Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity

Thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity are studied. The cavity surface is subjected to ramp-type heating of its internal boundary, which is assumed to be traction free. Lord–Shulman and Green–Lindsay models for the generalized thermoelasticity theories are selected since they allow for second-sound effects and reduce to the classical model for an appropriate choice of the parameters. The temperature, radial displacement, radial stress, and hoop stress distributions are computed numerically using the finite-element method (FEM). The results are presented graphically for different values of the thermal relaxation times using the three different theories of generalized thermoelasticity. Excellent agreement is found between the finite-element analysis and analytical and classical solutions.     

Shear properties and a stress analysis obtained from vinyl-ester losipescu specimens

The use of losipescu specimens for the determination of the shear properties of a vinyl-ester resin was investigated. The antisymmetric four-point bend and the Adams and Walrath fixtures were studied for their suitability in loading these specimens. Photoelastic and strain-gage data in addition to published finite-element results show that the latter fixture distorts the stress field in the gage section. The antisymmetric four-point bend fixture is found to give the purest shear-stress field in the gage section and to yield the most reliable shear-modulus values. A refined photoelastic analysis shows that the shear-stress distribution between the notch roots is essentially uniform with a relative maximum or minimum at the centroid depending on the depths of the notches. Also, stress risers of up to 30 percent are observed near the notch roots. Except at the roots, finite-element predictions are presented which are in excellent agreement with photoelastic data. The failure mode of this vinyl-ester resin is tensile and the corresponding tensile stress calculated from the average shear stress in the gage section of the losipescu specimen is in excellent agreement with failure data acquired in tension.     

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.     

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.     

New developments in the localized hybrid method of stress analysis

Developments of the localized hybrid method which combines an experimental technique, moiré interferometry, and a numerical method, finite-element analysis, are presented. In this localized hybrid method, the displacement fields which the moiré experiments provide in some local regions of interest are used as input data for finite-element stress analyses. Based on finite-element theory, several variations on this localized hybrid method, associated with different displacement boundary conditions, are developed. Applications and limitations of the localized hybrid method are discussed in detail. In particular, applications of the localized hybrid method of stress analysis are presented for three-dimensional problems in the mechanics of solids. It is shown that this localized hybrid analysis not only provides a powerful and efficient technique for the reduction of moiré experimental data, but also gives a good insight into the mechanics of the experimental observations.     

Integration of laser-speckle and finite-element techniques of stress analysis

A study of the combined use of laser-speckle and finite-element methods for stress analysis is described. The speckle technique provides displacement data which can be directly input to a finite-element computer program for the determination of stresses. The displacement data can be used as boundary conditions for the examination of a subregion of the structural component to be analyzed. A substantial reduction in computational effort can be realized over conventional finite-element analysis of the entire structure. Also, a sizeable reduction in the required amount of experimental data may occur since direct numerical differentiation of the data is not required for strain evaluation. Acceptable accuracy may be obtained even when experimental displacement data may be too scarce for traditional numerical differentiation. Random error in experimental displacement is illustrated to have localized effects on the calculated stress field. Paper was presented at 1983 SESA Spring Meeting held in Cleveland, OH on May 15–19, 1983.     

A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

Spectral/finite-element calculations of the flow of a maxwell fluid between eccentric rotating cylinders

The steady-state, two-dimensional creeping flow of an Upper-Convected Maxwell fluid between two eccentric cylinders, with the inner one rotating, is computed using a spectral/finite-element method (SFEM). The SFEM is designed to alleviate the numerical oscillations caused by excessive dispersion error in previous finite-element calculations and to resolve the stress boundary-layers that exist for high elasticity, as measured by the Deborah number De. Calculations for cylinders with low eccentricity (ϵ = 0.1) converged to oscillation-free solutions for De ≈ 90, extending the domain of convergence over traditional finite-element methods by a factor of thirty. The results are confirmed by extensive refinement of the discretization. At high De, steep radial boundary layers form in the stress, which match closely with those predicted by asymptotic analysis. Calculations at higher eccentricity require extreme refinement of the discretization to resolve the variations in the stress field in both the radial and azimuthal directions associated with the existence of the recirculation region. Results for ϵ = 0.4 show that the recirculation region present for the Newtonian fluid (De = 0) shrinks and then grows with increasing De. Calculations for ϵ = 0.4 are terminated by a limit point near DeL ≈ 7.24 for the finest discretization used. The Fourier series approximations are not convergent for this mesh, so the limit point must be considered to be an artifact of the discretization.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.     

Finite-element analysis of creep and plasticity tensile-test specimens

Traditionally, mechanical properties as determined from sensile-test specimens are assumed to be truly uniaxial and are used directly in finite-element codes for design purposes. In this paper, the stress and strain distributions in two test geometries, an hourglass specimen and a cylindrical specimen, are critically examined by means of the nonlinear finite-element code CREEP-PLAST. Since some triaxiality of the stress state is inevitable in any region with a transition, it is difficult to have a truly uniaxial test specimen. The determination of the internal stress and strain distributions makes it possible to assess the accuracy of the mechanical properties as indicated by tests on a particular specimen. Furthermore, the data given here guide the choice between the hourglass and the cylindrical specimen for applications in creep, plasticity and fatigue. Extensometry techniques permit measurements to be made only on the surface of the specimen. Thus, trouble can be caused by the nonuniform strain state present in both geometries. With the finite-element analysis, the strain field within the specimens is correlated to that on the surface; extensometry correction factors are given for selected cases.     

Finite-element solutions for thermal stresses in steel-concrete composite bridges

The objective was to determine experimentally and analytically steady-state temperature distributions produced in the cross-sectional planes of steel-concrete composite simple-span bridges. The upper and lower surfaces were exposed to different temperatures. The research included the development of finite-element solutions for steady-state temperature distributions from known boundary conditions and the calculation of strains and stresses. Temperature and stress distributions were generally nonlinear with linear strains through the finite elements. Temperatures were predicted to ±1° F (±0.6° C). The experimental strains are linear through the composite section, with the computed finite-element strains generally giving slightly higher stresses. The concrete-slab stresses were overestimated for positive curvature and slightly underestimated for negative curvature. Concrete-slab stresses were relatively small when compared to their permissible stress. Temperature stresses in the steel beam were shown to be significantly large to warrant consideration in the design of these bridges. Stresses were calculated for short-term steady-state temperatures. Transient field conditions producing greater thermal stresses are now under investigation.     

A finite-element technique to analyze the data measured by the hole-drilling method

A finite-element technique to analyze the data obtained by the hole-drilling strain-gage method is presented. In this study, residual stresses are assumed as initial stresses existing in the structural material or component. It is also assumed that the elimination of the initial stresses in the region of the drilled hole changes the measured strains. After putting initial stresses into displacement finite-element equations and comparing the stiffness matrix and the initial stresses matrix with those of the previous increment, equations relating unknown initial stresses and measured strains were obtained. By solving these equations, residual stresses were obtained. In this paper three examples are studied. In the first two examples, calibration constants C1 to be used in determining residual stress were calculated which varied with depth. In the third example, the data obtained by using the hole-drilling method are analyzed. All examples show good agreement with previous studies. Using the present method allows greater flexibility of choice of specimen shape, materials, and experimental procedure than would be possible if only analytic solutions were used.     

Determination of residual stresses by an optical correlative hole-drilling method

In conjunction with the incremental hole-drilling method, a new evaluation procedure is presented for determining the residual stress state in components. In contrast to the classical method, the whole displacement field around the drilled hole is measured using the electronic speckle pattern interferometry technique. The displacement patterns, measured without contact to the surface, are then correlated with those obtained by finite-element simulations using statistical methods. The simulated displacement patterns, used for calibration purposes, result from the application of properly defined basic loads. In this way, the values and the orientation of the residual stresses can be determined by superposition of these properly scaled and shifted basic loads. Even complex states of stress can be evaluated. The theoretical background and experimental results are presented.     

Constitutive equations for porous plane-strain gradient elasticity obtained by homogenization

This paper addresses the problem of plane-strain gradient elasticity models derived by higher-order homogenization. A microstructure that consists of cylindrical voids surrounded by a linear elastic matrix material is considered. Both plane-stress and plane-strain conditions are assumed and the homogenization is performed by means of a cylindrical representative volume element (RVE) subjected to quadratic boundary displacements. The constitutive equations for the equivalent medium at the macroscale are obtained analytically by means of the Airy’s stress function in conjunction with Fourier series. Furthermore, a failure criterion based on the maximum hoop stress on the void surface is formulated. A mixed finite-element formulation has been implemented into the commercial finite-element program Abaqus. Using the constitutive relations derived, numerical simulations were performed in order to compute the stress concentration at a hole with varying parameters of the constitutive equations. The results predicted by the model are discussed in comparison with the results of the theory of simple materials.     

Image-processing techniques in laser-speckle photography with application to hybrid stress analysis

Six techniques for analyzing speckle halo fringes for fringe spacing and orientation using a digital image analyzer are presented. Each of the techniques were tested for range, accuracy, and computer run-time through analysis of a known case of rigid-body motion. Application of these techniques to two-dimensional hybrid stress analysis is described where speckle-displacement data around the high-stress region of a notched bar in tension is used as input data to a plane-stress finite-element program. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

Comparison of residual-stress variation with depth-analysis techniques for the hole-drilling method

Numerous data-analysis techniques have been developed to determine residual-stress information from strain data obtained from the hole-drilling method. The most commonly used technique for data analysis was developed by Rendler and Vigness (which forms the basis of the standard described in ASTM E837-85). A numerical development which was a model of the hole-drilling procedure has been used to determine stress variation with depth. A rigorous finite-element method to specifically analyze stresses in discrete hole increments has been developed. To evaluate these data-analysis techniques, three different computer-simulated stress fields are compared. The stress fields include a uniaxial stress that is constant with depth, a bending stress that varies linearly with depth, and a subsurface stress reversal. (The basis for this comparison is a finite-element developed technique. Its accuracy will be discussed later.) All data-analysis techniques showed excellent agreement for the uniaxial stress constant with depth test case. However, for the other two stress fields, significant discrepancies were apparent. Results are compared and discussed.     

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.     

三维势流场的比例边界有限元求解方法

比例边界有限元法(SBFEM)是线性偏微分方程的一种新的数值求解方法。该方法只对计算域边界利用Galerkin方法进行数值离散,相对于有限元方法(FEM)减少了一个空间坐标的维数,而在减少的空间坐标方向利用解析方法进行求解;相对于边界元法(BEM),比例边界有限元方法不需要基本解,避免了奇异积分的计算,所以它结合了有限元和边界元方法的优点。本文建立了利用比例边界有限元法求解三维Laplace方程的数值模型并用于计算三维物体周围的水流场,将计算结果与解析解和边界元方法进行了对比,结果表明此方法可以很好地模拟水流场,且具有较高的计算精度。     

颗粒填充复合材料强韧化效应的力学分析

颗粒填充复合材料中基体微损伤形式对材料韧性产生决定性影响。本文通过二相或三相材料中基体应力分布的分析计算，结合损伤萌生的力学条件，对颗粒填充的强韧化效应作出定性分析。计算结果表明，若颗粒刚度高于基体，随着颗粒模量的提高，开裂与银纹趋势逐步增强，由此可知单纯使用硬粒子填充难以实现增韧，但若粒子与基体间有柔性界面相存在，基体屈服趋势将随界面厚度迅速增长，它将在损伤引发机制的竞争中占据优势，成为损伤的主导形式，并由此可成功地实现材料的强韧化。