Thermal-stress concentration caused by structural discontinuities

The transient thermal-stress concentrations produced by cracks, sharp and round notches, and fillets, in plates were measured photoelastically and compared to values computed numerically by finite element and finite-difference techniques. The stresses near the tips of the cracks and the notches were singular and observed to agree with isothermal linear elastic fracture mechanics. Stresses near the root of the fillets were always less than the theoretical maximum, αE(T?T _initial ), but often greater than the maximum stresses measured in a straight-edged plate subjected to similar thermal conditions.     

Influence of the Coefficients of Thermal Expansion on the Nature of Stresses and Local Effects in a Uniformly Heated Sandwich Plate

Thermal stresses are determined in a sandwich plate uniformly heated under plane-strain conditions. Linearly elastic isotropic bodies model the plate components. An approximate solution is found by the finite-difference approach. The influence of the coefficients of thermal expansion on the nature of stress concentration regions is studied.     

Thermal stress investigation in unidirectional composites under the hyperbolic energy model

The hyperbolic energy model is applied in this paper for determining transient temperature variation across a unidirectional composite plate subjected to different temperature changes at the boundaries. Thermal stresses developed are then analyzed for different material properties. Governing equations are solved numerically using implicit methods. The results are presented over a wide range of variables commonly found in most composite materials. The transient thermal stresses generated inside the plate were found to fluctuate between compressive and tensile quantities, a result that was not predicted using the classical heat model. Consequently, this will lead to an earlier crack initiation and failure of the material.     

Natural frequencies of composite plates with tailored thermal residual-stresses

Thermal residual-stresses introduced during manufacture and their effect on the natural frequencies and vibration modes of stringer stiffened composite plates is investigated. The principal idea in the work is to include stiffeners on the perimeter of a composite plate in which the laminate design of the stiffeners and plate are different. Such an arrangement yields manufacturing induced thermal residual-stresses; these stresses result from the difference in manufacturing and operating temperatures as well as the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. The analysis is based on an enhanced Reissner–Mindlin plate theory and involves two separate calculations. In the first, the thermal residual-stress state is determined for an unconstrained plate. In the second, the free vibration problem is solved; thermal effects from the first calculation are included by way of nonlinear membrane-bending coupling which in turn defines the free vibration reference state. The problem is solved using a 16-node bi-cubic Lagrange element in a finite element formulation. Three different plate-stiffener geometries are used to illustrate the effects of stringer size, stringer placement and temperature difference. Two principal results are obtained: first, it is shown that thermal residual-stresses can have a significant effect on the natural frequencies; secondly, thermal residual-stresses can be tailored to increase natural frequencies. Therefore it is concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design of this class of composite structures.     

Repair of a Plate with a Circular Hole by Applying a Patch

The stressed state of a thin elastic infinite plate with a circular hole covered by a circular patch of a greater radius is considered. The center of the hole coincides with the center of the patch. The patch is attached to the plate along its entire boundary. Stresses are prescribed at infinity on the plate and at the hole boundary. Complex Muskhelishvili potentials are found by the method of power series, and the behavior of stresses on the patch–plate interface and at the hole boundary is studied.     

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为研究金属-FGM-陶瓷 EFBF 复合板的稳态热应力,从热传导规律出发,结合热应力计算公式,建立了该复合板稳态热应 力的研究模型,用有限元和辛普生法分析了T_a=500K和T_b=1800K时,该 复合板的稳态热应力分布并与无梯度两层复合板的结果进行了比较. 结果表明：FGM梯度层的厚度、组分和孔隙率对该EFBF复合板的热应力有不同程度的影响, 此外,有梯度三层复合板的热应力比较缓和,最大拉应力减小29.18%. 此结果为该复合板的设计和应用提供了准确的计算依据.     

Non-linear stresses in a rubber cylinder sheared by pressure at one end

Normal stresses are set up by shearing a rubber block or tube. They depend strongly on the end conditions, even for relatively long specimens [A.N. Gent, J.B. Suh, S.G. Kelly III, Mechanics of rubber shear springs, Int. J. Non-Linear Mech. 42 (2007) 241-249; J.B. Suh, A.N. Gent, S.G. Kelly III, Shear of rubber tube springs, Int. J. Non-Linear Mech. 42 (2007) 1116-1126]. We have now examined a solid rubber cylinder bonded within a rigid cylindrical tube and subjected to pressure at one end. In this case, the correct end conditions for a simple shear deformation are met, at least approximately. Theoretical analysis and finite element calculations show that inwardly directed second-order stresses are set up at the wall, in contrast to the outwardly directed stresses generated by shearing a block or tube. However, for the particular geometry considered, the stresses were rather small in comparison with the applied pressure. Conditions are described under which they would be significantly larger. Stresses in a non-linearly viscous fluid under steady shear flows are expected to be similar, depending strongly on the geometry, end shapes and stress conditions.     

Thermal bending analysis of shear-deformable laminated anisotropic plates by the GDQ method

The generalized differential quadrature (GDQ) method was used to determine the inter-laminar stresses and deflections in a laminated rectangular anisotropy plate under thermal bending involving the effect of shear deformation. We obtained the non-dimensional stresses and transverse center deflection in cross-ply and angle-ply anti-symmetric, anisotropic laminates subjected to thermal load with sinusoidal temperature distribution. We found that the shear deformation has significant effects on the stresses and deflections for laminated anisotropic plate with moderately side-to-thickness ratio under thermal load and bending state.     

Progress in tire rating based on soil compaction potential

The general trend in soil protection is to reduce the detrimental soil compaction by loaded wheels of power and transport equipment. This paper reports on the progress in research of soil compaction risk assessment by means of Compaction Capacity (CC) tire rating originally introduced as compaction number (CN) rating [Grečenko A. Tire load rating to reduce soil compaction. J Terramech 2003;40:97–115]. The CC rating evaluates soil dry density along a vertical column 20–50 cm below the ground surface. The unique feature of the CC approach is that it converts laboratory compaction measurements directly to soil compaction profiles under evaluated tires without touching the stresses in the ground. The laboratory soil compaction is done with round pressure plate and similarly the tire contact area is represented by a virtual plate loaded by the same mean contact pressure. This paper describes laboratory testing procedures with fundamentals of data conversion and gives examples of CC rating application.     

简支及悬臂箱梁在角隅轴向荷载作用下的翼板纵向应力

基于能量变分原理,拟定轴向荷载作用下箱梁的纵向位移函数,得到关于翼板剪切变形引起的位移差函数的基本微分方程,继而推导出箱梁翼板纵向应力表达式,并首次得出角隅轴向荷载作用下翼板出现应力不均匀分布的荷载及边界条件。通过对一模型箱梁进行计算,并与通用有限元软件ANSYS壳单元计算结果进行比较,验证了该方法和所推导公式的正确性。研究结果表明,当作用于简支箱梁截面角隅处的轴向荷载（合力无偏心）为集中或分布荷载时,翼板不产生纵向应力不均匀现象;当作用于悬臂箱梁截面角隅处的轴向荷载（合力无偏心）为集中荷载时,翼板不产生纵向应力不均匀现象,而当荷载轴向分布时,翼板将产生纵向应力不均匀现象。实际工程中,横力弯曲使悬臂箱梁产生剪力滞效应,这种效应会与轴向分布荷载产生的效应叠加,设计时对此应予以充分考虑。     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

Measurements in the vicinity of a stagnation point

This paper presents measurements of a plane jet impinging onto a normal flat plate placed up to five jet widths from the jet outlet. The small spacing ensured that the stagnation streamline remained in the potential core of the jet. The plate shear stress distribution compared well to that from an analytical solution for the laminar development of the plate boundary layer whose external velocity was determined from the measured pressure. By comparing the shear stress measured under the present low level of free stream turbulence (0.35%) at the jet exit with that of Tu and Wood [Exp. Thermal Fluid Sci. 13 (1996) 364–373] made at about 4%, it is concluded that the turbulence level at the nozzle exit has only a second-order influence on the surface shear stress around the stagnation point. Some spanwise non-uniformity was observed in the plate shear stress, but this was confined largely to the transition region. The mean velocity, Reynolds stresses, and fluctuating pressure were measured along the stagnation streamline using a fast-response pressure probe. A significant increase in the streamwise normal stress and the mean square of the pressure fluctuations occurred before they were eventually attenuated by the plate. This increase occurred in the region where the streamwise velocity was decreasing close to the plate causing extra energy production through the normal stresses. Spectra of the velocity and pressure fluctuations showed that the increase in level was mainly due to the low frequency motion, whereas the subsequent decrease occurred at higher frequencies.     

Fracture under initial stresses acting along cracks: Approach, concept and results

The problems of fracture under initial stresses acting along cracks in [A.N. Guz’, Mechanics of Brittle Fracture of Materials with Initial Stresses, Naukova Dumka, Kiev, 1983 (in Russian)] is studied. Other approaches and concepts are also briefly discussed. Results for isolated and near-the-surface cracks are given.     

Mircopolar Model of Fracture for Composite Material

Failure of a composite is a complex process accompanied by irreversible changes in the microstructure of the material. Microscopic mechanisms are known of the accumulation of damage and failure of the type of localized and multiple ruptures of the fibers delamination along interphase boundaries, and also mechanisms associated with fracture of fibers. In this work, we propose a mathematical model of the local mechanism of failure of a composite material randomly reinforced with a system of short fibers. We implement the Cosserat moment model of crack tip for filament material, reinforced with whiskers or in fiber- reinforced polycrystalline materials. It is assumed that the angular distribution of the fibers is isotropic and the elastic characteristics of the fibers are considerably higher than the elastic constants of the matrix. We implement the homogenization procedure for the effective Cosserat constants similarly to the effective elastic constants. The singular solution in the vicinity of the crack tip in the Cosserat moment model is found. Using this solution, we examine the bending stresses in the filaments due to effective moment stresses in the material. The constructed model describes the phenomenon of fracture of the fibers occurring during crack propagation in those composites. The following assumptions are used as the main hypotheses for the micromechanical model. The matrix contains a nucleation crack. When the load is increased the crack grows and its boundary comes into contact with the reinforcing fibers. A further increase of the stress causes bending of the fiber. When~the fiber curvature reaches a specific critical value, the fiber ruptures. If the stress at infinity is given, the fibers no longer delay the development of failure during crack propagation The degree of bending distortion of the fiber in the vicinity of the boundary of the crack is determined by the moment model of the material. The necessity to take into account the moment stresses in the failure theory of the reinforced material was stressed in [Muki and Sternberg (1965) Zeitschrift f angew Math und Phys 16:611–615; Garajeu and Soos (2003) Math Mech Solids 8(2):189–218; Ostoja-Starzewski et al (1999) Mech Res Commun 26:387–396]. The moment Cosserat stresses were accounted also for inhomogeneous biomechanical materials by Buechner and Lakes (2003) Bio Mech Model Mechanobiol 1: 295–301. We should also mention the important methodological studies [Sternberg and Muki (1967) J Solids Struct 1:69–95; Atkinson and Leppington (1977) Int J Solids Struct 13: 1103–1122] concerned with the moment stresses in homogeneous fracture mechanics.     

Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section

In this article, the wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section is discussed, using the Fourier expansion collocation method. The solid medium is assumed to be linear, isotropic, and dependent on the rate of temperature. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. By imposing the continuity conditions the frequency equation corresponding to the problem is obtained using the Fourier expansion collocation method based on Suhubi’s generalized theory [Suhubi, E.S., 1975. Thermoelastic Solids. In: Eringen, A.C. (Ed.), Continuum Physics, vol. 2. Academic, New York, Chapter 2]. To compare the model with the existing literature, the results of a generalized thermoelastic solid cylinder are obtained and they are compared with the results of Erbay and Suhubi [Erbay, E.S., Suhubi, E.S., 1986. Longitudinal wavepropagationed thermoelastic cylinder. J. Thermal Stresses 9, 279–295]. It shows very good degree of agreement. The computed non-dimensional wavenumbers are presented in figures for various values of the material parameters. The general theory can be used to study any kind of cylinders with proper geometrical relations.     

Three-dimensional photoelastic and finite-element analysis of a propellant grain

The results of a three-dimensional photoelastic analysis of a propellant-grain model are compared with the results obtained from a three-dimensional finite-element analysis of the same model. The loading considered was differential thermal expansion between the case and the grain model. The model analyzed was the Stage I Minuteman propellant grain which consists of a six-point-star configuration with a head-end web. Stresses and strains determined from the two analyses in the star valley are compared. The excellent correlation between the stresses determined from the photoelastic analysis and the stresses calculated by the three-dimensional finite-element computer program established the validity of the computer program.     

电测法确定压力容器角变形及错边处附加弯曲应力

本文根据内压容器的电测应力，研究了电测法确定角变形及错边处附力。弯曲应力的原理及方法，用此法可将弯曲应力从组合应力中分离出来，从而得到被测部位附加弯曲应力分布曲线，并由此给出残余应力限值，为工程技术人员采取相应措施改善这种部位的应力状况提供科学依据。     

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 multiscale (visco)-hyperelastic modelling for particulate composites

The aim of this work is to pursue, in the wake of the paper [Martin, C., Dragon, A., Trumel, H., 1999. Mechanics Research Communications 26, 327], a non-classical micromechanical study and scale transition for highly filled particulate composites with a viscoelastic matrix. The present extension of a morphologically-based approach due to Christoffersen [Christoffersen, J., 1983. J. Mech. Phys. Solids 31, 55] carried forward to viscoelastic small strain context by Martin et al. [Martin, C., Dragon, A., Trumel, H., 1999. Mechanics Research Communications 26, 327], Nadot-Martin et al. [Nadot-Martin, C., Trumel, H., Dragon, A., 2003. Eur. J. Mech. A/Solids 22, 89], consists in introducing large strain (visco)-hyperelastic behaviour of the constituents (notably the matrix). The form of a local problem is analytically stated for compressive constituents. Numerical simulation for simplified hyperelastic behaviour and regular microstructure, employing different grain/matrix contrast parameters, is discussed in order to illustrate salient features of the advanced approach.     

Limit analysis of multi-layered plates. Part II: Shear effects

In the first part of this work [Dallot, J., Sab, K., 2007. Limit analysis of multi-layered plates. Part I: the homogenized Love-Kirchhoff model. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2007.05.005], the limit analysis of a multi-layered plastic plate submitted to out-of-plane loads was studied. The authors have shown that a homogeneous equivalent Love-Kirchhoff plate can be substituted for the heterogeneous multi-layered plate, as the slenderness (length-to-thickness) ratio goes to infinity. In fact, the out-of-plane shear stresses are shown to become asymptotically negligible when compared to in-plane stresses, as the slenderness ratio goes to infinity. Actually, failure of thick multi-layered structures often occurs by shearing in the core layers and sliding at the interfaces between the layers. Both shearing and sliding are caused by the out-of-plane shear stresses. The purpose of the present paper is to build an enhanced Multi-particular Model for Multi-layered Material (M4) taking into account shear stress effects. In this model, each layer is seen as a Reissner-Mindlin plate interacting with its neighboring layers through interfaces. The proposed model is asymptotically consistent with the homogenized Love-Kirchhoff model described in the first part of the work, as the slenderness ratio goes to infinity. Kinematic and static methods for the determination of the limit load of a thick multi-layered plate which is submitted to out-of-plane distributed forces are described. The special case of multi-layered plates under cylindrical bending conditions is studied. These conditions lead to simplifications which often allow for the analytical resolution of the Love-Kirchhoff and the M4 limit analysis problems. The benefit of the proposed M4 model is demonstrated on an example. A comparison between the heterogeneous 3D model, the Love-Kirchhoff model and the M4 model is performed on a three-layer sandwich plate under cylindrical bending conditions. Finite element calculations are used to solve the 3D problem, while both the Love-Kirchhoff and the M4 problems are analytically solved. It is shown that, when the contrast between the core and the skins strengths is high, the Love-Kirchhoff model fails to capture the plastic collapse modes that cause the ruin of the sandwich plate. These modes are well captured by the M4 model which predicts limit loads that are very consistent with the limit loads predicted by the heterogeneous 3D model (the relative error is found to be smaller than 1%).