极限下限分析的正交基无单元Galerkin法

基于极限分析的下限定理，建立了用正交基无单元Galerkin法进行理想弹塑性结构极 限分析的整套求解算法．下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接 得到，所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模 拟．这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到．通过对自平衡应力场 子空间的不断修正，整个问题的求解将化为一系列非线性数学规划子问题，并通过复合形法 进行求解．算例表明该方法有效地克服了维数障碍问题，使计算效率得到了充分的提高，是 切实可行的．     

轴对称结构极限下限分析的自然单元法

作为一种基于自然邻近插值的新型无网格法,自然单元法克服了大多数无网格法难以施加本质边界条件的困难．将自然单元法与减缩基技术相结合,建立了一种轴对称结构极限下限分析的数值格式和求解算法．通过不断修正自平衡应力场,轴对称结构极限下限分析可转化为一系列的非线性数学规划子问题,并由复合形法求解．在每个非线性规划子问题中,自平衡应力场表示为一组带有待定系数的自平衡应力场基矢量的线性组合,并且这些自平衡应力场基矢量可由弹塑性增量分析的平衡迭代结果得到．算例结果表明,本文所提的轴对称结构极限下限分析方法行之有效．     

下限原理在岩土工程中的应用

采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合，把整个结构离散化，设定每个结点的应力，把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数，以结点应力为优化变量，以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题，得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场，解决了三维可静应力场的构造问题。算例分析表明，本文的方法是正确、可行的。     

梁系结构上限极限分析的弹性模量缩减法

结合线弹性梁系有限元法和弹性模量缩减法,提出了梁系结构上限极限的分析方法。该方法根据构件截面广义屈服准则定义了梁系结构的单元承载比,得到了弹性模量缩减法的模量调整策略,利用梁系有限元法构造出了逼近极限状态的广义应力场以及系列机动允许位移场;同时推导出考虑弯矩和轴力共同影响下的梁单元弹性应变能和塑性耗散功计算公式,建立了梁系结构上限荷载乘子迭代算法。该算法继承了弹性模量调整法原理简单、应用方便等优点,并可应用于具有不同几何特性和材料特性构件构成的复杂结构中。算例分析表明:本文算法具有良好的计算精度和迭代稳定性,通常可在30个线弹性迭代步以内得到与解析法或其他算法在4%以内的极限分析结果。     

接触问题应力分析的混合解法

接触问题是一个极其复杂的非线性问题，单独使用数值方法或实验方法求解应力都有一定的困难．有限元计算与平面光弹性实验相结合的混合法是对接触问题进行应力分析简单而有效的途径．     

基于圆筒模型的热障涂层安定分析

热载荷作用下,由于热障涂层(thermal barrier coatings, TBCs) 各层材料的热不匹配以及材料参数的温度相关等因素,会使热障涂层界面区域存在复杂的应力应变场,影响系统安定性,并导致涂层开裂和剥落. 将热障涂层外凸和内凹微观界面结构简化为多层圆筒模型,借助经典机动安定定理,利用特雷斯卡(Tresca) 屈服准则和增量破坏准则处理对时间的积分问题,避免了常规安定性分析的数学规划问题,建立了热障涂层安定极限分析方法,将材料屈服强度随温度变化关系简化为双线性关系,利用补偿变换的方法简化求解过程,对典型热障涂层安定性进行了研究. 结果表明,利用基于圆筒的安定极限分析方法,能够方便求解安定极限,便于工程应用;热障涂层安定极限值明显高于弹性设计值,且界面外凸区域安定极限高于内凹区域极限值,结构首先在内凹处失效;圆筒模型基体曲率和涂层厚度越大,结构安定极限越高,分析结果与试验结果一致;所建立的热障涂层安定分析方法,对进一步研究考虑蠕变因素影响的热障涂层安定性具有重要意义.      

柔弹性结构空间形态的非线性分析

计算力学领域柔软弹性结构的非线性分析是特别复杂的课题,更加困难与令人易于受挫的研究方向就是柔软弹性结构在各种复杂外力作用下的成形分析（Form Finding)或者平衡构形曲线的寻找,迄今为止的研究者大都局限于周边固定约束下求解柔软弹性结构的平衡曲线,因此其计算方法不具备广泛适用性,本文提出的动边界支座位移非线性迭代法成功地解决了这一问题,在工程上具有重要的应用价值。     

不排水双层粘性土地基极限承载力的数值分析

采用弹塑性有限元分析了条形基础作用下不排水条件的双层粘性土地基极限承载力性状。采用修正的地基承载力系数表征,并将不同的几何与土层参数条件下的数值解与上下限解和经典的经验解进行比较。表明弹塑性位移有限元法可以很好地求解地基的极限承载力问题,其求解得到的修正地基承载力系数与基于下限原理的有限元解很接近,而上限解高估了地基的极限荷载值,传统的经验解在某些条件下却偏小。     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

用材料力学解的切应力求解弹性力学问题

分析了切应力与正应力的关系,讨论了导出切应力公式的条件,提出按切应力求解弹性力学问题的方法.证明凡是σ_y与x无关的梁或者已知切应力为零的问题,按切应力求解都是可行的.用这种方法求解比传统方法方便,运算简单.该文给出了用切应力求解弹性力学平面问题的两个算例.     

A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead of the finite element method is used to perform lower bound limit and shakedown analysis of structures. The self-equilibrium stress fields are constructed by a linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains and obtained through elastic-plastic incremental analysis. The complex method is used to solve nonlinear programming and determine the maximal load amplifier. The limit analysis is treated as a special case of shakedown analysis in which only the proportional loading is considered. The numerical results show that SGBEM is efficient and accurate for solving limit and shakedown analysis problems. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctorial Dissertation of China (No. 200025) and the Basic Research Foundation of Tsinghua University.     

Lower bound limit analysis of three-dimensional elastoplastic structures by boundary element method

IntroductionThelimitanalysisofstructuresisoneofthemostpracticalandusefulbranchesinplasticity .Ithasimportantapplicationbackgroundforproblemssuchasthedeterminationofloadcarryingcapacityandplasticformingofmetal.Thepurposeofthelimitanalysisofstructuresistoprovidereliabletheoreticalbasesforengineeringdesignandsafetyassessment.Asasimplifiedmethodforelastoplasticproblems,limitanalysisneednotrequirethehistoryofloadandcancomputethelimitloadsdirectlyinsteadofelastoplasticincrementalcomputationwhichisus…     

Upper-bound limit analysis based on the natural element method

The natural element method (NEM) is a newly-developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic theorem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nonsmoothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.     

弹性——粘弹性复合结构的动态载荷识别

提出了一种识别弹性－－粘弹性复合结构动态载荷频域方法。首先将复合结构利用约对值模态应变能方法（ＡＶＭＳＥ）进行模态分析而获得模态参数，其次在频域中通过模态变换法求得动态载荷谱。通过两个算例说明方法的应用，其结果表明该方法是有铲的，识别精度是好的。并对该方法应用中的一些问题进行了讨论。     

含凹坑缺陷圆柱壳的数值极限分析

使用文［１］提出的三维结构塑性极限分析的一般计算方法，我们对含凹坑缺陷的圆柱壳进行了数值极限分析．对凹坑和筒体各种组合的几何参数，本文给出了筒壳极限压力的上限．计算结果与现有的理论、实验和数值解进行了比较．本文调查和评估了各种形状和尺寸的凹坑对筒壳极限承载能力的影响规律，研究了对应于不同凹坑尺寸的筒壳两种典型的破坏模式．根据以上数值结果，本文采用几何参数Ｇ来反映凹坑各参数对筒壳极限压力的综合影响，并给出了估计带凹坑筒体极限压力的拟合公式．本文结果对含凹坑缺陷压力容器的安全评估具有重要参考价值     

Spinning rods, elliptical disks and solid ellipsoidal bodies: Elastic and plastic stresses and limit spins

The analysis of the stresses in one-, two- and three-dimensional spinning bodies is discussed in a systematic and comprehensive way. First elastic solutions are derived for rods, for elliptical-shaped flat disks and for ellipsoidal solid bodies spinning about their sideways axes. Then the spins for first plastic yield are found in each case using each of the Tresca and the von Mises yield conditions. Then upper and lower bounds on the maximum allowable limit spins where the body would globally fail assuming perfectly plastic behavior are derived. The elastic solutions at first yield always give a lower bound to that limit spin, but global failure generally does not occur until the spin is increased. A way to calculate an improved lower bound is illustrated. Upper bounds are found in a simple and new way. The method uses the fact that the volume-averaged stresses can be calculated directly from the loadings without the need for any actual stress solutions, and then it is proved that the use of those average stresses in the yield functions always gives an upper bound to the limit loads. That use of the statically determinate average stresses to obtain meaningful plastic upper bounds to limit loads is though to be a new method, and can be applied to any shape. Finally, several finite element calculations are used to determine the quantitative relations between the lower and upper bounds and the actual limit spins for ellipsoidal bodies.The results are of interest in the spin of planetary bodies, where they explain the nature of an average-stress approximate method, and in the analysis of spinning bodies in general. In addition, the approach gives a very interesting example of the utility of the limit analysis approaches of plasticity theories.     

PLASTIC LIMIT ANALYSIS OF DUCTILE COMPOSITE STRUCTURES FROM MICRO-TO MACRO-MECHANICAL ANALYSIS

The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.     

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.     

Structural stability and failure analysis using peridynamic theory

The peridynamic theory has been successfully utilized for damage prediction in many problems. However, the elastic stability of structures has not been studied using the peridynamic theory. Therefore, this paper investigates the elastic stability of simple structures to determine buckling characteristics of the peridynamic theory by considering two sets of problems. The first set of problems involves rectangular columns under compression to find the effects of the cross-sectional area and boundary conditions on buckling load. The second set involves rectangular plates under a uniform temperature load to establish the effects of plate dimensions and material properties on the critical buckling temperature. The predictions of the peridynamic theory agree with those published in the literature. The solution method is based on reducing the peridynamic equations of motion to discrete forms by using collocation points. These discrete equations are then solved using adaptive dynamic relaxation. Furthermore, perturbation method using geometrical imperfections is utilized to trigger lateral displacements in the numerical solutions.