Thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion

On the basis of the complex variable method for determining the stationary two-dimensional thermal stresses, the thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion under a steady state temperature field is considered. The solution is found by the analytic continuation argument and the modified mapping-collocation technique. Numerical results indicate a dependence of the orthotropic stress intensity factors on the thermal, elastic and geometrical constants over a certain parameter range     

Thermal stress singularities at tips of a Griffith crack in a finite rectangular plate

This paper is concerned with a method for calculating the thermal stresses in a finite rectangular plate with a Griffith crack under a steady state temperature field. In the analysis, based on the complex variable method for determining the stationary two-dimensional thermal stresses, the analytic continuation and the modified mapping-collocation methods are effectively employed. Numerical calculations for the strength of thermal stress singularity of the symmetric and the skew-symmetric types are carried out, and the results are shown in graphs.     

Non-linear elastic thermal stress analysis with phase changes

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading.     

Thermal analysis of plates with circular inclusions

A least square boundary point matching method is employed to determine the temperature distributions and deformations of rectangular plates with circular elastic inclusions. Solutions for two problems have been obtained. The first problem is concerned with the determination of the temperature distribution in a finite rectangular plate having a circular inclusion and subjected to prescribed temperature distribution and thermal conditions along the edges. The plate is heated uniformly through the thickness. The second problem is concerned with the deflection and moment distribution in the same plate model with simply supported edges and prescribed temperature variation across the thickness but no temperature variation over the plate surface. Numerical results are presented.     

The influence of transient thermal loading on the Bree plate; A simplified method of analysis

The paper describes a simplified technique, based upon an extension of the upper bound shakedown theorem, for the evaluation of ratchet boundaries for a plate subject to a through-thickness temperature transient and in-plane loading. The study of a range of cases indicates that transient effects can have a significant effect upon the deformation properties and that strain growth can occur for zero applied loads at quite moderate levels of thermal loading. As a result the identification of transient thermal stresses as F stresses in ASME design codes does not seem acceptable.     

Thermal stresses in rectangular plates: Variational and finite element solutions

This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach.     

Creep analysis of rotating orthotropic disks

The present paper is devoted to a study of creep deformation and stress distribution in rotating disks of orthotropic materials. Assuming the creep rate to be a function of stress multiplied by a function of time (time-hardening law), expressions for stresses and creep-rates in radial and tangential directions, have been obtained. The basic equations obtained have been solved using a method of successive approximations. A numerical example has been worked out. The effect of transient (non-steady) creep and orthotropicity of the material on stress and strain distributions in the disk has been discussed and depicted graphically.     

Transient thermal stresses and displacements in a transversely isotropic semi-infinite circular cylinder subjected to an arbitrary surface heat generation and a convective heat loss

The transient thermal stresses and displacements in a traction-free, transversely isotropic, semi-infinite circular cylinder subjected to a convective heat loss on the end surface is analyzed by means of a set of stress functions and a generalized Fourier-integral representation for exponential function.The purpose of this paper is to present the results of theoretical analysis which considers the effects of the thermal and elastic anisotropes of the material properties on the thermal stresses and displacements in the transversely isotropic, semi-infinite circular cylinder due to an arbitrary cylindrical surface heat generation.A detailed numerical result of the thermal stresses and displacements is given for various values of the ratios of the thermal conductivity coefficients, Young's moduli and linear thermal expansion coefficients in the axial and radial directions and it is demonstrated that the sensivity of the maximum stress and displacement to the anisotropy of the thermal conductivity coefficient is significant.     

Free vibration of orthotropic super-elliptical plates on intermediate supports

Free vibration analysis of rectilinearly orthotropic super-elliptical plates of uniform thickness was investigated by the Ritz method. Various plate shapes ranging from an ellipse to a rectangle with rounded corners were considered for three types of support configurations: (1) completely free plate, (2) point-supported plate, and (3) plate supported along multiple concentric circular ring supports. The results were compared with those of elliptical and rectangular plates where possible and good agreement was obtained.     

Transient thermal stress intensity factors for Mode I edge-cracks

Stress intensity factors are analytically derived for an edge-cracked circular disk subjected to transient thermal stresses using symplectic technique. The transient temperature function for the time independent boundary conditions is obtained by a generalized symplectic approach and the method of separation of variables. From the obtained temperature function, quasi-static solutions of the thermoelasticity problem are derived analytically. The stress intensity factors together with the close form solutions for both displacements and stresses are found simultaneously. The results obtained are in good accordance with those cited in the literature for some special cases of steady state problem. In addition, a parametric study is performed in the numerical examples.     

Thermal stress problems in tokamak surfaces

The density of power deposited on some surfaces of a tokamak can easily reach the level where the surface may be destroyed by thermal stress. This report is an examination of the thermal stress problem under tokamak conditions. The magnitude of the maximum power density is given for some existing and future devices. As examples which furnish a guide to power absorption limits for surfaces in high-power plasma devices, we have made estimates of thermal stress in a thick wall subjected to transient heating On one side. Also, detailed results are given for a flat plate heated on one face and cooled on the other. Comparative power density limits are tabulated for various materials of interest for plasma device construction.     

对流换热条件下换热器管板的应力分析

给出对流换热条件下换热器管板中应力场的有限元分析方法。分析中将管板布管区折算为受管孔削弱并被管束支承的横观各向同性均质等效板；在计算位移场时采用具有附加内部自由度的ｗｉｌｓｏｎ非协调元，以保证计算应力的精度与温度场精度相匹配。计算结果得到了试验验证。典型算例说明过厚的管板将引起过大的温度应力。对于核工业中各种以温度载荷为主的换热器，应注意合理选择管板厚度。     

Calculation of thermoplastic stresses of a reactor pressure vessel with cladding from stress-relief annealing up to a thermal shock

The distribution of stresses in the cylindrical section of a reactor pressure vessel is evaluated for transient temperature and pressure loads. The calculation takes particularly into account the thermoplastic stresses of the cladding and the transition zone to the base material.The considered load history comprises stress-relief annealing, pressure test, start-up and shut-down of the reactor, followed by start-up, pressure drop with subsequent thermal shock.The stresses and strains are determined by the Prandtl-Reuss equations and the v. Mises flow condition depending on temperature. Creep effects are additionally included for stress-relief annealing.The problem is approximated by a second order time step method and the resulting changes in stress and strain are calculated using a shooting method. The results of the elastoplastic calculation for thermal shock differ from the linear calculation particularly in the cladding layer and its immediate vicinity.     

The use of analytic continuation in solutions of plane thermal stresses in an orthotropic elastic medium

This paper describes a general method for plane thermoelasticity in an orthotropic elastic medium of doubly-connected shape. The analysis is based upon the complex variable method and the analytic continuation is effectively employed. Numerical calculations are carried out for orthotropic rectangular plates with an elliptical hole subjected to heat flow and results illustrating the influence of geometry and orthotropy of the plates are obtained.     

Thermal stresses around an elliptic hole in an infinite thick plate subjected to a uniform heat flow

A theoretical three-dimensional analysis is presented for determining the state of thermal stresses around an insulated elliptic hole in an infinitely long thick plate subjected to a uniform heat flow. The maximum stress is found to depend on the ratio of thickness to length of the semi-major axis of the hole and also on Poisson's ratio. In the limiting cases, the solution reduces to the corresponding circular hole solution obtained by Lee, and also to the two-dimensional solution of the elliptic hole problem as given by Florence and Goodier.     

Three-dimensional transient thermal stresses of reactor graphite subjected to internal heat generation and asymmetric surface heating

The present paper is concerned with three-dimensional transient thermal stresses of graphite in a nuclear reactor. In analyzing this problem, reactor graphite may be approximated by a transversely isotropic finite circular cylinder subjected to internal heat generation and asymmetric heating on an end surface. Thermal stresses are analyzed by means of the transversely isotropic potential functions method proposed by Takeuti and Noda. Numerical calculations were carried out for a special type of heating conditions, and time variations of temperature and thermal stresses of graphite are shown in figures.     

Structural considerations for a Tokamak fusion reactor

Several preliminary structural analyses are presented which validate a design for the experimental power reactor. Three components are singled out as requiring special attention: the magnetic coils, the blanket support structure, and the blanket modules. Repeated loading of a coil structure by magnetic forces should produce only linear elastic deformation. An analysis for minimum preload necessary to ensure this is presented. Using axisymmetric thin shell theory, a stress analysis of the blanket support structure is described. To account for the welded ring structure, a perforated plate analysis is used to compute the structural displacements and the ligament stresses. Temperature distributions and thermal stresses in the blanket module are determined using both finite element and analytical analysis. The stresses are all acceptable, including the effects produced by creep and fatigue. Thermal stress in the liner produced by a nonlinear temperature gradient is also shown to be acceptable.     

Thermal and gravity stresses in hyperboloidal cooling towers

Nuclear power plants usually require particularly large cooling towers, the design of which necessitates detailed analyses of the structural behavior under thermal and mechanical loadings.Thermal stresses are obtained in this paper for a reinforced hyperboloidal cooling tower for a wide range of foundation constants. The temperature field in the tower is assumed to be asymmetric with a linear variation through the thickness of the tower and an arbitrary variation along the height. The effects of the weight of the tower are included. The reinforcing material is assumed to have an equivalent orthotropic distribution along meridional and circumferential coordinate lines, and it is taken to be symmetrically located relative to the middle surface of the tower. The partial differential equations of equilibrium of the tower are based upon thin elastic shell theory and utilize the Love-Kirchhoff approximation. Fourier expansions in the circumferential variable are used to reduce these equations to ordinary differential equations in the meridional variable. Numerical solutions to the ordinary differential equations are obtained by the finite element subdomain collocation method.Numerical results are presented for thermal stresses in the Beaver Valley Station cooling tower for assumed temperature distributions on the inner and outer tower surfaces. The results show that the difference in temperature distributions on the inner and outer tower surfaces gives rise to significant thermal stresses in the tower. An example of a hot spot on a cylindrical shell is also presented. The analysis is particularly applicable to reinforced concrete cooling towers with hot spots.     

基于运行数据的船用堆波动管热分层现象研究

基于运行数据将船用堆波动管热分层划分为升功率、降功率、变工况、小喷淋流量4类典型瞬态,对4类典型瞬态分别进行无量纲里查德森数（Ri）分析、瞬态工况数值模拟计算,得到波动管在4类典型瞬态下水平管段的热分层区间长度、持续时间和最大温差。结果表明,升功率和降功率瞬态热分层仅单次贯穿波动管,升功率瞬态的接头部位循环的热波动以及小喷淋流量瞬态水平段的长区间、长时间、大温差的热分层现象和变工况导致的热应力波动可能影响到波动管的安全。本文提出的基于运行数据的波动管热分层现象研究方法为后续热应力和热疲劳分析奠定了基础,同时可以为其他容积设备热分层研究提供参考。      

Thermal fatigue damage in monofilament reinforced copper for heat sink applications in divertor elements

In fusion reactor systems extreme conditions require materials with high temperature and radiation resistance. The divertor component consists of a plasma facing W plate attached to a Cu heat sink to extract the heat from the nuclear reaction chamber coolant. The Coefficient of Thermal Expansion (CTE) mismatch between the W plate and the Cu heat sink causes interface delamination reducing the long term stability of the divertor.To avert this problem, composites are developed as interlayer materials with a high thermal conducting Cu matrix reinforced with up to 50 vol.% SiC or W monofilaments to increase the mechanical strength and to reduce the CTE mismatch. Thermal stresses are transferred from the macroscopic interface between the components into the bulk of the composite. Oscillating micro stresses may lead to fiber delamination and matrix damage during thermal cycling. Different matrix alloys, fiber materials and interface designs are investigated.In situ neutron diffraction performed during thermal cycling show the effect of bonding strength on the stress amplitudes expected under service conditions. The long term stability is tested by measurements after further ex situ cycling. Thermal fatigue damage and its propagation are visualized by in situ as well as ex situ high resolution synchrotron tomography. The combination of both methods helps to understand the strain induced damage mechanisms. Weak bonding leads to delamination of the fiber-matrix interfaces. Strong bonding causes severe matrix deformation and damage. Fiber cracks originating from sample production cause accumulating thermal fatigue damage during thermal cycling.