Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi ₁, Biot number for convection on the outside surface Bi ₂, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.     

柴油机缸内壁面边界层的数值模拟

利用二维边界层微分方程数值模拟了缸内壁面速度和热边界层,获得了不同工况下的速度和热边界层厚度,将二维边界层微分方程的数值计算结果和在TY1100柴油机上的测量结果进行了对比分析,结果表明,二者的变化趋势是一致的,建立的数值模拟模型可以较好地预测缸内壁面速度和热边界层的变化规律．     

Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed.     

MHD Flow and Heat Transfer of a Dusty Fluid Over a Stretching Hollow Cylinder with a Convective Boundary Condition

In this study, we deal with the problem of a steady two‐dimensional magnetohydrodynamic (MHD) flow of a dusty fluid over a stretching hollow cylinder. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary condition. The multi‐step differential transform method (multi‐step DTM), one of the most effective methods, is employed to find an approximate solution of the system of highly nonlinear differential equations governing the problem. Comparisons are made between the results of the proposed method and the numerical method in solving this problem and excellent agreement has been observed. The influence of important parameters on the flow field and heat transfer characteristics are presented and discussed in detail. The results show that both the thermal boundary layer thickness and the heat transfer rate at the wall increases with increasing Biot number Bi, while it has no effect on the skin friction coefficient. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 221–232, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21073     

Thermal Bending Analysis of Doubly Curved Composite Laminated Shell Panels with General Boundary Conditions and Laminations

Thermal bending analysis of doubly curved laminated shell panels with general boundary conditions and laminations is presented. The equations of equilibrium are derived in the form of two coupled sets of ordinary differential equations based on a general shell theory and solved through the state-space approach in a repeated manner. It is depicted that the results of the present method are in great agreement with analytical solutions. Cylindrical shell panels with general boundary conditions and laminations, where no analytical solution is available, are solved. It is found that the present method exhibits a high convergence rate as well as presenting accurate results in all cases.     

Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium

Applying the eigenvalue approach method along with Laplace transform, a general solution scheme for the thermoelastic deformation of an unbounded transversely isotropic medium has been developed on fractional order generalized thermoelasticity with an instantaneous heat source. Solution has been achieved in Laplace transform domain for the perturbed temperature field and other field variables. Several graphs have been presented, and analyses of the results have been made.     

Exact Solution for Thermal Buckling of Functionally Graded Plates Resting on Elastic Foundations with Various Boundary Conditions

In this article, we investigate the buckling analysis of plates that are made of functionally graded materials (FGMs) resting on two-parameter Pasternak's foundations under thermal loads. Three different thermal loads were considered, i.e., uniform temperature rise (UTR), linear and non-linear temperature distributions (LTD and NTD) through the thickness. The mechanical and thermal properties of functionally graded material (FGM) vary continuously along the plate thickness according to a simple power law distribution. Employing an analytical approach, the five coupled governing stability equations, which are derived based on first-order shear deformation plate theory, are converted into two uncoupled partial differential equations (PDEs). Considering the Levy-type solution, these two PDEs are reduced to two ordinary differential equations (ODEs) with variable coefficients. Then, the ODEs are solved using an exact analytical solution, which is called the power series Frobenius method. The appropriate convergence study and comparison with previously published related articles was employed to verify the accuracy of the proposed method. After such verifications, the effects of parameters such as the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the critical buckling temperature difference are illustrated and explained. The critical buckling temperatures of functionally graded rectangular plates with six various boundary conditions are reported for the first time and can serve as benchmark results for researchers to validate their numerical and analytical methods in the future.     

Transient Thermal Stress Problem of a Functionally Graded Magneto-Electro-Thermoelastic Hollow Cylinder Due to a Uniform Surface Heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic hollow cylinder due to uniform surface heating. We analyze the transient thermal stress problem for a functionally graded hollow cylinder constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite model as one of theoretical approximation under a plane strain state. As an illustration, we carry out numerical calculations for a functionally graded hollow cylinder constructed of piezoelectric and magnetostrictive materials and examined the behaviors in the transient state. We investigate the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential, and the effect of the applied electric potential on the thermal stress σ_θθ.     

A new numerical method to simulate the non-Fourier heat conduction in a single-phase medium

Many non-equilibrium heat conduction processes can be described by the macroscopic dual-phase lag model (DPL model). In this paper, a numerical method, which combines the dual reciprocity boundary element method (DRBEM) with Laplace transforms, is constructed to solve such mathematical equation. It is used to simulate the non-Fourier phenomenon of heat conduction in a single-phase medium, then numerically predict the differences between the thermal diffusion, the thermal wave and the non-Fourier heat conduction under different boundary conditions including pulse for one- and two-dimensional problems. In order to check this numerical method's reliability, the numerical solutions are still compared with two known analytical solutions.     

基于随机边界元法的连杆可靠性分析

在确定性边界元数值方法的基础上,通过采用非统计逼近的处理方法建立了基于一阶二次矩法的二维弹性随机边界元数值方法的基本方程和可靠度分析公式,进一步运用开发的相应软件分析了内燃机连杆小头的应力数字特征量,并与采用蒙特卡洛随机模拟方法对连杆小头得到的随机应力数字特征量进行了比较,验证了本提出的方法的可靠性。在此基础上,对连杆小头疲劳强度可靠度进行了计算,结果表明本提出的方法不仅用于复杂结构的可靠度进     

Heat Conduction Analytical Solutions to be Applied in Boundary Conditions Obtained from Discrete Data

Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.     

渗流自由面计算的边界元法

用边界元法求解渗流自由面需预先设定自由面的初始位置.先对自由面初始位置进行优化,以便得到合理的计算网格,再按常规方法迭代求解.计算结果表明,与有限元法相比计算精度较高,具有更好的收敛性与更高的计算效率.     

A closed-form solution of DPL bioheat transfer problem with time-periodic boundary conditions

A closed-form (long-time) solution of one-dimensional dual-phase lag bioheat transfer problem with consistent time-periodic boundary conditions (BCs) is presented in this paper for planar, cylindrical, and spherical skin tissue for a newly developed solution methodology. The steady-periodic solution is composed of a steady-state part and an oscillating part; corresponding to the constant and oscillating parts of BCs, respectively. Using the superposition principle, these two parts are split into two problems, which are solved separately. The steady-state part is fairly straightforward to obtain, while for the oscillating part, an alternate Laplace transform (LT) approach is proposed in this work. It is demonstrated that for sinusoidal BCs, a closed-form solution in the time domain can be obtained by evaluating an approximate convolution integral, which emulates the effect of the inverse LT. The obtained closed-form solution is free of any series summation or numerical inversion, thereby, making it computationally very efficient compared with conventional LT and eigenfunctions-based approaches. The current methodology is verified with the established eigenfunctions expansion-based methodology. It can be seen that the long-time solutions obtained by these two approaches are almost identical. The verified methodology is further extended for the time-periodic nonsinusoidal BCs. The ease of implementation and simplicity of the new methodology for both sinusoidal and nonsinusoidal BCs is demonstrated using a few test cases. It is evident from the results that the developed methodology leads to an efficient and accurate solution.     

Analytical study of heat and mass transfer effects on unsteady Casson fluid flow over an oscillating plate with thermal and solutal boundary conditions

In this study, the impacts of heat and mass transfer characteristics on an isotropic incompressible Casson fluid flow over an oscillatory plate with the incidences of solutal and thermal boundary conditions have been investigated. Exact solutions of the fundamental equations governing the fluid flow are determined by using the Laplace transform technique. Numerical results based on analytical solutions are presented in graphical and tabular illustrations to clarify the behaviors of the fluid. Most interestingly, both fluid velocity and species concentration increase with an increment of mass transfer coefficient, whereas the fluid velocity diminishes as oscillating frequency increases near the surface of the plate. This happens due to the presence of high fluctuation of the plate in the flow system. Finally, this investigation is helpful to the scientific community, and the obtained results can be used as benchmark solutions for solving nonlinear flow governing problems fully via various numerical methods.     

光弹性法在弹性联轴器挠性杆上的应用研究

应用光弹性方法,通过模型的应力分析,经过模型与原型的转换关系,将模型分析得到的结果还原到原型中,最终得到了高弹性联轴器挠性杆在轴向拉伸时内部的应力分布。     

Compliance Based Assessment of Stress Intensity Factor in Cracked Plates with Finite Boundary Restraint: Application to Thermal Shock Part II

A Compliance Adjusted Weight Function (CAWF) approach has been recently developed to enable the estimation of stress intensity factor in thermal shocked cracked plates with finite boundary restraint. In this article the CAWF approach is used to analyse three case studies that collectively encompass the plate configurations, crack configurations and load configurations with which the CAWF is currently formulated. The results of these analyses highlight that the CAWF approach is suitable for estimates within 5–10% of benchmark fracture mechanics finite element values for a wide range of targeted cracked plate configurations and boundary restraint. An exception occurs for the semi-elliptical surface cracked plates where a free boundary effect can be observed at a free or near free boundary restraint condition.     

An Exact Solution for the Thermoelastic Deformations of Cross-Ply Laminated Arches with Arbitrary Boundary Conditions

Thermal deformations in symmetric and antisymmetric cross-ply laminated arches are investigated. The state-space approach has been used to generate exact solutions for the thermoelastic response of cross-ply arches for arbitrary boundary conditions and subjected to general temperature field. A rigorous first-order arch theory is used in the analysis. Deflections are computed for arches with various lamination schemes and boundary conditions undergoing uniform and linearly varying temperature through the thickness. The effect of shallowness of the arch on the maximum deflection is studied.     

Nonlocal Flugge Shell Model for Thermal Buckling of Multi-Walled Carbon Nanotubes with Layerwise Boundary Conditions

Presented herein is the thermal buckling analysis of multi-walled carbon nanotubes on the basis of nonlocal Flugge shell model capturing small scale effects. Based upon the continuum mechanics, a multiple-shell model is adopted in which the nested tubes are coupled with each other through the van der Waals interlayer interaction. The utilized van der Waals model incorporating the interlayer interactions between any two layers, whether adjacent or non-adjacent is curvature dependent. To analytically solve the problem, the Rayleigh–Ritz method was implemented to the variational form equivalent to the Flugge type equations. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. It is shown that the shell-like thermal buckling is significantly sensitive to the nonlocal parameter variation, whereas the column-like thermal buckling remains unaffected when the nonlocal parameter is varied.     

声边界无法在内燃机机体辐射噪声预报中的应用研究

本文结合振动有限元法和声边界元法建立了内燃机机体辐射噪声预报模型，开发了相应的通用计算程序。复式声强测量结果表明该计算程序有较高的计算精度。是低噪声内燃机设计的基础。