压电智能结构荷载识别方法的研究

采用压电智能结构实测荷载的输出响应，基于BP神经网络与有限元逆分析提出一种识别荷 载位置及大小的方法. 首先在结构的不同位置施加单位荷载由有限元方法计算得到网络的学 习样本，经网络作逆分析识别荷载位置，继而通过有限元逆逼近方法确定荷载大小的最小二 乘解. 数值算例表明，该方法计算速度快、精度高，不受结构几何形状和边界条件的限制， 用于识别实际压电智能结构不确定荷载的位置及大小是可行的.     

组合截面轴压短柱的非线性有限元分析

圆管或方管内填充另一种工程材料构成的组合截面构件（如钢管混凝土）在工程结构中得到了广泛的应用。本文借助商用有限元分析软件ABAQUS，利用软件子程序接口，引入应力场变量，来考虑两种材料本构关系的非线性以及受力过程中Poisson比、模量的变化等因素，建立了组合截面短柱在轴心压力作用下的非线性有限元计算模型。并通过数值算例，计算了组合截面短柱在轴心压力作用下两种材料共同受力工作的荷载－变形曲线，与试验结果基本符合，同时得到了管材对核心材料约束的变化规律。     

改进的随机有限元法

本文以有限元方法为基础,导出了结构荷载效应特征函数算式。由此,可确定结构荷载效应分布概型及其数字特征。     

考虑动荷载响应的结构形状优化设计研究

以产生相同位移场为基础，将动荷载转化为一系列的等效静荷载，然后将这些等效静荷载作为多个载 荷工况进行有限元优化设计分析. 通过几个算例的验证，表明这种基于动荷载等效转换的算 法能够反映动荷载对结构的动力响应，对具有大规模自由度的结构形状优化问题是有效的.     

爆炸冲击震动对砖墙破坏作用的数值模拟

砖墙在爆炸冲击震动作用下的动力反应非常复杂，本构关系很难精确建立。本文阐述了砖墙几种常用的有限元模拟方法，分析各种方法的优缺点，确定采用一种砖块和砂浆分开的精细化建模的三维砖墙有限元模型；通过LS-DYNA软件，得到砖墙在水平爆炸冲击震动荷载下的破坏过程，计算结果与实验现象很好。研究表明:该种分析模型综合考虑了砖块和砂浆之间复杂的相互作用，并且对砂浆层进行了单独建模，保证了砖墙在数值模拟上的真实性和正确性，因此可以准确地模拟出实验中砖块之间砂浆层的损伤积累破坏。     

跨中集中荷载作用下弹性约束圆弧拱的稳定性分析

研究了跨中集中荷载作用下两端由不同转动刚度弹性约束的铰支圆弧拱的面内稳定性。由变形几何关系、变分原理得到了拱的非线性平衡方程,建立了外荷载、结构内力、径向位移的对应关系,通过定义拱的深浅参数和约束刚度参数进行分析,并得到了跳跃屈曲和分岔屈曲的发生条件及存在区间。通过数值分析可知本文方法所得屈曲路径和屈曲荷载与有限元法所得结论吻合良好,极值点、临界荷载相对差值在1%左右。对不同结构参数区间圆弧拱在集中荷载作用下的屈曲路径和临界荷载进行了分析,结果表明约束刚度对屈曲路径和临界荷载起决定性的作用,深浅参数决定屈曲发生条件、屈曲形式、极值点对数。     

一种变厚度的精化壳体理论及其应用

在Reddy型高阶壳体理论的基础上，采用沿壳体厚度方向的剪切应变呈抛物线分布并且能够满足在壳体的上下表面为零的假设，发展出了一种适合于对变厚度壳体进行非线性分析的方法。该方法利用Ritz原理得到问题的控制方程。通过对一种典型的变厚度壳体结构（子午线轮胎）的结构分析，该方法的计算结果与商用有限元软件的三维分析结果能够很好的吻合。表明了该方法的适用性和有效性。     

爆炸荷载作用下地下拱形结构动力响应样条小波有限元研究

采用小波有限元方法研究爆炸荷载作用下地下结构的动力响应,克服在模拟过程中由于材料的奇异性、地质条件的复杂性和加载的快速性出现的应力集中和计算效率低下,根据样条有限点法,构造了单向和双向区间B样条圆环扇形小波单元,用尺度函数作为插值函数;结合工程实例,通过Matlab软件编程对爆炸荷载作用地下拱形结构的动力响应进行了数值模拟,并与应用传统有限元程序模拟结果进行对比。结果表明,小波有限元用很少单元取得了较高的精度,计算效率比传统有限元提高一倍。     

动力松弛法在应变软化类结构有限元静力分析中的应用

结构静力分析中常因材料应变软化使得相应定解问题失去适定性，从而导致有限元分析不收敛。为解决此问题，在已有的相关研究基础上，采用动力松弛法（DRM）求解结构非线性有限元静力分析的增量步，将其应用于损伤型本构所描述的结构软化问题。本文方法依据两个原理，其一是苏联《数学百科全书》论述的原理——定义于时间域的任何定解问题适定可解，其二是DRM所用的原理——质量系统静力解为相应动力解的稳态部分。且DRM无需进行隐式静力分析时的总体刚度矩阵组装和求逆计算。本文用加荷载增量求解静力平衡路径硬化段，用加位移增量求解极值点和软化段。数值试验表明，本文方法能完成应变软化类结构的静力平衡路径求解。     

含模糊参数结构有限元方程的一种新解法

实际工程问题中，常常会包含一些难以准确描述的系统参数。本文根据模糊集理论，将结构中的不确定参数转化为模糊参数，从而建立起含模糊参数的有限元平衡方程，应用一般模糊线性方程解的基本原理，对模糊有限元平衡方程解的概念及方法进行了讨论，并在此基础上提出了一种改进解的概念以及以摄动法为基础的求解方法。该方法假定当不确定参数相对于其清晰值的分解度不很大时，可以将其在清晰值附近作摄动展开。文中也简要讨论了改进解与现有的模糊有限元方程组各种解之间的关系。相对于现有的其它解法，本文建议的方法更易于与常规的有限元软件结合，用于处理工程实际问题。对算例结果的分析表明，本文方法可较好地符合实际要求。     

A variational asymptotic micromechanics model for predicting thermoelastic properties of heterogeneous materials

A variational asymptotic micromechanics model has been developed for predicting effective thermoelastic properties of composite materials, and recover the local fields within the unit cell. This theory adopts essential assumptions within the concept of micromechanics, achieves an excellent accuracy, and provides a unified treatment for 1D, 2D, and 3D unit cells. This theory is implemented using the finite element method into the computer program, VAMUCH, a general-purpose micromechanics analysis code. Several examples are used to validate the theory and the code. The results are compared with those available in the literature and those produced by a commercial finite element package.     

Analytical and numerical analysis of sheet metal instability using a stress based criterion

Strain based Keeler–Goodwin diagrams are widely used in forming processes to predict onset of local necking. Plastic instability is determined once the forming limit strain is exceeded. Use of these diagrams requires proportional strain paths, which is not necessarily the case in sheet metal forming operations. In many forming processes, the strain path changes during deformation. This may change the forming limit curve significantly. In the paper, a stress based forming limit criterion is adopted to deal with strain path non-linearities. Comparisons with earlier published work on forming limits are made through analytical considerations. Furthermore, the criterion is implemented into the finite element code LS-DYNA and verified numerically against results from large scale bulge tests.     

Extension of the Linear Matching Method to frame structures made from a material that exhibits softening

This paper considers the problem of evaluating the maximum load that an elastic–plastic frame structure can withstand when material or element softening is present. Here we propose an extension of the Linear Matching Method to take into account material softening. The technique has two major steps: reduction of the total potential energy to obtain the solution of a linear problem and scaling of the resulting mechanism of deformation to maximize the load. Two procedures are evaluated for the second of these steps; a direct approach which simply examines how the solution evolves along a radial path in degree of freedom space, and an incremental method which takes into account how the solution might evolve along paths away from this radial line. It is demonstrated that the incremental approach is more robust and provides stable solutions for high and low levels of softening, but numerical instabilities in the procedure can occur for intermediate degrees of softening.     

一种随机裂纹结构的裂纹扩展路径分析方法

裂纹结构中存在大量不确定性因素,如裂纹长度、材料性质、外部载荷等,裂纹扩展路径的不确定性分析对研究随机裂纹结构损伤和断裂的力学特性并预测其性能及可靠性具有重要意义。本文提出了一种适应于混合载荷模式下随机裂纹结构的裂纹扩展路径分析方法。该方法考虑了裂纹长度、材料性质和外部载荷等的随机性,并通过蒙特卡洛方法对随机参数空间进行采样。采用比例边界有限元方法计算结构应力强度因子,进而模拟单次裂纹扩展路径。在此基础上,通过概率分析方法获得随机裂纹结构中裂纹扩展路径的统计特性。最后给出了两个数值算例验证了本文方法的有效性。     

ENRICHED GOAL-ORIENTED ERROR ESTIMATION APPLIED TO FRACTURE MECHANICS PROBLEMS SOLVED BY XFEM

Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM), which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.     

弹塑性板壳结构非线性有限元分析

本文根据塑性流动理论的基本公式，由隐式积分导出了与路径无关的变量更新算法和一致切线模量。采用单元广义应力应变直接离散塑性流动定律，构造了杂交应力单元一致切线刚度矩阵的显式表达式，编制了结构有限元程序ＳＡＦＥ，数值算例表明：本文的计算方法和计算程序是正确可靠的，可用于弹塑性板壳结构的非线性分析，计算结果屈曲临界载荷和极限承载能力。     

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K _II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.     

Assessment of multiple flat elliptical cracks with interactions

The failure of aging aircraft, pressure vessels and many welded structures is frequently due to elliptical cracks, which arise due to in service operation or the initial fabrication processes. Cracks have the potential to interact. Determination of the residual strength of structure requires an accurate knowledge of the stress intensity factor distribution around the crack front. When interacting cracks prevail, the lack of interaction effect in among multiple cracks may lead to an inadequate evaluation. A hybrid formulation capable of representing stiffness change is developed. This enables the accurate analysis of multiple load path structures containing multiple three dimensional cracks. This procedure complement the standard finite element alternating technique.     

Finite element analysis of the fatigue crack growth rate in transformation toughening ceramics

The fatigue crack growth rate in the zirconia tetragonal polycrystal is analyzed through the finite element method. In order to achieve this purpose, a continuum based constitutive law for materials subjected to phase transformations has been suitably implemented into a commercial finite element code. The fatigue crack growth in a notched beam, subjected to a cyclic four points bending load, has been investigated through a sensitivity analyses with respect to the two most relevant constitutive parameters: one accounting for the amount of the transformation strain and one accounting for the activation energy threshold. The fatigue crack growth rate typical of transforming materials is characterized by two distinct stages: at the beginning of the crack propagation process, the crack growth rate exhibits a negative dependency on the applied stress intensity factor; thereafter, a linear positive dependency is observed. This two stage process is well caught by the finite element model presented in this paper. Moreover, the response of the computational analyses has shown that the strength of the transformation process is determinant for the crack growth process to be arrested.     

考虑结构整体的组合梁极限抗火性能分析

随着对钢结构整体抗火能力的深入理解,人们意识到单个构件的抗火能力与处于结构整体中的构件抗火能力具有很大不同。实际结构是一个高次超静定体系,在火灾下能够进行承载路径的改变和承载方式的调整,从而具有比单个构件更高的抗火能力,同时,处于结构整体中的构件在火灾下的温度膨胀应力对其抗火能力的影响是不可忽视的因素之一。文章推导了组合梁的轴力——弯矩相关曲线,绐出了考虑结构整体性的平板式组合梁结构抗火极限分析方法,并与有限元分析结果进行了对比,为考虑结构整体性的平板式组合梁抗火设计提供了依据。