Photothermoelastic analysis of transient thermal stresses

Photothermoelasticity by means of heating is used to obtain an experimental solution to the quasi-static problem of transient thermal stresses around elliptical holes. Empirical equations are obtained for the maximum stresses due to step temperature changes at the edges of the plates.     

Normalized stresses around an elliptic hole in a finite plate of linear material subjected to large uniform in-plane loading

Stress-concentration factors associated with the large deformations of in-plane loaded plates with elliptic holes are presented in a form with which designers are familiar. An analytic expression to obtain the stress-concentration factor is included.     

Patterned bilayer plate microstructures subjected to thermal loading: Deformation and stresses

We studied the deformation of a series of gold/polysilicon patterned plate microstructures fabricated by surface micromachining. The patterned plate microstructures were subjected to a uniform temperature change from 100 °C to room temperature that was intended to induce linear and geometrically nonlinear deformation. We used interferometry to measure full-field deformed shapes of the microstructures. From these measurements we determined the spatially-averaged curvature of the deformed microstructures within individual lines and across the entire plate. The deformation response of the patterned plates can be broadly characterized in terms of the average curvature as a function of temperature change and exhibits linear and geometrically nonlinear behavior. We modeled the deformation response of the patterned plates using geometrically nonlinear plate theory with the finite element method. Good agreement was obtained between predictions and measurements for both local curvature variations across lines and for the evolution of curvature of the entire plate with temperature change. Using a generalized plane strain approach with the finite element method we also modeled the spatial dependence of the stress distribution in the lines and substrate. For thick plates, our results agree with those of previous studies, showing a decrease in the von Mises stress in the metal lines with decreasing linewidth. For thinner substrates, though, we find the behavior with linewidth is opposite and there is a critical substrate thickness (about 10 μm for the system in our study) where the behavior with linewidth changes. These results have important implications in the design of patterned structures for micro-electro-mechanical systems (MEMS) applications where films are of comparable thickness to the underlying substrate.     

Dynamic thermal stresses in a circular cylinder subjected to asymmetric heating

Summary This paper is concerned with the two-dimensional dynamic thermal stress problems in an infinitely long circular cylinder subjected to two kinds of asymmetric heatings at the lateral surface, assuming that the cylinder is initially undeformed and at zero temperature. The equations of motion including the inertia terms are expressed in terms of the dilatation and rotation and solved by applying the Fourier-cosine, Fouriersine transforms and the Laplace transform to the resulting differential equations. The solutions to the dynamic thermal displacements and stresses in the cylinder valid for the short period after the asymmetric heatings are obtained and the numerical calculations are carried out for the thermal boundary condition of the prescribed temperature distribution.

---

Dynamische Wärmespannungen in Kreiszylindern bei asymmetrischer Erwärmung

übersicht Es werden dynamische WÄrmespannungsprobleme für einen unendlich langen Kreiszylinder untersucht, der zwei verschiedenen Arten von ErwÄrmung der OberflÄche unterworfen ist. Die Bewegungsgleichungen schlie\en die TrÄgheitsterme ein; sie werden in der Dilatation und der Rotation geschrieben und mit Hilfe von Fourier- und Laplace-Transformationen gelöst. Asymptotische Lösungen für kurze Zeiten werden ebenfalls hergeleitet, und numerische Ergebnisse werden grafisch dargestellt.

     

Displacement field around a circular hole in a viscoelastic plate

Moiré experimental techniques are used to measure displacement fields in viscoelastic plates undergoing large deformations at elevated temperatures. These experimental procedures are applicable to determining displacement fields in nonlinear materials. As preliminary information, the material properties are determined from creep studies. The moiré method is used to determine the strains under constant load and isothermal conditions. Tests are conducted for several combinations of load and temperature for 2.5 decades of time. Assuming thermorheologically simple behavior, the data are shifted to establish the creep extensional compliance over ten decades in time. The constitutive equations are formulated as integral equations, the kernels of which are the functions that were measured in this work. These equations are solved exactly for the infinitesimal case. The finite case is then approximated by an incremental superposition of a series of successiye infinitesimal solutions. The results are applied to a plate initially containing a circular hole, and are shown to agree closely with the experimental measurements.     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

Transient thermal stresses in a strip with an eccentric hole

A procedure is presented for dealing with the constraint associated with the direction of the thickness of a thin model and for obtaining transient thermal stresses under plane-stress conditions; the stresses are induced by severe thermal loads. Thermal-stress-concentration factor in an unrestrained strip with an eccentric circular hole placed near the thermally loaded edge is obtained. One straight edge of the strip is cooled and the others are insulated. Consequently, two cases for which the hole acts remarkably as a stress raiser are found.     

横向爆炸载荷下开孔板的动应力集中因子

基于ANSYS 5.7/LS-DYNA程序,对3 m3 m0.25 m四边固支和简支、中心具有0.3 m0.3 m方孔的开孔板和无孔板对应点在两种下三角爆炸载荷作用下的应力响应进行了分析;由开孔板和无孔板边对应点的主应力时程曲线,对提出的能量密度时间分布函数的绝对值平方进行变上限积分,按其比值确定动应力集中因子,该方法简单易行。     

Photothermoelastic study of stress concentrations in a plate with internal heating

This paper describes a photothermoelastic method for simulating, in a three-dimensional model, the temperature gradients that occur in structural parts subjected to internal heating such as is frequently encountered in certain areas of nuclear-reactor design. The method is applied to a plate which has a step change in thickness and sustains a nonlinear temperature gradient through its thickness. The shapes of the gradients simulate internal heating of the plate material. The values for the highest stresses on the free surfaces of the plate, within the thickness of the plate, and at the root of the step are presented in graphical form for a range of internal heat-generated conditions. Thermal-stress-concentration factors are presented for a step change in the thickness of a plate under this type of heating. Its design significance is discussed. The same stress and stress-concentration values are shown to also apply to nonnuclear problems. During shut-down in conventional thermal plants, when the walls sustain linear steady-state temperature drops across their thicknesses, temperature profiles exactly analogous to those presented in this paper occur. The stresses can then be computed from the values presented here.     

Experimental investigation of transient thermal stresses in a solid sphere

An experimental investigation was made to determine if a transient-thermal-stress distribution could be effectively analyzed using scattered-light photoelasticity. the problem selected for investigation was a solid sphere at one temperature subjected to a spherical symmetric temperature distribution at a different temperature. The results and techniques are discussed.     

Photoelastic analysis of a thick plate with an elliptical hole subjected to simple out-of-plane bending

A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions.     

Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate

The aim of this work is to present an analytical solution to reduce the stress concentration factor (SCF) around a circular hole in an isotropic homogeneous plate subjected to far-field uniaxial loading. In this paper the elastic response of an inhomogeneous annular ring made of functionally graded material (FGM), inserted around a hole of a homogeneous plate, is studied. By assuming that Young’s modulus varies in the radial direction with power law and that Poisson’s ratio is constant, the governing differential equations for plane stress conditions are obtained. Using stress function a general solution in explicit closed form is presented and the SCF investigated to highlight the inhomogeneity effects. Furthermore, the explicit solution for an inner homogeneous ring, with different properties with respect to those of the plate, is explicitly obtained and numerical results are compared between homogeneous ring and FGM ring.     

Dynamic focusing effect of piezoelectric fibers subjected to thermal shock

Based on finite Hankle transforms, this paper presents a theoretical method for analyzing the dynamic focusing effect of piezoelectric fibers subjected to the thermal shock of a transitory temperature change produced by a sudden electric current pulse. From analytical expressions and example calculations for two kinds of piezoelectric fibers, PZT-4 and BaTiO₃, it is found that the dynamic focusing effect is dependent on the material property of the piezoelectric fibers so that the maximum dynamic stress amplitude of the two kinds of piezoelectric fiber occur at different radial points. The mechanism of the dynamic focusing effect in piezoelectric fibers is relevant to the evaluation of the dynamic strength and electric signal of the piezoelectric fiber. The results carried out may be used as a reference to solve other transient coupled electrothermoelasticity problems in piezoelectric structures.