幂强化弹塑性材料平面应变反问题

幂强化弹塑性材料在工程领域诸如金属管材制备、岩土工程分析中都具有广泛的应用。幂强化弹塑性材料的本构参数（例如弹性模量）和结构的边界条件（例如位移）往往不容易确定。在这种情况下,反问题为确定这些参数提供了一种新思路。将ABAQUS二次开发的子程序和复变量求导法结合,用于求解基于幂强化弹塑性材料的平面应变力学反问题:以传统的用户单元子程序为框架,将程序中实数变量转换为复数,建立了复数用户单元;采用复变量求导法确定测点位移对反演参数的灵敏度矩阵;结合最小二乘法和高斯消去法对反问题进行迭代求解。给出应用算例讨论了复变量求导法对正问题计算精度影响、算法在反问题求解过程中的精度,以及反演初值、测量误差对反演结果的影响。     

探讨混凝土坝空间位移场的正反分析模型

本文应用场论和力学分析,提出了结合实测资料,建立坝体、坝基和库盘整体的空间位移场正反分析模型的方法,以及考虑因子相关与不相关两种情况时,提出了反演坝体、坝基和库盘分区分层与整体变形参数的方法.上述理论和方法已成功地应用于龙羊峡工程,解释了该坝蓄水以来运行中出现的变形疑点的成因.     

结构物理参数时域识别的子结构方法研究

研究了输入、输出信息皆不完备情况下的结构参数识别以及荷载反演问题。阐述了一种通用的子结构动力方程及其参数识别方程建立的基本原理和方法,并针对实际工程检测中子结构参数识别方程的输入特性,分别采用一种与之相适应的分解反演算法或统计平均算法。子结构技术与分解算法或统计平均算法的有效结合,为有限测点条件下的结构参数识别及荷载反演问题提供了一个较好的解决方案。大量的数值计算结果表明,本文提出的方法具有很好的参数识别精度及荷载反演效果。     

弹塑性位移反分析的遗传算法研究

弹塑性位移反分析问题的目标函数具有多个极小值, 用常规的数学优化方法求解该优化问题时,时常出现陷入局部极小而无法继续寻优的状态。为了克服这一缺陷,应用遗传算法原理建立了弹塑性位移反分析的遗传算法,并应用其对所设定的弹塑性问题进行了反演,反演结果的精度达90%以上。     

非均匀损伤介质中利用波传播理论对损伤参数的反演

介绍了波在非均匀损伤介质中的传播的反问题,根据波的响应来反演介质的损伤。首先应用Newton迭代法把非线性问题化为线性问题,得到一组不适定的线性方程式组,采用Tikhonov正则化求解,对于正则参数选取采用L线曲线准则,求出了原问题的稳定的、有效的解,获得了与真实损伤度较为吻合的反演参数。工程实例的模拟分析计算证明了上述算法的有效性。     

动态卸荷诱发节理岩体松动的数值模拟

高地应力条件下岩体开挖面临着初始地应力动态卸荷诱发的节理松动问题。为了提出控制节理松动方案,采用理论与数值模拟方法研究了初始地应力动态卸荷诱发节理松动机理。首先,将计算模型与简单的初始应力瞬态卸载理论结果进行了对比,验证了计算模型及其参数的正确性。其次,采用动力松弛法对地应力初始化,计算了地应力水平、卸荷路径以及卸荷时长对节理岩体松动的影响。结果表明:节理岩块张开位移与卸荷时长成负相关,与地应力水平成正相关;相同条件下,指数型卸荷路径引起的节理岩体刚体位移最大,三角函数型卸荷次之,线性卸荷最小。建议工程中通过改善装药结构和孔间距等钻爆参数来增加卸荷时长,从而有效地控制节理岩体松动效应。     

蚁群算法求解弹性本构参数区间反问题

建立了弹性本构参数区间反问题的数值模型,利用区间参数摄动有限元方法和基于网格划分策略的连续域蚁群算法进行求解,探讨了非均质、不确定区间半径、初值选择及数据噪音对反演结果的影响,数值验证给出令人满意的结果。     

基于ObjectARX的三维分形参数化绘图系统的研究

三维分形图形对自然景物的模拟具有较好的效果,为方便三维分形图形在AutoCAD软件中的使用,对三维分形图形的参数化设计进行了研究,并基于ObjectARX开发了三维分形参数化绘图系统。以三维分形岩石为例介绍了该绘图系统的参数化设计过程,即在研究三角形中点位移法生成分形曲面的基础上,提出了一种改进的中点位移法算法,使其生成为多面体,通过对多面体的参数控制可使之生成形态各异的三维分形岩石,经过着色渲染后,具有较强的真实感。     

模拟退火算法在线热源反问题数值求解中的应用

提出采用模拟退火算法(simulated annealing,SA)来数值求解线热源反问题.探讨了如何设计算法使之适合反问题求解,并给出了算法求解的伪代码;通过线源正问题的模拟数据,使用设计的SA算法进行反问题求解,以此来验证算法求解的准确性和可靠性,并对一组实测数据进行了计算.结果表明,该算法不但可以实现两个参数同时、快速反演,而且具有求解精度高,对初始条件依赖少,编制容易等优点.     

基于合成孔径雷达图像内波参数反演方法

总结了目前已有的通过合成孔径雷达图像反演内波参数的方法,并按照内波深度、波速、特征宽度以及振幅的分类对不同的方法进行了描述.将各种参数反演方法应用于合成孔径雷达图像,对内波反演结果与同一区域的实测数据进行了比较.首次对同一内波参数的不同反演方法进行对比,并对各参数反演方法的适用条件进行了讨论.     

地应力条件下爆破载荷破岩的DDA模拟研究

为探究地应力条件下的岩石爆破破岩特征与机理,基于非连续变形分析(DDA)方法建立岩石爆破力学模拟模型,分别考虑爆生气体压力和爆炸应力波的爆破载荷作用形式,对双向等值和不等值地应力条件下均质岩石的单孔爆破进行数值模拟,研究地应力对爆生气体压力和爆炸应力波破岩效果的影响。结果表明:对于均质岩石,在双向等值初始地应力条件下,爆破裂纹区近似为圆形,其面积随初始地应力的增大而减小,且双向等值初始地应力大小的变化对爆炸应力波的破岩作用影响更大;在双向不等值初始地应力条件下,爆破裂纹区呈扁平形,裂纹主要朝较大压应力方向扩展,且侧压系数的变化对爆生气体的破岩作用影响更大。研究结果对爆破工程实践具有一定的理论参考意义。     

Inverse analysis of geomechanical parameters by the artificial bee colony algorithm and multi-output support vector machine

Geomechanical parameters play a very important role in geotechnical engineering design and construction. Inverse analysis provides a powerful tool to characterize geomechanical parameters based on the behaviour of rock under certain boundary conditions. In this paper, a new method for inverse analysis that takes advantage of multi-output support vector machine (MSVM) and artificial bee colony (ABC) is proposed and applied to solving a real field problem. MSVM is used to map the relationship between geomechanical parameters and displacements. ABC is adopted in inverse analysis to find the optimal geomechanical parameters. The proposed method is used to recognize the parameters of the permanent shiplock slope of the Three Gorges in China. Results show that the proposed method can effectively determine geomechanical parameters.     

A deforming finite element method analysis of inverse Stefan problems

A deforming FEM (DFEM) analysis of one-dimensional inverse Stefan problems is presented. Specifically, the problem of calculating the position and velocity of the moving interface from the temperature measurements of two or more sensors located inside the solid phase is addressed. Since the interface velocity is considered to be the primary variable of the problem, the DFEM formulation is found to have many advantages over other traditional front tracking methods. The present inverse formulation is based on a minimization of the error between the calculated and measured temperatures, utilizing future temperature data to calculate current values of the unknown parameters. Also, the use of regularization is found to be useful in obtaining more accurate results, especially when the interface is located far away from the sensors. The method is illustrated with several examples. The effects of the location of the sensors, of the error in the sensor measurements and of several computational parameters were examined.     

First-order perturbations of reflective surfaces and their effects in interferometric testing of mirrors

The equations are derived which relate first-order perturbations of a mirror surface to the optical path difference (OPD) function observed during interferometric centre-of-curvature null tests. Rigid body displacements in particular and their effects on the Fourier coefficients of the OPD function are then considered. Next, the linearity of the rigid body component of the OPD is shown to lead to a method, based on the generalized matrix inverse, for aligning mirrors. Finally, the limits of the validity, in terms of the magnitude of local displacements, of our linear model are analysed. The result of the analysis is a concise, conceptually appealing treatment of general surface deformations in the interferometric regime and a matrix formulation for the particular case of rigid body displacements in the centre-of-curvature null interferometer configuration. This robust formulation treats interferometrically measured OPD functions as state vectors and small deformations as linear transformations of these vectors.     

Application of optical deformation analysis system on wedge splitting test and its inverse analysis

An alternative approach of fracture tests evaluation based on optical measurements of displacements is investigated in this paper. The non-linear hinge model based inverse analysis outgoing from the optically measured crack mouth opening displacements is introduced for the wedge splitting test. Results of the inverse analysis are compared with traditional inverse analysis based on clip gauge data. Then the optically measured crack profile and crack tip position are compared with predictions done by the non-linear hinge model and a finite element analysis. It is shown that the inverse analysis based on the optically measured data can provide material parameters of the fictitious crack model matching favorably those obtained by classical inverse analysis based on the clip gauge data. Further advantages of using of the optical deformation analysis lie in identification of such effects as aggregates bridging and crack branching. These effects would remain hidden if the crack profile is simulated by a model based on the fictitious crack model.     

An inverse method for determining elastic material properties and a material interface

A numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two-dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg-Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.     

结构影响线识别：反问题可识别性分析与降维贝叶斯不确定性量化

结构影响线识别是移动荷载下既有结构评估的理论基础,其本质上是基于系统输入-输出含噪数据反向对静力系统指定截面的响应函数进行识别。已有研究虽然取得了进展,但它们在以下两个方面存在局限性：缺乏反问题可识别性分析;缺乏不确定性量化。反问题可识别性分析是为了厘清系统识别的参数的解的情况。不确定性量化是基于测量输入-输出含噪数据估计影响线参数的后验概率密度函数。针对上述两个局限性,该文在贝叶斯概率框架的基础上开展关于影响线识别的反问题可识别性分析与贝叶斯不确定性量化。该文进行基于直接参数化的影响线识别,包括系统输入与输出、反问题可识别性分析、参数最优值。经分析得出：一方面,直接参数化无法保证全局模型可识别;另一方面,现有方法即使是全局模型可识别的情况下也无法进行不确定性量化。为保证反问题是全局模型可识别且同时获取参数后验概率密度函数,该文提出基于降维贝叶斯不确定性量化的影响线后验识别,包括系统输入与输出重构、反问题可识别性分析、后验概率密度函数。该文进行模拟数据下新光大桥吊杆拉力影响线识别,与实测及模拟数据下简支梁桥应变影响线识别,验证提出方法的有效性。     

软岩巷道全断面锚注加固的力学原理与应用

通过对全断面锚注加固巷道周边围岩应力分布规律、极限平衡区范围及周边位移的计算分析，系统地论证了软岩巷道全断面锚注加固的力学原理，给出了确定锚注加固参数的理论设计计算公式；对全断面锚注加固维护巷道的作用机制作出了科学的解释。结合现场工业性试验软岩巷道传统锚喷加固方式和全断面锚注加固方式维护效果的对比，证明了全断面锚注加固的理论意义和实际应用价值。     

Determination of the state parameters of explosive detonation products by computational inverse method

A computational inverse method is presented to determine the state parameters of Jones-Wilkins-Lee (JWL) equation of explosive detonation products based on cylinder test. In this method, the inverse problem of identifying the JWL parameters is formulated through minimizing the errors of the measured radial displacements on the cylinder surface and those computed by the forward solver. An available numerical model simulated by finite element method is built for the sake of obtaining results using the given JWL parameters. Because of the difference of coordinate systems between experiment and numerical model, it is necessary to conduct the transformation between the two coordinate systems. The sensitivity analysis method is adopted to evaluate the influence of the JWL parameters on the responses and find out the parameters those are suitable to be identified. In order to improve the computational efficiency, radial basis function approximate model is constructed to replace the time-consuming numerical model. In the process of constructing approximate model, the truncated singular value decomposition method is used to deal with the ill-condition of the model. At last, the intergeneration projection genetic algorithm is adopted to identify the parameters. The numerical results demonstrate that the proposed inverse method is potentially available to effectively identify the JWL parameters.     

Finite element analysis of rubber-like materials by a mixed model

A Reissner type variational principle is utilized to formulate a mixed finite element model for a finite-strain analysis of Mooney-Rivlin rubber-like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four-node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick-walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is decreasing.