On divergence-free stress fields and zero-energy stress functions in elasticity

Applying two identities for divergence-free non-symmetric and symmetric second-order tensors, novel type of first- and second-order stress functions are proposed for three-dimensional elasticity problems. It is shown that self-equilibrated but non-symmetric 3D stress fields can be generated by one first-order stress function vector, whereas a self-equilibrated and symmetric 3D stress field can be generated by one Airy-type second-order stress function. Assuming linearly elastic materials, the zero-energy modes of the stress functions introduced are derived and investigated. It is pointed out that the structure of the zero-energy modes of the proposed first-order stress function vector is the same as that of the rigid-body displacements in the linear theory of elasticity.     

Determination of effective stress range and its application on fatigue stress assessment of existing bridges

This paper presents a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miner's law and a new effective stress range based on the nonlinear fatigue damage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplitude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridge––the Tsing Ma Bridge in Hong Kong.     

A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model

A new modified couple stress theory for anisotropic elasticity is proposed. This theory contains three material length scale parameters. Differing from the modified couple stress theory, the couple stress constitutive relationships are introduced for anisotropic elasticity, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. However, under isotropic case, this theory can be identical to modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The differences and relations of standard, modified and new modified couple stress theories are given herein. A detailed variational formulation is provided for this theory by using the principle of minimum total potential energy. Based on the new modified couple stress theory, composite laminated Kirchhoff plate models are developed in which new anisotropic constitutive relationships are defined. The First model contains two material length scale parameters, one related to fiber and the other related to matrix. The curvature tensor in this model is asymmetric; however, the couple stress moment tensor is symmetric. Under isotropic case, this theory can be identical to the modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The present model can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model of couple stress theory including only one material length scale parameter for modeling the cross-ply laminated Kirchhoff plate is suggested. Numerical results show that the proposed laminated Kirchhoff plate model can capture the scale effects of microstructures.     

Topology optimization design of continuum structures under stress and displacement constraints

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High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics. The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization. To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM) is proposed. The derivatives of the shear stress on the calculation path are determine...     

一种SPH应力修正算法及自由表面流中的应用

提出了一种SPH应力修正算法,即模型中的拉应力和压应力分别采用不同的插值核函数和状态方程来处理,改善应力稳定性问题。介绍了一种改进的Quintic核函数,用于改善模型中压应力的稳定性。通过增加钟型核函数的光滑长度,改善模型中拉应力的稳定性。采用该应力修正算法模拟了无重力条件下方形液滴的震荡变形过程,对比分析了不同算法的模拟结果。此外,为进一步验证算法的适用性,模拟了溃坝算例。研究表明,改进的Quintic型核函数明显改善了粒子聚集现象,该SPH应力修正方法可以使液滴具有更均匀的粒子分布以及更光滑的自由表面,有效改善了SPH方法中的压应力不稳定作用以及自由表面流的模拟精度。     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

Free-edge interlaminar stress analysis of piezo-bonded composite laminates under symmetric electric excitation

A stress function-based approach is proposed to analyze the free-edge interlaminar stresses of piezo-bonded symmetric laminates. The proposed method satisfies the traction free boundary conditions, as well as surface free conditions. The symmetric laminated structure was excited under electric fields that can generate induced strain, resulting in pure extension in the laminated plate. The governing equations were obtained by taking the principle of complementary virtual work. To verify the proposed method, cross-ply, angle-ply and quasi-isotropic laminates were analyzed. The stress concentrations predicted by the present method were compared with those analyzed by the finite element method. The results show that the stress function-based analysis of piezo-bonded laminated composite structures is an efficient and accurate method for the initial design stage of piezo-bonded composite structures.     

Wedge corner stress behaviour of bonded dissimilar materials

A contour integral, based on Betti’s reciprocal theorem, is used in conjunction with the finite element method to evaluate the magnitude of the wedge corner stress intensities associated with the higher order terms of the singular stress field near the interface corner of a bi-material joint. It is shown that using a different auxiliary field can eliminate the dependence of the wedge corner stress intensity on the integration path observed by [W.C. Carpenter, Int. J. Fracture 73 (1995) 93–108]. Finite element analysis of a typical joint geometry is used to demonstrate the path-independence of the magnitude of the stress intensities evaluated using the proposed method, and to show the effects of higher order terms on the stress state near the interface corner.     

Experimental stress analysis for process of nonsteady inelastic deformation by photoviscoplasticity

The proposed photoviscoplasticity is a method for determining the stress distribution in nonsteady inelastic deformation during creep. The governing fundamental relations are derived by considering the effect of time as involved in the viscoplastic strain rate and the stress rate, and by considering the distinctive deformation properties of celluloid as model material. The validity of the fundamental relations are evaluated according to calibration test by using celluloid. The proposed method is applied for two practical applications of the compression of blocks by elastic punches and the compression of strip having a circular hole or semicircular notches. The time-dependent variation of stress states can be analyzed with the same accuracy as in the photoelasticity.     

复合材料切口应力奇性指数计算

提出一种计算广义平面应交状态下复合材料切口应力奇性指数的新方法.在切口尖端的位移幂级数渐近展开式被引入正交各向异性材料的物理方程后,将用位移表示的应力分量代入切口端部柱状邻域的线弹性理论控制方程,切口应力奇性指数的计算被转化为常微分方程组特征值的求解.采用插值矩阵法求解该常微分方程组,可一次性地获取切口尖端多阶应力奇性指数.本法适合平面和反平面应力场耦合或解耦的情形,并可退化计算裂纹或各向同性材料切口的应力奇性指数.算例表明,所提方法对分析复合材料切口应力奇性指数是一种准确有效的手段.     

An hysteretic quadrilateral plane stress element

In this work, a new plane stress element is proposed for the nonlinear static and dynamic analysis of plane stress/plane strain problems. The four node quadrilateral element formulation for the elastic case is extended by introducing a novel hysteretic constitutive relation, based on the Bouc–Wen model of hysteresis. The hysteretic model introduced is directly derived from the governing equations of classical plasticity based on the flow rule and specific hardening law. The stiffness matrix of the element is formulated using the principle of virtual displacements, where the elastic stress–strain relation is substituted by the hysteretic relation proposed. The derived stiffness matrix is expressed as a smooth function of the internal stress field both in the elastic and inelastic regime. The efficiency of the proposed element in the simulation of the cyclic behavior in plane structures is presented through illustrative examples.     

A reined global-local approach for evaluation of singular stress ield based on scaled boundary inite element method

A reined global-local approach based on the scaled boundary inite element method(SBFEM) is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.     

A finite element implementation of the stress gradient theory

In this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.

     

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON＇S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.     

Local stress measurement using the thermoelastic effect

A technique for measuring local stresses in metallic specimens is proposed and tested. The technique depends on the experimental measurement of temperature changes in stressed members due to adiabatic elastic deformation. At a free boundary in a body under plane stress, these temperature changes are directly related to the value of the tangential principal stress. The technique is suited for measurement of stress-concentration effects, since the temperature changes can be measured with thermocouples featuring extremely small junctions. A simple stress-concentration geometry, the finitewidth strip with a central circular hole, is chosen as a model system for this study. Heat transfer in this geometry due to the temperature gradients produced by elastic deformation is analyzed. It is shown that the ratio of the temperature change at a reference section to the change at the locale of the stress concentration can be used to determine the stress-concentration factor, allowing for heat-transfer effects. An experimental measurement system capable of obtaining reproducible results with the thermal-measurement technique is described, and experimental results are given for the model geometry which agree favorably with theoretical predictions. Application of the technique to other problems is discussed.     

Practical limitations to the influence of through-thickness normal stress on sheet metal formability

According to a recent (original) model, when hardening properties and the ratio of through-thickness normal stress to the first principal stress (γ≡σ₃/σ₁) are held constant, sheet metal formability can be increased dramatically through the introduction of a compressive through-thickness normal stress, σ₃. In practice, however, both the hardening properties and γ evolve with the progression of deformation. To manage most efficiently the evolution of the hardening properties and γ, the original model is cast into a more compact form and presented as a proposed alternative form (proposed model). When the evolution of the hardening properties and γ is considered, the proposed model is shown to be in very good agreement with observed data; the influence of through-thickness normal stress on sheet metal formability is quite small for all practical purposes. Because the structure of the original model is similar to that of the proposed model, the original model is also validated. Ultimately, it is verified that although the theory of the original and proposed model may be acceptable, the implications of such theories are less profound than those first proposed when practical limitations are considered. This work serves as a useful basis for: (1) further understanding the limitations of the influence of compressive through-thickness normal stress on sheet metal formability and (2) exploring opportunities for improving sheet metal formability.     

An application of holography to complete stress analysis of photoelastic models

A new procedure is proposed by which holographic principles may be extended to include stress analysis of three-dimensional photoelastic models. A sixth independent equation can be obtained to permit a complete stress solution by using the double-exposure hologram technique in conjunction with an immersion tank. The salient feature of the method is that no stress relieving is necessary between exposures of the hologram. Two experiments were performed to compare the stress-relieving method to the immersion method. In both experiments, a two-dimensional model was used to simplify the demonstration of the general techniques, which are also applicable to slices from frozen-stress models.     

Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam

A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlinear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Compared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However, the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models also have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.