the resonance frequency increases by about 33%. Therefore, it is essential to take into account the effect of viscous damping when designing a microtweezer.

A Computational Study of Solid Si Target Dynamics under ns Pulsed Laser Irradiation from Elastic to Melting Regime

The dynamic behavior of solid Si targets irradiated by nanosecond laser pulses is computationally studied with transient, thermοmechanical three-dimensional finite element method simulations. The dynamic phase changes of the target and the generation and propagation of surface acoustic waves around the laser focal spot are provided by a finite element model of a very fine uniformly structured mesh, able to provide high-resolution results in short and long spatiotemporal scales. The dynamic changes in the Si material properties until the melting regime are considered, and the simulation results provide a detailed description of the irradiated area response, accompanied by the dynamics of the generation and propagation of ultrasonic waves. The new findings indicate that, due to the low thermal expansion coefficient and the high penetration depth of Si, the amplitude of the generated SAW is small, and the time and distance needed for the ultrasound to be generated is higher compared to dense metals. Additionally, in the melting regime, the development of high nonlinear thermal stresses leads to the generation and formation of an irregular ultrasound. Understanding the interaction between nanosecond lasers and Si is pivotal for advancing a wide range of technologies related to material processing and characterization.

A Nonlinear Fractional BEM Model for Magneto-Thermo-Visco-Elastic Ultrasound Waves in Temperature-Dependent FGA Rotating Granular Plates

The primary goal of this study is to create a nonlinear fractional boundary element method (BEM) model for magneto-thermo-visco-elastic ultrasound wave problems in temperature-dependent functionally graded anisotropic (FGA) rotating granular plates in a constant primary magnetic field. Classical analytical methods are frequently insufficient to solve the governing equation system of such problems due to nonlinearity, fractional order heat conduction, and strong anisotropy of mechanical properties. To address this challenge, a BEM-based coupling scheme that is both reliable and efficient was proposed, with the Cartesian transformation method (CTM) used to compute domain integrals and the generalized modified shift-splitting (GMSS) method was used to solve the BEM-derived linear systems. The calculation results are graphed to show the effects of temperature dependence, anisotropy, graded parameter, and fractional parameter on nonlinear thermal stress in the investigated plates. The numerical results validate the consistency and effectiveness of the developed modeling methodology.

On the Rarefied Thermally-Driven Flows in Cavities and Bends

This study examined rarefied thermally-driven flow in a square cavity (Case 1) and rectangular bend (Case 2), with various uniform wall temperatures in two dimensions. We employed the direct simulation Monte Carlo (DSMC) to solve problems with a wide range of Knudsen numbers Kn = 0.01 to 10, and the discrete unified gas kinetic scheme (DUGKS) solver was used at Kn = 0.01. The scenario was that, in case 1, the bottom side and its opposite were set hot, and the other sides were set cold. Diffuse reflector boundary conditions were set for all walls. The imposed temperature differences created four primary vortices. The results of the continuum set of equations of the slow non-isothermal flow (SNIT) solver proved that the primary vortices in the square cavity were caused by nonlinear thermal stress effects, and other smaller vortices appearing at Kn = 0.01, 0.1 were brought about by thermal creep processes. As the Kn increased, vortices generated by thermal creep disappeared, and eddies created by nonlinear thermal stress occupied the cavity. In case 2, i.e., a rectangular bend, two sides were set cold, and the others were hot. Two primary vortices were formed, which were caused by nonlinear thermal stress effects. The direction of streamlines in the two main vortices was opposite, from the warm to the cold zone, as some eddies on the left were counterclockwise, and others were clockwise.

Nonlinear thermal stress analysis of functionally graded spherical pressure vessels

In this study, nonlinear analysis of functionally graded spherical pressure vessels composed of metal/ceramic mixture for both high strength and high thermal resistance is discussed. The originality of this study is to think that all material properties change with temperature as well as thickness by using a realistic and physically meaningful graded material model with the Halpin–Tsai homogenization scheme. These conditions results in nonlinear differential equation that may not be solved with conventional methods. The nonlinear temperature and stress distributions of the functionally graded sphere under the thermo-mechanical loads are determined by using the pseudospectral Chebyshev method. Some stress results based on the assumptions of temperature-dependencies and temperature-independencies of the material properties are derived and effects of various parameters on the thermoelasticity are studied. Besides, elastic limits based on the von Mises’ yield criterion are also discussed according to whether the material properties are dependent on temperature or not. Benchmark linear examples are used to check the accuracy of the method. The nonlinear solutions are verified with the finite element method using the ANSYS package program.

On the nonlinear thermal stress, thermal creep, and thermal edge flows in triangular cavities

Here, rarefied thermally driven flow is investigated in two-dimensional equilateral triangular cavities with different uniform wall temperatures. We used three different solvers, i.e., the direct simulation Monte Carlo solver, discrete unified gas kinetic scheme solver, and continuum set of equations of a slow non-isothermal flow solver. Two main cases were considered; in the first case, the cavity's base is considered hot, and the other sides were set cold. In the second case, the right half of the bottom wall was regarded as a diffuse reflector with high temperature, while the left half of the bottom border was set as a specular reflector. The adjacent side walls were set cold with diffuse reflector boundary conditions. The imposed temperature difference/wall boundary condition induces various vortices in the geometry. In case 1, we observe that principal vortices appearing in the triangle are due to nonlinear thermal stress effects, and the thermal creep effects cause other smaller, confined ones. In case 2, a thermal edge flow is set up from the specular wall on the way to the diffusive hot wall, creating a large vortex in the geometry. As the Knudsen number decreases, another small vortex appears near the left cold border.

Boundary element modeling of fractional nonlinear generalized photothermal stress wave propagation problems in FG anisotropic smart semiconductors

The main aim of this article is to develop an efficient boundary element method (BEM) modeling of the fractional nonlinear generalized photo thermal stress wave propagation problems in the context of functionally graded (FG) anisotropic smart semiconductors. Due to nonlinearity, fractional order heat conduction and strongly anisotropy of mechanical properties, the governing equations system of such problems is often very difficult to solve using classical analytical methods. Therefore, a reliable and efficient coupling scheme based on BEM was proposed to address this challenge, where, the Cartesian transformation method (CTM) has been implemented to calculate the domain integrals, and the generalized modified shift-splitting (GMSS) has been implemented for solving the linear systems arising from BEM. The calculation findings are depicted in graphical forms to display the impacts of temperature-dependent, anisotropy, piezoelectric, graded parameter and fractional parameter on the nonlinear photo thermal stress wave propagation in the considered structure. The numerical findings confirm the consistency and efficacy of the developed modeling methodology.

A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties

The main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

Bolt Load Calculation for Hybrid Joint Considering Friction and Nonlinear Stiffness under Combined Thermal and Mechanical Loads

An improved analytical method for calculating the bolt load distribution in single-lap or double-lap multi-bolt composite-metal joint structure considering material nonlinear behaviour and thermal stress is proposed in this paper. The analytical method is based on the stiffness method and the composite material mechanics. The bolt load ratios calculation results of a three-bolt joint structures by the improved method is compared with the results from finite element (FE) method and the relative error less than 7%. The great agreement verifies the accuracy of the analytical method. Besides, this improved has more considering factors and higher accuracy than traditional stiffness method and less calculating cost than FE method.

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

Nonlinear Thermal Stress Analysis of Functionally Graded Thick Cylinders and Spheres

Nonlinear thermal stress analysis in a functionally graded hollow thick cylinders and spheres under the effect of high temperatures and temperature differences is considered by taking into account the material properties of the body both temperature dependent and radially graded, except Poisson’s ratio which is taken to be constant for simplicity. These conditions result in nonlinear governing differential equation that is adopted to solve numerically. The effect of the temperature-dependent material properties on the temperature distribution, radial displacement, and thermal stresses is presented in a graphical form. The importance of the effect of temperature on the material is shown in functionally graded materials manufactured to be exposed to high temperature and temperature difference. Benchmark solutions available in the literature are used to validate the results and to emphasize the convergence of the numerical solutions.

Numerical analysis of nonlinear thermal stress flow between concentric elliptical cylinders

The present study numerically investigates nonlinear thermal stress in a rarefied gas flow between two coaxial elliptic cylinders with a hot outer wall. Monatomic argon is considered, and isothermal boundary conditions are implemented on the walls. Three different numerical methods are used to solve this problem, i.e., first, the direct simulation Monte Carlo (DSMC) method is used and validated against the numerical solution of the Boltzmann equation available in the literature. The results of the DSMC algorithm are compared with the results of the discrete unified gas kinetic scheme and the continuum set of equations of slow non-isothermal flows, which includes nonlinear thermal stress terms compared to the Navier–Stokes equations. For the first time, the flow is examined in a wide range of Knudsen numbers in the slip regime from the Knudsen number (Kn) of Kn = 0.005 to Kn = 0.1. At a minimal Knudsen number, there is just one vortex due to the nonlinear thermal stress flow; however, as Kn increases, the velocity peak near the inner cylinder is replaced with another vortex, which is created due to the second-order thermal creep effects on the inner wall of the cylinder. We show that as Kn increases, the inner vortex increases in size, while the outer vortex shrinks. The mechanisms of the formation of both vortices are described in detail. Other flow characteristics, including walls’ velocity slip, shear stress, and vorticity, are discussed.

Parameters Effect on Predicting Fire Resistance of Ultra-high Strength Concrete Filled Protected Square Steel Tubular Columns

Ultra-high strength concrete (UHSC) with compressive strength greater than 100 MPa at room temperature has been developed for concrete filled square steel tubular column for use in high-rise buildings. The fire resistance of UHSC filled protected square steel tubular columns exposed to the standard ISO fire is investigated in this paper. For this purpose, numerical heat transfer analysis and nonlinear thermal stress analysis were conducted by taking into account the existing material properties, such as the thermal and mechanical properties of UHSC and high strength steel. The numerical analyses were carried out and the results were validated against the test results in terms of heat distribution and mechanical behavior. Comparison with the test results showed a reasonable agreement with finite element results in terms of temperature field prediction and load displacement behavior during the fire. Finally, based on the validated finite element model, the effects of fire protection thickness, load ratio, the strengths of concrete and steel, steel contribution ratio, and relative slenderness ratio on the fire resistance of UHSC filled square steel tubular columns were carried out and discussed.

Integration of Dielectric and Ferroelectric Hafnium Aluminum Oxides for Thin‐Film Transistor Applications

Herein, the integration of dielectric and ferroelectric HfAlOx within a one‐transistor and one‐capacitor thin‐film transistor (TFT)‐based device structure is successfully demonstrated. It is found that the origin of gate stress for enhancing ferroelectricity is mainly ascribed to nonlinear thermal stress distribution, and the ferroelectricity of HfAlOx is further improved by nitrogen plasma treatment without sacrificing leakage current during post metal annealing. Notably, the p‐type SnO TFT in series with a ferroelectric HfAlOx capacitor with nitrogen plasma treatment achieves an almost 43% improvement on threshold voltage shift (5.45 V) at a low operating voltage of 3 V. Therefore, the ferroelectric nitridation treatment not only strengthens the ferroelectric domain switching of HfAlOx but also improves capacitance matching with the HfAlOx dielectric layer of p‐type SnO TFT.

Hygro-Magnetic Vibration of the Single-Walled Carbon Nanotube with Nonlinear Temperature Distribution Based on a Modified Beam Theory and Nonlocal Strain Gradient Model

In this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or longitudinal magnetic field which is also exposed to both the hygroscopic as well as thermal environments. The thermal environment is considered as nonlinear thermal stress field based on the Murnaghan’s model whereas the hygroscopic environment is assumed as a linear stress field. The size effect of the SWCNT has been captured by both the nonlocal and gradient parameters by employing the Nonlocal Strain Gradient Theory (NSGT). Governing equation of motion of the proposed model has been developed by utilizing the extended Hamilton’s principle and the non-dimensional frequency parameters have been computed by incorporating the Navier’s approach for Hinged–Hinged (HH) boundary condition. The proposed model is validated with the existing model in special cases, by comparing the non-dimensional frequency parameters, displaying an excellent agreement. Further, a parametric study has been conducted to analyze the impact of nonlocal parameter, gradient parameter, thermal environment, hygroscopic environment, and magnetic field intensity on the non-dimensional frequency parameters. Also, results for some other theories like Classical Elasticity Theory (CET), Nonlocal Elasticity Theory (NET), and Strain Gradient Theory (SGT) have been presented along with the NSGT.

Nonlinear temperature and thermal stress analysis of annular fins with time dependent boundary condition

PurposeThe purpose of this paper is to propose the Laplace Adomian Decomposition Method (LADM) for studying the nonlinear temperature and thermal stress analysis of annular fins with time-dependent boundary condition.Design/methodology/approachThe nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root is studied by the LADM. The radiation effect is considered. The convective heat transfer coefficient is considered as a temperature function.FindingsThe proposed solution method is helpful in overcoming the computational bottleneck commonly encountered in industry and in academia. The results show that the circumferential stress at the root of the fin will be important in the fatigue analysis.Originality/valueThis study presents an effective solution method to analyze the nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root by using LADM.

Slow nonisothermal flows: Numerical and asymptotic analysis of the Boltzmann equation

Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in the momentum equation. Appropriate boundary conditions are determined from the asymptotic analysis of the Knudsen layer on the basis of the Boltzmann equation. Boundary conditions up to the second order of the Knudsen number are studied. Some two-dimensional examples are examined for their comparative analysis. The fluid-dynamic results are supported by numerical solution of the Boltzmann equation obtained by the Tcheremissine's projection-interpolation discrete-velocity method extended for nonuniform grids. The competition pattern between the first- and the second-order nonlinear thermal-stress flows has been obtained for the first time.

Thermo-elastic response of SUS316-Al2O3 functionally graded beams under various heat loads

Geometric nonlinearity and temperature dependent material properties are accounted for in the theoretical analysis of time dependent thermo-elastic response of thin functionally graded material (FGM) SUS316-Al2O3 beam subjected to various heat loads. A two dimensional Lagrangian rectangular finite element is used to obtain the temperature distribution on the transverse plane of the beam. Nonlinear thermo-elastic deflection and thermal stresses are evaluated for various structural and thermal boundary conditions. Thermo-elastic oscillations are observed in case of beams subjected to step, concentrated line and shock heat load whereas thermo-elastic deflection is observed for beams subjected to moving heat load. As the thermal load increases, the nonlinear thermal deflection of FGM beam are higher compared to linear analysis. In general, temperature dependency of material properties influence the amplitude of thermal oscillations. High thermal stresses are induced in beams with pin-pin and clamp-pin boundary condition as compared to hinge-hinge beam.

Proposal of the Penalty Factor Equations Considering Weld Strength Over-Match

Abstract This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the K e analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, S n to over-match degree of yield strength, M F . For the effect of over-match on K n × Κ ν , dispersion of the K n × Κ ν analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, S p-lt by M F . Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous K e factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous K e factor equations.