Thermoelastic Stress Analysis of Structures Under Natural Vibrations

The paper focuses on stress analyses of structures subjected to excitation forces operating at resonant frequencies. The structures are analysed experimentally using the Thermoelastic Stress Analysis (TSA) technique. Experiments are carried out for fixed-free beams of different dimensions and materials, and also for a steel rectangular plate with clamped edges. These structures are excited by a shaker via a stinger. For materials with low thermal conductivity, the agreement between the theory, numerical results and experimental results is excellent. As the thermal conductivity of the material is increased, the correspondence is not as close. This is because of non-adiabatic behaviour. The implications of these results are discussed in detail in the paper and a means of deriving the severity of heat transfer is provided. Other factors that influence the TSA results from structures under natural loading are also discussed.     

Thermoelastic Stress and Damage Analysis Using Transient Loading

Thermoelastic stress analysis (TSA) is often regarded as a laboratory based technique due to its requirement for a cyclic load. A modified methodology is proposed in which only a single transient load is used for the TSA measurement. Two methods of imparting the transient load are validated against calculations and the conventional TSA approach. Specimens with different damage severities are tested and it is shown that the modified TSA method has the potential to be applied in the field as a non-destructive evaluation tool.     

Determining Individual Stresses Throughout a Pinned Aluminum Joint by Reflective Photoelasticity

Pinned (bolted) joints are an extremely important, but difficult to analyze, structural or mechanical element. They are a class of inverse problems in which the stresses at the pin/hole interface are typically unknown. Moreover, stresses vary non-linearly with applied load. Failures of mechanical or structural systems frequently initiate at connections. Although almost always present, many stress analyses of such mechanical connections ignore friction for simplicity. The stresses are evaluated here in an aluminum connector using a series solution of an Airy stress function, the coefficients being evaluated from known boundary tractions (near, but not including the contact region on the hole) and photoelastically measured data obtained from a bonded birefringent coating. Both friction and pin/hole clearance are accounted for, and individual stresses are evaluated full-field, including on the contact boundary of the hole.     

Full-Field Thermoelastic Stress Analysis of a Finite Structure Containing an Irregularly-Shaped Hole

An assessment of the structural integrity of members containing irregularly-shaped cutouts necessitates knowing the associated stresses. Stress analysis of such structures can be challenging as theoretical solutions are seldom available for finite geometries having non-simple shaped discontinuities and, like numerical methods, they require accurate knowledge of external loads. The latter are often unavailable in practice. This paper describes the ability to process load induced temperature information with an Airy stress function in real polar coordinates to determine the stresses in an isotropic linear elastic finite tensile plate containing an irregularly-shaped hole. Using polar coordinates is significant in that while a relatively simple general solution to the governing biharmonic equation is available in polar coordinates, this is seemingly not so with orthogonal curvilinear coordinates. Compared with displacement-based experimental or finite element techniques, important advantages of the present technique include not having to differentiate recorded data, or know constitutive properties or external loads.     

Assessment of Non-adiabatic Behaviour in Thermoelastic Stress Analysis of Composite Sandwich Panels

Thermoelastic stress analysis (TSA) is used to derive the surface stresses in large sandwich structure panels with honeycomb core and carbon fibre face sheets. The sandwich panels are representative of those used for secondary aircraft structure. The panels were subjected to a pressure load, similar to that experienced in-service, using a custom designed test rig. To achieve the necessary adiabatic conditions for TSA, cyclic loading is regarded as an essential feature. As the panels were full-scale, the maximum loading frequency that could be imparted to the panels by the rig was 1 Hz, which is below the usual range recommended to achieve adiabatic behaviour. To assess the effectiveness of TSA at low frequencies two approaches to calibration are investigated and compared with the stress distribution obtained from independently validated FE models. The thermoelastic response was calibrated into stress data using thermoelastic constants derived experimentally from tensile strips of the sandwich panel face sheet material. It is shown that by using thermoelastic constants obtained from the tensile strips manufactured with the same lay-up as the sandwich panel face sheets, and at the same cyclic load frequency used in the full-scale tests, quantitative stress metrics can be derived from the TSA data. More significantly, a deeper insight into the importance of the thermal characteristics in TSA of laminated materials is provided. It is demonstrated that, for the material used in this work, it is possible to use the global material behaviour to obtain quantitative results when adiabatic conditions do not prevail.     

Assessment of Non-Adiabatic Behaviour in Thermoelastic Stress Analysis of Small Scale Components

The classical thermoelastic equation and the generalized heat conduction equation are developed to deal with a non-adiabatic response in thermoelastic stress analysis. A FE simulation procedure is set up to solve the heat conduction equation over a range of loading frequencies. A small disc (20 mm diameter) loaded under three-point diametric compression is used to examine the effect of in-plane heat conduction. As the disc has regions of zero, moderate and high stress gradients it is an ideal component for this analysis. A regime is developed that provides a basis for an assessment of the nature of the response and allows a minimum loading frequency to be identified so that adiabatic behaviour is obtained. This validity of this approach is demonstrated on steel disc of 20 mm diameter. A special loading device has been designed to obtain the three-point loading and a recently introduced Instron Electropuls test machine is used to achieve the high levels of cyclic loading required for the adiabatic conditions.     

功能梯度平板的二维热弹性分析

本文研究正交各向异性功能梯度平板的二维热弹性问题.该平板在y方向无限长,x方向对边简支且温度恒定.从热弹性力学的基本方程出发,假设材料参数沿板厚方向(z方向)按同一函数规律变化,基于状态空间法,在板的上下表面作用机械荷载和热荷 载的情况下,获得了功能梯度平板二维热弹性问题的Peano-Baker级数解.通过算例,验证了Peano-Baker级数解的正确性;同时也分析了材料参数沿板厚方向不同的幂函数分布对平板响应的影响.     

The Potential for Assessing Residual Stress Using Thermoelastic Stress Analysis: A Study of Cold Expanded Holes

Thermoelastic stress analysis (TSA) is a well established tool for non-destructive full-field experimental stress analysis. In TSA the change in the sum of the principal stresses is derived, usually when a component is subjected to a cyclic load. Therefore the mean stress or any residual stress in a component cannot be obtained from the thermoelastic response. However, modifications to the linear form of the thermoelastic equation that incorporate the mean stress may provide a means of establishing the residual stresses. It has also been shown that the application of plastic strain modifies the thermoelastic constant in some materials, causing a change in thermoelastic response, which may also be related to the residual stress. The changes in response due to plastic strain and mean stress are of the order of a few mK and are significantly less than those expected to be resolved in standard TSA. Recent developments in infra-red detector technology have enabled these small variations in the thermoelastic response to be identified, leading to renewed interest in the use of TSA for residual stress analysis in realistic components. The component studied in this work is an aluminium plate that contains a cold expanded hole, hence providing an opportunity to examine any changes in thermoelastic response caused by the residual stress in the neighbourhood of the hole. The variations in thermoelastic response due to residual stress are shown to be measurable and significant; validation of the residual stress field is provided by laboratory X-ray diffraction. The potential for a TSA based approach for residual stress analysis is revisited, and the feasibility of applying it to components containing realistic residual stress levels is assessed.     

尖锐夹杂角端部局部应力场杂交有限元分析

本文首先利用作者曾提出的一维有限元特征分析方法计算所得到的尖锐夹杂角端部应力奇异指数和奇异应力场、位移场角分布函数,并依据Hellinger-Reissner原理,开发出了一个特殊的、能够反映夹杂角端部局部弹性现象的n结点多边形超级角端部单元,然后将该超级单元与标准的4结点杂交应力单元耦合在一起构建了一种分析异形夹杂角端部奇异弹性场的新型特殊杂交应力有限元方法.文中给出了两个应用算例,算例结果表明:本文方法不仅使用单元少、计算结果精度高,而且适用范围广,可拓展应用于分析复合材料微结构组织与力学行为关系.     

正交各向异性平面热弹性问题的边界元分析

给出了正交各向异性平面热弹性问题的边界积分方程、内点应力公式和常单元离散化时计算奇异积分的解析式，计算了正交各向异性板的热应力强度因子，结果表明了文中所导公式的正确性     

一种求解层合圆柱壳的杂交应力单元

根据修正的余能原理，推导出一种求解复合材料层合圆柱壳的杂交应力单元。取用六面体等参单元，此单元反映了各层材料性质不同及应力分布沿整个厚度不连续现象，同时计入横向剪切变形和法向挤压变形，适用于厚层壳体。文章通过实例说明此单元能准确求出各层内的应力值，实用价值高。     

Thermoelastic stability of a double-layered spherical shell

In the paper the axi-symmetrical thermoelastic stability of free double-layered spherical shells at uniform temperature is considered. The basic equations are derived from Reissner's theory of thin shells and assumptions that materials of the layers are linear thermoelastic. The conditions for the buckling of shells are determined. The temperature-deflection diagrams are calculated by using the collocation method.     

功能梯度矩形厚板的三维热弹性分析

直接从三维热弹性力学基本方程出发，通过引入两个位移函数和两个应力函数，导出了一个二阶的齐次状态方程和一个四阶的非齐次状态方程。分析中采用了层合近似模型，即将板划分成厚度足够小的若干薄层，从面可将每一层内的材料常数近似为常数。给出了任意厚度的四边简支横观各向同性功能梯度矩形板的热弹性分析，特别当板较薄时，与薄板理论进行了数值对比，发现两者结果吻合很好。最后研究了材料梯度指标对热弹性场的影响，结果显示梯度指标对热应力和位移都有着显著的作用：在不同的区间，梯度指标对它们有不同的影响；并且在同一区间，梯度指标对两者的影响程度也有所不同。     

Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method

0Introduction Photoelasticityisanopticalmeasurementmethodforstressanalysis.Itcanperformwhole field measurementduetotwo dimensionalsignalprocessingoflight.Alsoitcanperformnon contact measurementbecauseoftransmissionorreflectionoflightonaspecimen.Photoelast…     

热电材料孔边周期裂纹问题的热电弹分析

论文研究了均匀电流密度和能量流作用下,热电材料中带4k个周期径向裂纹的圆形孔口问题.考虑非渗透型电和热边界条件,运用复变函数理论和保形映射方法,得到了热电材料中电流密度、能量密度和应力场的精确解.依据断裂力学理论,运用Cauchy积分公式得到了周期裂纹的电流、能量和应力强度因子.数值结果分析了场强度因子随各个参数的变化...     

Thermoelastic axisymmetric problem for a two-layer cylinder

The majority of devices and units of microelectronics are multilayer structures made of materials with differing coefficients of thermal expansion and elastic constants. Thermal stresses which arise in such systems due to temperature changes when manufactured or in operation may result in a breakdown, or plastic deformation or in a change of the physical properties of materials. At the same time, due to adopted assumptions the existing design models do not describe the stressed states in real systems of finite dimensions. The designs in [1–3] are obtained on the basis of the engineering theory of beams, and in [4, 5] the obtained solution was for the infinite strip in a half-space. In the present article a right circular cylinder of radius R was used as a mathematical model which was cut by the plane z = 0 into two layers of thickness H or H* (Fig. 1). In our considerations the quantities referring to the layer 2 are distinguished by an asterisk. The cylinder deformation problem due to the temperature lowering from t₁ to T₂ was solved within the framework of the linear theory of thermoelasticity. It was assumed that the material of each layer is homogeneous and isotropic, that the temperature is independent of the coordinates, and that the coefficients of thermal expansion and * are independent of T. Two formulations are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 132–138, January–February, 1978.