Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension

The effect of the material property inhomogeneity on the stress concentration factor (SCF) due to a circular hole in functionally graded panels is numerically investigated. The multiple isoparametric finite element formulation is used to simulate the elastostatic boundary value problem. A parametric study is performed by varying the functional form and the direction of the material property gradation. The material property inhomogeneity is characterized by the intrinsic inhomogeneity length scale, modulus ratio and the power-law index. The results from our parametric study showed that the SCF is reduced when Young's modulus progressively increased away from the hole. The angular position of the maximum tensile stress on the surface of the hole remains unaffected by the material property inhomogeneity. The SCF is seen to be most influenced by the power-law index, followed by the variation of the inhomogeneity length scale. The SCF is least affected by the modulus ratio.     

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters.     

Plastic mechanism analysis of circular tubes under pure bending

There are a number of solutions available to predict the response of a circular steel tube under pure bending. However, most of these solutions are based on an elasto-plastic treatment, which is complex and difficult to use in any routine design. This paper describes a theoretical treatment to predict the moment-rotation response of circular hollow steel tubes of varying D/t ratios under pure bending. The Mamalis et al. (J. Mech. Sci. 1989;203:411–7) kinematics model for a circular tube under a controlled moment gradient was modified to include the effect of ovalisation along the length of the tube. Inextensional deformation and rigid plastic material behaviour were assumed in the derivation of the deformation energy. The plasticity observed in the tests was assumed to spread linearly along the length of the tube. Two local plastic mechanisms (Star and Diamond shapes) were studied to model the behaviour observed in the tests especially during the unloading stage. The theoretical predictions are compared with the experimental results recently obtained by Elchalakani et al. (Quartral. J. Struct. Eng. 2000;3(3):1–16). Good agreement was found between the theoretical predictions and experimental moment-rotation responses, particularly for the Star shape mechanism. A closed-form solution is presented suitable for spreadsheet programming commonly used in routine design.     

On the stress concentration around a hole in an infinite plate subject to a uniform load at infinity

In this paper stress concentration around a hole in an infinite plate that is subjected to a uniform load at infinity is considered. The stress is calculated by using a modified Muskhelishvili complex variable method. The method is illustrated by several examples of stress distribution around polygonal holes of a complex geometry utilizing the Schwartz-Chistoffel mapping function.     

Stress and residual stress distributions in plane strain bending

Stress and residual stress distributions in bending are important in calculating springback and loading capacity of a sheet-metal bending part. Great differences have been found in springback prediction with the same input (benchmark problems) among different researchers. In order to find out the root cause of these differences, stress and residual stress calculation methods in plane strain bending are briefly reviewed or developed. The influence of deformation theory and incremental theory, repeating bending, unbending and re-bending, cyclic material models and springback calculation methods on the stress or residual stress distributions are examined and shown to be large. This emphasizes the importance of careful selection of these variables in a simulation model in addition to other general input variables, such as material properties, tool geometry and friction condition. This fact also helps to explain the great differences among different research results, and presents a challenge to both the programmers and the users of finite element packages.     

A new approach for bending analysis of thin circular plates with large deflection

This paper is concerned with bending analysis of an axisymmetric simply supported circular plate with large deflection. Based on the linear theory of thin plates, the incremental load technique is developed for solving the bending problem of a thin circular plate with large deflection. In the proposed method, the total applied load is divided into various small load steps. In each load step, the plate stress behavior is simplified to be linear. The incremental formulations are presented for the deflection and stresses of the plate when external loads increase. A numerical example is given to show simplicity and accuracy of the present method. It is found that the proposed method can be an alternative useful tool for engineering applications.     

Closed form solutions of axisymmetric bending of circular plates having non-linear variable thickness

A new analytical method for evaluation of elastic stresses and deformations in axisymmetric plates having variable thickness according to a power of a linear function, either solid or annular, subjected to symmetrical bending due to lateral loads either distributed on upper surface or distributed along the inner or the outer edges. The proposed procedure is based on two independent integrals of the hypergeometric differential equation describing the rotation field and constitutes the generalization of the one found in the literature. This method allows to study a wide range of plates, be they solid or annular, converging or diverging with linear or non-linear thickness function, convex, concave or linear tapered, without the restrictions of the known procedures. Analytical results obtained by using this method utterly match both theoretical results which may be obtained in the specific case known (constant-thickness circular plate, linear variable thickness annular circular plate) and numerical results obtained by using FEA.     

Scattering of flexural wave in a thin plate with multiple circular inclusions by using the multipole method

The multipole method is presented to analytically solve the scattering of flexural wave by multiple circular inclusions in an infinite thin plate. The near-field dynamic moment concentration factor (DMCF) and the far-field scattering pattern are both investigated in this paper. The former has a connection with the fatigue failures and the defects in plate-like structures can be detected by the latter. Owing to the addition theorem, the multipole expansion for the multiple scattering fields can be transformed into one coordinate system centered at one circle where continuity conditions are required. In this way, a coupled infinite linear algebraic system is derived as an analytical model for an infinite thin plate with multiple circular inclusions subject to an incident flexural wave. The convergence analysis is conducted to provide the guideline of usage for the proposed method. The effects of the size and thickness of the flexible inclusion, and the central distance between inclusions on the near-field DMCF and the far-field scattering pattern are investigated in the numerical experiments. It shows that the scattering pattern correlates closely with the size and thickness of weakness, indicating the importance of the scattering pattern to detect the various defects. In addition, the DMCF of two corrosion defects is larger than that of one. Therefore, it is essential to evaluate structural safety when multiple circular defects are very close to each other. The effect of the space between the inclusions on the near-field DMCF is different from that on the far-field scattering pattern.     

Exact full-field analysis of strain and displacement for circular disks subjected to partially distributed compressions

The disk in diametral compression has been investigated frequently on developing experimental techniques, such as photoelasticity and Moiré interferometry, for several decades. Theoretically, the compression as a concentrated force is more conducive to analyze but it is impossible to achieve such loading condition experimentally. The distributed compression on a finite area at rim is important in many engineering applications and is relatively closer to actual testing conditions, but it is complicated to seek an analytical solution. This paper presents exact full-field solutions of strain and displacement of a circular disk subjected to partially diametral distributed compressions in explicit functional forms. Based on the theoretical solutions, full-field distributions of strain and displacement are easily provided in polar and Cartesian coordinates by numerical calculations. Interesting phenomena of strain and displacement are discussed in detail based on numerical results. The Saint-Venant's principle applied in circular disks subjected to diametral loadings is examined by comparing the full-field results for the concentrated load and the distributed compression with small angle. Experimental measurements of full-field displacement contours and isochromatic fringe patterns are used to compare with the theoretical predictions and good agreements of both results are found.     

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.     

Fatigue strength and fracture behaviour of CHS-to-RHS T-joints subjected to out-of-plane bending

The fatigue behaviour of six different hollow section T-joints subjected to out-of-plane bending moment was investigated experimentally using scaled steel models. The joints had circular brace members and rectangular chord members. Hot spot stresses and the stress concentration factors (SCFs) were determined experimentally. Fatigue testing was carried out under constant amplitude loading in air. The test results have been statistically evaluated, and show that the experimental SCF values for circular-to-rectangular (CHS-to-RHS) hollow section joints were found to be below those of circular-to-circular (CHS-to-CHS) hollow section joints. The fatigue strength, referred to experimental hot spot stress, was in reasonably good agreement with referred fatigue design codes for tubular joints.     

管道开孔接管和三通设计及应力分析

通过对管道开孔接管和三通设计研究及有限元应力分析,获得了内压作用下的管道开孔接管和三通的应力分布特性.同时,对管道开孔接管和三通的结构尺寸进行了探讨,讨论了各参数的变化对管道开孔接管和三通应力的影响,得出了一些有价值的结论,达到了为管道开孔接管和三通设计和制造提供参考的目的.     

Vibration of a three-layered viscoelastic sandwich circular plate

The equations of motion for a three-layer sandwich circular plate with viscoelastic core are derived. The Donnell–Mushtari–Vlasov assumptions follow to simplify. For the case of iso-symmetric annular plate, five equations are further reduced to three equations. The assumed-mode method then yields the free and the forced solutions being characterized by six generalized coordinates for each circumferential wave number n. Due to the splitting of transversal and in-plane terms the study of vibration response can be reduced to the consideration of the SDOF linear oscillator with hysteretic damping. Numerical results first illustrated the frequency response function (FRF) for two different visco models and slight difference is observed. The effects of frequencies changes and damping due to viscoelastic material (VEM) core for several core-to-face thickness ratios are studied. The results, via the FRF's, show that a relatively thin visco (VEM) core can reduce vibration effectively, but as the core thickness exceeds it the damping gradually reduces. The embedded VEM core decreases the frequencies as expected. The damping effects upon individual modes are looked into as well. The results show that the n=0 mode is affected the most by VEM core.     

利用附加因素降低含圆孔矩形板的应力集中

应力集中是机械工程中常见的问题,一般出现在构件形状急剧变化的地方,如缺口、孔洞、沟槽及有刚性约束处.对于常见的含孔板,利用附加因素降低板的应力集中是一种很好的方法.含一个圆孔的受拉薄板,若在拉伸方向靠近该孔附加一些圆孔,使之成为圆孔群,则对于降低应力集中是相当有效的.使用有限元法分别对附加圆孔半径、圆孔间距及圆孔数对含圆孔矩形薄板应力集中系数的影响进行了分析,并与光弹性实验结果进行了比较,两者基本一致.研究结果表明:在孔数一定时,对于不同的孔间距,存在不同的孔径比最佳值,使应力集中得到最有利的缓和.文中还给出最有利于降低应力集中的孔径和孔距条件.     

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.     

Three-dimensional stress analysis of cylindrically wound fibre reinforced annular discs surrounding a circular hole in a flat plate

A theoretical study is made of the title problem when the plate is subjected to a remote uniform radial tension and the annular discs are symmetrically disposed about the mid-plane of the plate. The three-dimensional treatment brings into consideration the shear lag effects normal to the plane of the plate. Detailed numerical results, including maximum stresses, are presented for discs of carbon fibre reinforced plastic bonded to plates of aluminium alloy. By considering families of discs of constant weight it is possible to optimise the disc geometry for any given ratio of plate thickness-hole diameter.     

Modelling of inelastic bending of a metal sheet with thermal coupling

The modelling and numerical analysis of inelastic bending of a metal sheet are presented. The distribution strains and stresses are found for slow and fast bending while taking into account the geometrical and material non-linearities. The constitutive relation of Klepaczko, (Int. J. Plast. 17 (2001) 87, Comput. Methods Appl. Mech. Eng. 175 (1999) 19) was used which includes strain hardening, strain rate sensitivity and temperature effect in material behaviour. The large strains are assumed under plane strain conditions. The results with complete thermal coupling are compared with solutions obtained in the isothermal conditions of bending.     

多传感器信息融合技术在提高孔板测量精度中的应用

针对孔板工作时由于受介质的温度、压力以及密度变化的影响,从而测量精度较低的不足,提出了应用多传感器信息融合技术来减小孔板测量误差的方法。4个传感器输出的信息反映了介质的实时工作特性,系统将它们送入融合中心进行融合处理。融合技术运用了神经网络学习率自适应调整的改进算法,仿真实验证实了该测量技术与方法的有效性,大大提高了孔板的测量精度,具有重要的实际意义。     

Plane strain elastic–plastic bending of a strain-hardening curved beam

Elastic–plastic analysis of plane strain pure bending of a strain-hardening curved beam has been presented. Only a linear hardening case has been analyzed as the nonlinear equations for a general hardening case could not be solved analytically. A numerical scheme for the computation of stresses and displacements in different stages of deformation has been given and limited FEM verifications have been presented.     

Validation of stresses and stress intensity factor in a notched bilayer system under four point bending, as determined by the solution of the Navier's equation

We use a previously formulated solution of the Navier's equation to calculate stress intensity factor in a notched bar bonded to a substrate. We evolve a procedure for determining the stress distribution. We validate the stress analysis in four-point bending by measuring surface strains for different combination of materials in the bilayer (the Young's modulus ratio of the materials in the bilayer varied from 28 to 86). We also determine the stress intensity factor (SIF) experimentally using a notched photoelastic bar bonded to a substrate and validate our estimation of SIF.