Photoelastic assessment of finite-element analysis of a pipe tee

A three-dimensional photoelastic analysis and a finite-element analysis of a pressurized pipe tee are compared. The pipe tee is a 152-mm typical commercial straight buttwelding tee, having a nominal wall thickness of 11.0 mm. The finite-element program employs a doubly curved shell element in which stresses vary linearly through the thickness. The three-dimensional photoelastic model was cast from the pattern of an actual pipe tee. The model was pressurized and stress-frozen. Its principal planes were analyzed for in-plane surface stresses, then subsliced and analyzed for transverse stresses. The photoelastic stresses are graphically compared to those from finite elements. For large regions of the tee there is substantial agreement in the stresses from the two methods. Considerable disagreement is revealed in the sharply curved corners between the main pipe and the stem. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

A photoelastic and finite-element investigation of a nonsymmetrical plug-hatch configuration

A photoelastic investigation to evaluate the reliability of the finite-element method of shell analysis was carried out for models with nonsymmetric plug-hatch configurations. The stress distributions in the spherical-shell models with combined hatch and anchor-boss configurations were determined experimentally and compared with those predicted through the use of a finite-element computer program.     

A pseudo two-dimensional photoelastic method of testing axisymmetric geometries

Problems involving three-dimensional bodies which possess axial symmetry reduce to two-dimensional analytical problems. If a wedge-shaped portion of an axisymmetric body is tested subjected to the proper boundary condition, then a pseudo two-dimensional photoelastic method of testing may be used. This results in tremendous simplification in testing procedures, particularly when slight changes in model geometry are to be made during the course of testing. This method has been applied to axisymmetric solidpropellant rocket grains to conduct a parametric study of various conicyl geometries. Both pressure and thermal loads were considered for a case-bonded grain. Six parameters were required to define the geometry. The effects of these parameters and of the material properties of the grain were investigated, and parametric curves showing the variation of the maximum stress with those parameters are presented. The experimental results are compared with results obtained from a finite-element computer solution. Good agreement is obtained.     

Three-dimensional scattered-light stress analysis of discontinuous fiber-reinforced composites

This paper reports an investigation of three-dimensional stresses in models of composite materials with discontinuous fibers using the scattered-light photoelastic method. A special scattered-light polariscope with loading system was designed and constructed for this research. Two models were used in this investigation. The first was a cylindrical tension model with a single discontinuous axially aligned aluminum fiber surrounded by a polyester matrix. The second was a five-fiber cylindrical compression model with a central discontinuous fiber surrounded by four continuous ones and polyester matrix. The experimentally determined stress distribution from each model along chosen lines was presented. The stress distribution on the same lines in the single-fiber case was calculated using the finite-element method. The calculated result showed fair agreement with the experimentally determined results.     

Single-strand strainwire technique: Comparison with existing methods and a proposed photostrain technique

This paper is the third of three papers evaluating a refined internal strainwire technique. This final paper evaluates the technique by comparing it with two elastic solutions, with a photoelastic solution, and with a new proposed photostrain technique. The problem chosen as the basis of comparison was a plane-stress problem of a plate with a circular hole under uniform tension. The proposed technique is experimental in nature and combines parts of the results of a photoelastic solution with those yielded by a three-wire internal strain-gage-rosette analysis to completely fix the state of stress in the model. The scientific techniques used to compare the three-wire strain technique and photostrain technique are as follows: two elastic solutions, one evaluated at a point and one arrived at by integrating the stress functions over a finite length; a finite-element solution; a photoelastic analysis using the shear-difference technique to separate the principal stresses; and a three-wire-rosette analysis. A comparison is made of the values of principal stresses yielded by these methods.     

Scattered-light analysis of a surface-flawed plate subjected to cylindrical bending

The scattered-light photoelastic technique was utilized to determine Mode I stress-intensity factors associated with a semi-elliptical surface flaw in a plate subjected to cylindrical bending. Stress-intensity factors were experimentally determined for the point of maximum flaw penetration and the point of intersection of the flaw border with the free surface of the plate. Experimental results compare favorably with those obtained in a three-dimensional finite-element analysis.     

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.     

Application of finite-element method to the analysis of high-capacity laminated elastomeric parts

Design and analysis of high-performance elastomeric components, in particular ‘high-capacity laminated’ (HCL) elastomeric components, present two difficulties: (1) a laminated geometry cannot be analyzed accurately by existing closed-form solutions and (2) the incompressibility or near-incompressibility of the elastomer makes computations impossible or very inaccurate. These difficulties are overcome by using a finite-element computer program that is capable of handling incompressibility. This paper discusses, in brief, the incompressibility and the difficulties and errors caused by it in stress calculations. The paper describes briefly the general features and capabilities of a finite-element computer program that can analyze rubber-like structures. Results of the analyses of three kinds of HCL bearings are then presented by using this computer program under different loading conditions. The paper presents test results of hoop stresses in the shims, stiffnesses of the bearings and maximum strain areas in the rubber layers of these bearings. These test results and the finite-element results are then shown to be in excellent agreement.     

Residual stresses in plastically encapsulated microelectronic devices

The residual stresses in a model of a plastically encapsulated microelectronic device are determined photoelastically using birefringent transfer-molding compounds. The measured stresses are compared with a laminated-platetheory analysis and then used to guide a two-dimensional finite-element analysis of the device. Photoelasticity was also used to determine the effects of postcure on the residualstress distribution.     

Design and stress evaluation of a nonsymmetric pressure vessel

Presently, the large variation in demand for electrical power at different periods of the day imposes new considerations in the evaluation of pressure components in large steam-generating equipment. In the past, pressure components such as valve bodies have been designed for static pressure conditions against bursting with sufficient stiffness to assure operation ability. In today's plant operation, the response of the valve body to thermal transients will have a major influence on the life of the valve. Since the valve body is a compact nonsymmetric body, the direct calculation of stresses is very complex. The evaluation of the behavior of nonsymmetric pressure components under the loads imposed by various operational modes requires information from both analytical and experimental methods of analysis. The contributions from modern computer-calculation programs and three-dimensional photoelasticity are discussed as applied to the evaluation of a valve body used in a large, supercritical steam generator. In the analysis, computer procedures are used to develop the preliminary geometry for pressure loading. Because of the close proximity of the nonsymmetrical openings, a three-dimensional photoelastic analysis is used to calibrate the computer model. Once a satisfactory computer model has been developed for pressure loading, it is used to calculate the thermal stresses. Since stresses have little meaning in themselves, a design basis is necessary to evaluate the significance of the calculated stresses. The design basis must consider the types of failures which are possible and is thus dependent on the temperature at which the valve must operate. A design basis is discussed for the evaluation of pressure components in a boiler system.     

封隔器卡瓦接触应力研究

封隔器上的卡瓦锚定后起到支撑封隔器、锁定胶皮筒的作用,其性能好坏直接影响到油井的产量和生产安全。卡瓦与套管间的咬合力分布决定了封隔器在使用中的成败。咬合力的分布是否合理,将直接关系到套管的损伤程度及卡瓦的寿命。文中同时应用有限元法和三维光弹性技术对封隔器卡瓦进行了接触应力分析,介绍了实验模型的建立和实验步骤以及计算模型的建立和边界条件的考虑,比较了数值计算与三维光弹实验的结果,分析了造成误差的原因。实验应力分析结果为有限元计算模型的建立及边界条件的确定提供了重要的实验保证。研究工作获得了一些重要的结果,为封隔器卡瓦的优化设计提供了相关的参数。     

A new look at the bending strength of gear teeth

This paper reports on an extensive two-dimensional photoelastic study of the basic deformation behavior of gear teeth under load. Limitations of existing bending-strength design procedures are used to formulate a test program which considers the magnitude of the critical root-fillet stresses, the effects of varying the load position on the flank, the effects of friction forces at contact and the relationship between bending and shearing deformations. Particular interest is devoted to a study of the observed movement of the maximum-stress position around the fillet as load moves up the tooth flank and to the associated variation in stress-concentration factors (around the fillets) due to radial, bending and shear loads. Note is also made of the problems associated with observed ‘proximity effects’ and of the procedures carried out in an attempt to qualify the nature of the effect. The results of the program have been used to, explain certain anomalies observed in earlier three-dimensional photoelastic model tests^1.7 and reference is made to the development of a new design procedure for the bending strength of helical gears.     

Evaluation of an applied plane-stress tensor distribution using ultrasonic shear waves

Most acoustoelastic stress measurements using shear waves that have been carried out so far are strongly related to photoelastic experiments: the velocity difference of the birefringent waves is evaluated. Absolute time-of-flight measurements potentially give more information about stresses but are also likely to be inaccurate. A technique is developed enabling time-of-flight and polarization angle measurements in an aluminum plate that are reproducible within 1/3 ns and one-deg respectively. Based on a previous calibration of the acoustoelastic effect, a plane-stress tensor field caused by applying a load to an aluminum 2024-T351 compact-tension specimen is evaluated. The results are compared to those of a finite-element analysis.     

Determination of the stress distribution in assemblies of photoelastic particles

An optical measuring method and a calculation procedure for determining the distribution of the stress tensor in a plane-strained three-dimensional assembly of random-shaped photoelastic particles are described. The stress tensor at an arbitrary point of the model is determined by an integration procedure, based on the equations of equilibrium of stresses. The distribution of the principal-stress direction and the relative principal-stress difference and at least two normal stresses in a plane have to be known to perform the integration. The distribution of the principal-stress directions and their difference are measured optically by scanning the model with an optical filter system with a single rotating polarizer.     

Photoelastic study of centrifugal stresses in a single wheel and hub

Results of a photoelastic study of centrifugal stresses in a single wheel with integral hub are given. Stress distributions are determined on the bore and lateral surfaces, and on several radial interior lines. The results are compared with theoretical stresses.     

刚构连续梁桥墩梁固节点结构的光弹性试验及有限元分析

某铁路特大桥的主桥部分采用预应力混凝土刚构连续梁桥,本文采用光弹性模型冻结应力法对该刚构连续梁桥墩梁固节点结构进行了应力分析,给出了结构边界应力分布和主应力迹线。应用ANSYS软件对墩梁固节点实际结构进行了有限元计算。将实验与有限元分析结果进行了比较,结果表明,实验应力分析法与有限元数值法吻合较好。在有限元分析中,对墩梁固节点结构梁端加载边界的影响区进行了研究,通过合理选择梁的长度可以有效减小局部应力。模型实验和有限元计算的结果为结构的优化设计提供了重要的依据。     

Analytical prediction of ROPS static elastic-plastic behavior

This paper outlines a method for accurately predicting the elastic-plastic force-vs.-deflection curve for a rolover protective structure (ROPS). A knowledge of the plastic behavior of structural members is combined with a finite-element beam model to produce a piecewise linear analysis. Experimental and analytical results are compared. Intermediate results are used to update the model at various stages in the process. The paper does not discuss the computer program—only its use.     

Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.     

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

Photoelastic stress analysis of thick-walled closed-end cylinders

A three-dimensional photoelastic stress analysis was conducted on six thick-walled closed-end cylinders subjected to internal-pressure loading. The cylinders were approximately similar in design to the breech chamber of a large-caliber tank weapon. Maximum octahedral shear stresses were determined in the side wall-end wall juncture of essentially flat-ended cylinders (similar to actual weapon component) and in hemispherically-ended cylinders. The purpose of the study was to learn more about the stresses in the closed end of the cylinder so that future components of this type may be designed more efficiently with regard to stress and weight.