在复杂应力状态下厚壁圆筒的极限分析

应用双剪统一强度理论,考虑材料的拉压异性和同性,推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷计算公式,并且绘制了其极限载荷线图。在这些计算公式中,当其系数取不同的值时,就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果。应用其极限载荷线图,根据其承受的载荷大小,就能判断厚壁圆筒是否达到了屈服极限状态。绘制了在不同屈服准则下的极限载荷线图,以便对其差异进行比较。     

比塑性功求解线性载荷下简支圆板极限载荷

为了获得线性载荷作用下的简支圆板极限载荷的解析解,本文提出了刚塑性第一变分原理的运动许可应变场,并首次以GM(几何中线)屈服准则塑性比功进行了塑性极限分析.首次获得了GM准则下圆板极限载荷的解析解,该解为圆板半径a、材料屈服极限σs及板厚h的函数.与Tresca、TSS及Mises预测的极限载荷比较表明:Tresca准则预测极限荷载下限,TSS屈服准则预测极限载荷的上限,GM屈服准则比塑性功解析结果恰居于两者之间;GM解略低于Mises解,两者相对误差为3.38%.此外,文中还讨论了挠度与相对位置r/a之间的变化关系.     

用GM屈服准则解析薄壁筒和球壳的极限载荷

首次将GM（几何中线）屈服准则应用于内压薄壁圆筒和球壳的塑性极限分析,获得了解析解.薄壁筒和球壳极限载荷均为壁厚、内径及材料屈服极限的函数.屈服极限越高、壁厚越大,内径越小,极限载荷越大.与Mises准则、双剪应力准则（TSS）和Tresca准则相比,GM准则解居于TSS和Tresca解之间且靠近Mises解,恰好对应误差三角形中线.按GM准则计算的极限载荷随厚径比的增加而线性增加.     

MY准则解析受均布载荷简支斜板极限载荷

为了得到斜板极限载荷的解析解,用平均屈服(MY)准则,对受均布载荷的简支金属斜板进行了塑性极限分析.首次获得MY准则下斜板极限载荷的解析解,该解是斜板几何参数长l1,宽l2以及长宽夹角θ的函数.研究表明:随着θ的增大,极限载荷先增大而后减小;斜板面积增加,极限载荷减小.得到了菱形、矩形和方形板的解析解,并将方形板的解析解与Tresca、Mises以及TSS提供的极限载荷进行比较,对比表明:方板的极限载荷与边长成反比关系,Tresca屈服准则提供极限载荷的下限,TSS屈服准则提供上限,MY准则预测结果恰居二者中间,且最靠近Mises解.     

均布载荷作用下简支圆板塑性极限载荷的解析解

该文建立了受均布载荷作用简支圆板运动许可应变场,并首次以EA(等面积)屈服准则进行了塑性极限分析,获得了极限载荷的解析解。该解为圆板半径a、圆板厚度h以及屈服强度的函数。与Tresca、TSS以及Mises解比较表明,Tresca屈服准则预测极限载荷的下限,TSS屈服准则预测极限载荷的上限,EA和Mises屈服准则预测的极限载荷恰居二者中间,且EA解几乎与Mises解重合。此外,该文还讨论了挠度与相对位置r/a之间的变化关系。     

用双剪应力屈服准则计算壳体的极限载荷

本文导出轴对称壳体的双剪应力屈服准则下的屈服条件，并求出某些特殊荷载下的圆锥壳和圆柱壳的极限载荷。     

岩土材料破坏准则研究及其应用

讨论了线性Mohr-Coulomb屈服准则和Drucker-Prager屈服准则及其在工程计算中的应用。给出了线性Mohr-Coulomb准则在材料力学及岩石力学中的不同表达形式之间的关系;描述了线性Mohr-Coulomb准则屈服面和Drucker-Prager准则屈服面的几何性质;比较了Drucker-Prager准则采用三种不同近似方法逼近线性Mohr-Coulomb准则时的差别;最后给出了采用Drucker-Prager准则逼近线性Mohr-Coulomb准则计算桥桩基础工程实例,为了对比,同时也用Mises准则作了计算。     

弹塑性结构安定性上限分析的数值方法及应用

建立了复杂变化载荷作用下理想弹塑性结构安定上限分析的有限元数学规划格式。利用研究结构在基准载荷域各个角点处安定的办法,避开了机动定理中对时间积分的困难,提出了一种直接迭代算法求解,以克服目标函数非线性非光滑所导致的困难。该格式同时考虑了温度对屈服极限的影响。     

各向异性板料屈服轨迹的研究

针对建立的十字形双向拉伸试验系统,利用有限元模拟优化得到的十字形试件,采用载荷控制方式对SPEN钢板和2024-O铝合金板进行了不同加载路径下的双向拉伸试验,得到了不同硬化阶段下的实验屈服轨迹,并与现有屈服准则Hill48、Hill79、Hill90、Hill93、Gotoh、Hosford、Barlat-Lian以及Mises的理论屈服轨迹进行了对比.结果表明:对于SPEN钢板,Hosford各向异性屈服准则得到的理论屈服轨迹与实验屈服轨迹符合得最好,其次是Mises屈服准则,Hill48屈服准则最差;对2024-O铝合金板,Barlat89、Hosford屈服轨迹与实验屈服轨迹符合得最好,Mises屈服准则最差.     

考虑温度对材料性能影响时厚壁圆筒的安定分析

鉴于工程实际中的许多结构承受着随时间变化的温度—机械载荷作用,本文在考虑屈服极限随温度变化的情况下,对内压和温度共同作用的厚壁圆筒进行了安定分析,给出了几种典型加载模式下的安定范围。     

Generalized isotropic yield criterion for incompressible materials

Summary With the von Mises yield criterion as basis, a generalised isotropic yield function for incompressible yielding has been formulated. The proposed yield function includes as limiting forms, both the classical yield criterion of Tresca and that of von Mises. It is shown that the general yield criterion includes a twelve-sided, piece-wise linear condition of yielding. A method of relaxing the restrictions imposed by the vertices associated with a piece-wise yield criteria is described. The formulation of a composite yield condition, comprising a piece-wise, linear and continuous, yield function, together with a continuously differentiable form of yield function, is described. The use of the proposed yield criterion is reviewed in the context of the two different ypes of experiment for determining the yield condition satisfied by a given material.With 5 Figures     

Dynamic response of a slab of elastic-viscoplastic material that exhibits induced plastic anisotropy

Various 2-dimensional problems of the dynamic loading of a slab are solved for a material characterization that is elastic-viscoplastic and exhibits anisotropic work-hardening. The governing constitutive equations are based on a unified formulation which requires neither a yield criterion nor loading or unloading conditions. They include multi-dimensional anisotropic effects induced by the plastic deformation history. The theory also considers plastic compressibility which depends on the extent of the anisotropy. A numerical procedure for solving the equations is developed which incorporates the history dependent anisotropic hardening effects. Cases considered are the dynamic penetration of a slab by a rigid cylindrical indenter, and a distributed force rapidly applied over part of the slab surface. Both conditions of fixed and free rear surfaces of the slab are examined. A uniaxial problem is also considered in which different bases for the anisotropic hardening law are examined.     

Springback investigation of anisotropic aluminum alloy sheet with a mixed hardening rule and Barlat yield criteria in sheet metal forming

A mixed hardening model has been implemented based on Lemaitre and Chaboche non-linear kinematic hardening theory to consider cyclic behavior and the Bauschinger effect. The Chaboche isotropic hardening theory is incorporated into the non-linear kinematic hardening model to introduce a surface of nonhardening in the plastic strain space. The bending and reverse bending case study has verified the effectiveness of the mixed hardening model by comparison with the proposed experiment results. Barlat’89 yielding criterion is adopted for it does not has any limitation while Hill’s non-quadratic yield criterion is for the case that the principal axes of anisotropy coincides with principal stress direction. The Backward–Euler return mapping algorithm was applied to calculate the stress and strain increment. The mixed hardening model is implemented using ABAQUS user subroutine (UMAT). The comparisons with linear kinematic hardening model and isotropic hardening model in NUMISHEET’93 benchmark show that the mixed hardening model coupled with Barlat’89 yield criteria can well reflect stress and strain distributions and give a more favorable springback angle prediction.     

弹塑性杆非线性断裂问题的新型增强有限元法

针对一维弹塑性材料杆件的非线性断裂,该文提出了一种新型弹塑性增强有限元。该单元采用von Mises屈服准则和线性等向硬化模型描述开裂前的材料弹塑性变形,而结合利用内聚力关系来描述随后的裂纹萌生和非线性断裂过程。引入内部节点来描述单元内由于裂纹引起的位移不连续,通过单元凝聚获得含裂纹单元的刚度矩阵,并对数值稳定性问题进行了分析。通过与基于材料力学方法推导得到的解析解的对比验证了该新型弹塑性增强有限单元法在列式上的正确性和在数值上的高效性与精确性。     

Non-linear analysis for anisotropic materials

An elasto-plastic analysis of anisotropic work-hardening materials, using the finite element method is presented. The analysis is based on the generalized Huber-Mises yield criterion extended by Hill for anisotropic materials. General expressions for the anisotropic parameters in the yield criterion have been derived both for initial yielding as well as subsequent yielding in the case of work-hardening materials. The isoparametric ‘quadratic’ quadrilateral elements have been used for the analysis and the ‘initial stress technique’ has been adopted for the iterative solution of the non-linear problems. The results of the various numerical examples have been compared with the available solutions.     

A nonuniform hardening plasticity model for concrete materials

For the most part, the developments of constitutive models for for the concrete by the theory of plasticity have in the past been made to scarch for a suitable failure surface. The initial yield surface is usually assumed to have the same shape as the failure surface but with a reduced size. The subsequent loading surfaces are then obtained by the uniform expansion of the initial one. This approach is found generally inadequate in predicting the deformational behavior of concrete for a wide range of loading conditions.

The present non-uniform hardening plasticity model adopts the most sophisticated failure model of Willam-Warnke or Hsieh-Ting-Chen as the bounding surface; assume an initial yield surface with a shape that is different from the failure surface; proposes a nonuniform hardening rule for the subsequent loading surfaces with a hydrostatic pressure and Lode-angle dependent plasticity modulus; and utilizes a nonassociated flow rule for a general formulation.

The work-hardening stress-strain behaviors of concrete based on the present model are found in good agreement with experimental results involving a wide range of stress states and different types of concrete material. The important features of inelastic behavior of concrete, including brittle failure in tension; ductile behavior in compression; hydrostatic sensitivities; and volumetric dilation under compressive loadings can all be represented by this improved constitutive model.     

On the plastic zone and residual stresses within a strip and a half plane under a moving load

A quasi-steady solution has been obtained for the determination of the extent of plastic zones and the amplitude of the residual stresses in (1) an elasto-plastic strip lying on a rigid frictionless base and (2) a half-plane, under the first passage of a moving load. The load is assumed to be applied with a semi-elliptic pressure distribution which is of sufficient magnitude to cause plastic yielding in the body. A work-hardening material obeying von-Mises' yield criterion is considered. A numerical solution procedure, based on discretizing the plastic strain field in the coordinate system moving with the load into uniformly strained rectangular or semi-infinite elements has been developed. Numerical results are obtained for a strip with linear work-hardening material properties. The effect on the distribution of residual stresses created by the ratio of load half-width to strip thickness is also discussed.     

Elasto-plastic solution for a cylindrical inclusion in plane strain

Understanding the role of inclusions in the fracture process is of great importance and up to now there have been few continuum solutions which give elasto-plastic stress and strain fields around an inclusion. The incremental solution presented is for plane strain conditions, the cylindrical inclusion being assumed rigid, while the matrix obeys the Mises yield criterion and its associated flow rule and has a very small or zero linear work-hardening characteristic. On the infinite boundary, strains of up to nearly 16× yield strain are applied under various states of stress, varying from pure shear to the nearly purely hydrostatic state.The simultaneous governing equations in terms of displacements are solved using finite differences and successive over-relaxation.The results presented give distributions of radial stress and shear strain on the matrix-inclusion interface showing the variation with applied strain and stress state, and work-hardening characteristic: shear strains are found to be almost independent of stress state. Comparison is made with the linear viscoelastic solution and a slip-line solution is attempted from a plot of maximum shear strain trajectories.     

Development and application of the material constitutive model in springback prediction of cold-bending

The accuracy for cold-bending springback prediction is determined by the sensitivity and accuracy of the material constitutive model. Thus, the material constitutive model is developed and improved by many researchers, and the improved models are applied in the springback calculation with various materials in finite element simulation or theoretical analysis. To provide a reference for the researchers studying cold-bending springback problems, a review of the development and application of the material constitutive models is presented in this paper, which conducts from the elastic behavior, the anisotropy, and the work-hardening. It can be summarized as: (1) Springback prediction result is higher and more accurate when the variable elastic modulus and the nonlinear recovery are considered. (2) The isotropic hardening leads to an overestimation of the springback, which can be avoided by a hardening model describing the Bauschinger effect. (3) The hardening model has greater impact on springback than the yield criterion. (4) Good accuracy of the springback prediction can be achieved when the variable elastic modulus effect, the material anisotropy and the nonlinear hardening are considered together. It is also found the theory development and practical application of the material constitutive models are out of line, due to lacking further experiment, or that the stress loading–reloading history within a bending part may be not so complex as that “ratchetting behavior” discussed.     

The dynamic indentation of an elastic-viscoplastic work-hardening slab by a rigid punch

A unified theory for elastic-viscoplastic work-hardening materials, which requires neither a yield criterion nor loading or unloading conditions, is implemented to solve two-dimensional dynamic problems. Specifically, the theory is applied to the dynamic indentation by a rigid indenter of a slab made of an elastic-viscoplastic material. The contact area between the indenter and the slab at any time is not known in advance but should be determined from the process of the solution. An iterative numerical procedure is proposed by which the complete solution is determined from the dynamic elastic-viscoplastic equations, the moving mixed boundary conditions, the requirement that the contact normal stresses are compressive and that no interpenetration occurs outside the contact area. The method is applied to the indentation problem of a viscoplastic slab by a long rigid circular cylinder, and by a wedge-shaped die. Comparisons with the corresponding perfectly elastic problems are given.