非线性随动强化条件下的安定定理

基于经典的安定理论与随动强化模型的一般性质,将结构在强化过程中的背应力计入Von Mises屈服准则,建立了随动强化条件下结构的静力安定定理;将背应力与对应的塑性应变率的点积在一个载荷循环内的积分计入塑性耗散功,建立了随动强化条件下结构的机动安定定理,扩展了经典安定理论的应用范围。针对两种定理的存在格式进行了理论证明,并以推论形式给出了结构在随动强化条件下静力安定和机动安定另外两种存在格式。结果表明,随动强化材料的安定状态和安定极限不受强化过程的影响,只取决于材料的初始屈服应力和最终屈服应力。     

具有部分恒定载荷时机动安定定理的表达式

本文介绍了机动安定定理及其推理;导出了具有部分恒定裁荷时机动安定定理的实用形式,利用这些公式及机动安定定理的推理能够得到一些实际问题的完全解。     

半球封头圆柱壳的安定分析

半球封头圆柱壳结构的力学分析是工程实际中提出的一个重要课题。本文应用 Melan 静力安定定理和修正的运动安定定理对半球封头圆柱壳结构进行安定上下限分析和计算,编制了专门的程序,并就修正的运动安定定理与极限分析上限定理进行比较。     

固支圆板安定性的实验研究

本文利用机动法求解固支圆板在循环集中力作用下的安定问题,得到了安定载荷的理论解;利用激光全息的实验方法研究固支圆板的塑性累积现象,测得了安定载荷的上下限,并对实验结果进行了分析研究.     

基于能量原理的连续体结构安定分析

基于安定分析的静力定理,建立了一种以结构吸收的塑性能为安定判断准则,应用一种特殊的加载方式求解连续体结构安定问题的数值方法.应用这种能量方法对两个经典安定分析算例进行了计算,与相关结果进行对比表明能量法的有效性和可靠性.该方法摆脱了传统分析方法中的数学规划运算,有较高的求解效率,可方便地应用于实际工程中.     

影响弹塑性结构安定性的各种因素

安定分析是结构设计或承载能力研究的一个重要方面。本文首先简单介绍了经典安定理论、分析方法及其工程应用,然后从影响安定性的诸因素出发,对安定理论的近期发展进行了综述,包括安定理论在热载荷、几何效应、应变强化效应、动力效应等方面的推广和应用,塑性应变(或残余变形)的限制方法,以及安定性的实验成果等。      

动载荷下弹塑性随动强化结构的安定问题

本文讨论了弹塑性随动强化结构的动力安定问题,其加载面在应力空间中是任意形状的凸曲面。文中给出了相应的安定定理,指出如果能找到任何一个与时间无关的和虚设残余应力而使结构安定,则该结构将一定是动力安定的。此外,本文还给出了塑性功和塑性应变的上界估计式,并以在交变载荷作用下的Mises随动强化材料的简支圆板为例,对定理的应用进行了说明。     

应变强化模型的安定准则研究

基于Melan经典的安定理论和von Mises屈服准则,建立了塑性应变强化条件下结构安定的数学模型,根据与时间无关的应力场的特性,对结构中与时间无关的应力场进行了合理的数学变换,将其与载荷变化系数联系起来,推导出与其对应的结构安定极限范围的表达式,给出塑性应变强化模型安定性存在的简化条件.该结论有利于简化应变强化条件下结构的安定分析.     

变曲率连续滚滑接触安定性的数值方法研究

针对接触表面变曲率的特点,引入局部坐标系,构造出局部坐标下残余应力应变场的分布状态,建立了变曲率连续啮合过程中安定状态残余应力的计算方法。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,并采用增量映射方法求解特征应变决定的残余问题,可直接得到接触安定状态下的接触残余应力,并随之进行安定极限的判定。采用该数值方法计算了不同曲率处接触点的安定极限,给出了安定极限与摩擦因数之间的关系,并与有关数值结果相比较,验证了该算法的有效性。     

三维结构安定分析的直接算法

基于线性随动强化理论和Von. Mises屈服准则,对蒙板结构直接安定分析法进行了扩展,建立了结构的三维安定直接分析法。根据投射原理,推导出结构发生塑性安定的存在条件,便于调整控制加载步长和载荷历程。采用逐次增量加载方式,确定出背应力的偏移范围,克服了原始直接分析法不能获得安定极限的缺陷,并得到安定极限条件下结构中残余应力与应变的分布状况。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,节约计算时间,提高计算效率,将该算法应用于相关算例,并与有关数值结果相比较,验证了该算法的有效性。     

Bounds for shakedown of cohesive-frictional materials under moving surface loads

In this paper, shakedown of a cohesive-frictional half space subjected to moving surface loads is investigated using Melan’s static shakedown theorem. The material in the half space is modelled as a Mohr–Coulomb medium. The sliding and rolling contact between a roller and the half space is assumed to be plane strain and can be approximated by a trapezoidal as well as a Hertzian load distribution. A closed form solution to the elastic stress field for the trapezoidal contact is derived, and is then used for the shakedown analysis. It is demonstrated that, by relaxing either the equilibrium or the yield constraints (or both) on the residual stress field, the shakedown analysis leads to various bounds for the elastic shakedown limit. The differences among the various shakedown load factors are quantitatively compared, and the influence of both Hertzian and trapezoidal contacts for the half space under moving surface loads is studied. The various bounds and shakedown limits obtained in the paper serve as useful benchmarks for future numerical shakedown analysis, and also provide a valuable reference for the safe design of pavements.     

A minimum theorem for cyclic load in excess of shakedown,with application to the evaluation of a ratchet limit

Although the shakedown theorems for perfect plasticity have been known since Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not appeared in the literature. In this paper a generalisation of the upper bound theorem is derived which reduces to the upper bound shakedown theorem in the limiting case when the load point approaches the shakedown boundary. The new theory is used to develop a method for identifying the ratchet limit for a class of loading histories through the sequential minimisation of two functionals. A programming method, based on the Elastic Compensation method for shakedown is then derived and convergence proven. Numerical examples of the application of the method to practical problems are discussed by us in an accompanying paper.     

SIMPLE SHAKEDOWN OF STRUCTURES UNDER VARIABLE MULTI-LOADINGS

The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the self-equilibrium of fixed stresses field is analyzed. Elastic shakedown and plastic shakedown conditions are presented based on the fixed stresses field. The theorem is convenient to evaluate the shakedown limit of structures under cyclical variable multiloadings through solving positive scalar fields and fixed stresses field factors at a series of dangerous positions of the structure, and tedious computations are avoided. Finally the theorem is applied to a thick-walled cylindrical tube under variable pressure and temperature, and the rolling contact problem. The results are in good agreement with some computational results.     

Limit and shakedown analysis under hydrogen embrittlement condition

A modified shakedown theorem and its solving technique are presented to involve hydrogen embrittlement of steel into limit and shakedown analysis. Firstly, the shakedown theorem for hydrogen embrittled material is derived from a limited kinematic hardening shakedown theorem and hydrogen enhanced localized plasticity mechanism of hydrogen embrittlement. In the presented theorem, hydrogen’s effect is taken into account by the synergistic action of both strength reduction and stress redistribution. Secondly, a novel solving technique is developed based on the basis reduction method, in which the complicated constraints in the resulting nonlinear mathematical programming are released. At last, three numerical examples are carried out to verify the performance of the proposed method and to reveal hydrogen’s effect on the limit and shakedown load of structure. The numerical results are discussed and compared with those from literatures, which proves the accuracy and high efficiency of the introduced solving technique. It is concluded that the proposed theorem can predict the limit and shakedown load of hydrogen embrittled structure reasonably.     

不同应变强化模型下结构安定性的研究

变载作用下弹塑性结构的安定性研究是一个有实际意义的课题，而结构的安定性与材料的强化规律有很大关系。本文对几种典型的强化模型下的结构安定性进行了研究，给出了在随动强化和组合强化条件下结构实现安定的条件，所得结论简化了应变强化条件下结构的安定分析。     

ANALYSIS OF SHAKEDOWN OF FG BREE PLATE SUBJECTED TO COUPLED THERMAL-MECHANICAL LOADINGS

The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures.     

Shape optimization for elasto-plastic deformation under shakedown conditions

An integrated approach for all necessary variations within direct analysis, variational design sensitivity analysis and shakedown analysis based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behavior is formulated. Using an adequate formulation of the optimization problem of shakedown analysis the necessary variations of residuals, objectives and constraints can be derived easily. Subsequent discretizations w.r.t. displacements and geometry using e.g. isoparametric finite elements yield the well known ‘tangent stiffness matrix’ and ‘tangent sensitivity matrix’, as well as the corresponding matrices for the variation of the Lagrangian-functional which are discussed in detail. Remarks on the computer implementation and numerical examples show the efficiency of the proposed formulation. Important effects of shakedown conditions in shape optimization with elasto-plastic deformations are highlighted in a comparison with elastic and elasto-plastic material behavior and the necessity of applying shakedown conditions when optimizing structures with elasto-plastic deformations is concluded.     

An Improved Upper Bound to Maximum Deflections of Elastic-Plastic Structures at Shakedown

ABSTRACT

A method is presented providing an upper bound to the maximum shakedown deflections for elastic-perfectly plastic structures. The influence of plastic zones is taken into account. Residual stresses required by the Melan theorem can be expressed in terms of stresses due to ideal plastic hinges and of stresses due to the finite extent of plastic zones. Making use of this fact a bound on the total energy dissipated in a shakedown process as well as a bound to the permanent displacement have been derived. This bound permits an estimate of the deflections at shakedown. Application of the method is illustrated by means of two examples.     

含缺陷轴对称体的安定与极限分析

利用静力安全定理得到了计算轴对称体安定与极限载荷的统一格式，采用温度参数法构造安定分析所需的残余应力场，为了克服对工程实际问题进行安定分析时解题规模与计算精度的矛盾，针对轴对称体的特点，采用两种线性化方案对屈服面进行线性化处理，即直接内接法和在降维应力偏量空间中对屈服面的线性化处理，使安定分析转化为一线性规划问题，在简化过程中合理选择线性化方案以便使应力校核点接近精确的屈服面；为了减小计算量，在求