基于D-P准则的理想弹塑性本构关系积分研究

研究基于D-P准则的理想弹塑性本构关系积分的特点及相应的子增量法。研究说明,作者提出的基于D-P准则的转移应力解析解,从应力调整过程来说相当于线性预测-径向校正方法;从本构关系积分策略来说相当于最近点投射法。最近点投射法具有一阶精度而且是无条件稳定的,而数值稳定性和一致性条件是弹塑性计算收敛的充要条件;作为广义中点法的一个特例,最近点投射法最能适应大的应变增量。理论分析和计算实例都表明,该方法适合于极限分析,在采用较大的荷载增量步时仍能保持较高的数值稳定性和精度。提出了基于D-P准则的子增量法,其中确定子增量步数的公式兼容了Schreyer等人的子增量数表达式。计算实例说明计算精度的提高与子增量的步数大体成正比,在显著偏离比例加载的情况下,单步法仍能取得较高的精度。对一般极限分析课题采用单步法即可。     

广义协调元在薄板弹性皱曲分析中的应用

本文首次利用通用商业有限元软件ABAQUS[1]的用户单元接口功能对广义协调元[5]进行了研究，为广义协调元的发展与应用提供了一种新途径。推导了三角形广义协调平板型壳元GST18的UL格式增量求解方程，并将其引入ABAQUS，分析了在金属压力加工中具有代表性的薄板弹性皱曲问题，并与ABAQUS单元库中的三角形薄壳单元STRI3进行了比较。数值算例表明，广义协调平板型壳元GST18在弹性皱曲分析中具有更好的性能，适合于实际工程的应用。     

叠层复合材料厚板的频率分析

本文引入各向同性材料的弹性厚板理论,提出了一种改进的叠层板理论并给出了一些理论解.在数植分析中,用二次和三次B样条函数构成的样条基对诸独立位移分量进行插值.动力方程建立后,采用广义雅可比法和质量凝聚法联合求解特征值问题.文末给出了一些数值结果及其比较.     

具有非平凡零空间的第二类Fredholm积分方程的有限元解

本文利用线性算子理论中的一些结果,讨论了具有非平凡零空间的第二类Frcdholm积分方程的数值解,给出了正则化解和有限元正则化解的表达式,并得到了近似解的误差估计。     

解广义非线性两点边值问题的一种的O（h^4）方法

对于微分方程的广义两点问题数值解的计算，使用分割算法产生的基函数，陈述了一个高精度的算法。得到的数值例子表明算法是快速收敛的和高精度的。     

广义Pascal矩阵及其代数性质

Pascal矩阵及其推广形式的代数性质的研究在电子工程、组合数学、快速算法、微分方程数值解等领域有着广泛的应用。本文利用多项式空间基变换的方法,新给出了几类广义Pascal矩阵,即广义左-Pascal矩阵、广义右-Pascal矩阵和推广的广义Pascal矩阵的一些代数性质的简洁证明,同时给出了这几类广义Pascal矩阵一些新的代数性质。     

Duffing振子倍周期分岔谱特性

应用半数值近似解析方法验证分析Duffing振子倍周期分岔规律理论结论;用增量谐波平衡法获得高精度高阶谐波半数值近似解析解。该验证过程可弥补实验方法精度提高难及数值方法需通过计算高频分辨率频谱方能有效分析的缺点。结果表明,该分析方法与Feigenbaum理论结论较吻合,证明理论结论的正确性。     

对流占优扩散方程的楔形基无网格法

传统的微分方程数值解方法求解对流占优扩散方程时,往往产生数值震荡现象,为了消除数值震荡,本文构建了一种新的数值求解方法――无网格方法进行数值求解。该方法采用配点法并引入一种新的楔形基函数构建了楔形基无网格方法,不需要网格划分,是一种真正的无网格方法,可以避免因为网格划分而影响计算效率。通过对新的楔形基函数的理论分析,证明了本文方法解的存在唯一性。最后,分别通过一维和二维的数值算例,表明该算法计算精度高,可以有效消除对流占优引起的数值震荡,是一种计算对流占优扩散方程数值解的高效方法。     

碳纳米管水泥基复合材料电学性能数值模拟

采用ANSYS12.0和蒙特卡洛随机方法构建了碳纳米管水泥基复合材料的有限元模型,并基于有限元法分析了碳纳米管长径比、直径和掺量对复合材料有效电阻率的影响,并在此基础上通过有效介质方程对有效电阻率数值解和电阻率实验值进行了拟合。数值计算结果表明,碳纳米管水泥基复合材料有效电阻率的有限元解与解析解较为一致,证明采用有限元法进行电学分析具有可行性;碳纳米管水泥基复合材料有效电阻率随碳纳米管掺量和碳纳米管长径比增加而减小,随着碳纳米管直径的减小而减小;有效介质方程对碳纳米管水泥基复合材料有效电阻率实验值和有限元数值解拟合曲线变化趋势是一致的。     

基于平衡向量的刚架结构极限承载力分析的广义塑性铰法

广义塑性铰法能够保持传统塑性铰的比例特性并据此高效求解杆系结构在多内力联合作用下的极限承载力,克服了传统塑性铰法和精细塑性铰法的局限性。但是由于未考虑前序塑性铰上轴力增量对结构平衡状态的影响,导致刚架结构在部分荷载工况下的计算结果出现较大误差。为此,该文通过建立平衡向量,提出了修正的广义塑性铰法计算格式,从而有效消除了塑性铰上轴力增量导致的不平衡状态及其对计算精度的影响。利用强度折减因子确定各构件在多内力组合作用下的修正截面强度,在此基础上利用齐次广义屈服函数定义单元承载比;根据最大单元承载比及其与外荷载之间的比例关系确定新增塑性铰的位置和荷载增量;进而利用广义屈服准则和转角位移方程建立了平衡向量,据此修正当前加载步的塑性铰位置和荷载增量,从而解决了广义塑性铰法不适用于部分荷载工况的问题;通过与不同方法对比分析,验证了该文方法具有更高的计算精度和计算效率。     

Nonlinear model order reduction based on local reduced‐order bases

A new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced‐order bases is presented. It is particularly suited for problems characterized by different physical regimes, parameter variations, or moving features such as discontinuities and fronts. Instead of approximating the solution of interest in a fixed lower‐dimensional subspace of global basis vectors, the proposed model order reduction method approximates this solution in a lower‐dimensional subspace generated by most appropriate local basis vectors. To this effect, the solution space is partitioned into subregions, and a local reduced‐order basis is constructed and assigned to each subregion offline. During the incremental solution online of the reduced problem, a local basis is chosen according to the subregion of the solution space where the current high‐dimensional solution lies. This is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower‐dimensional solution space. Because it is also applicable to the process of hyper reduction, the proposed method for nonlinear model order reduction is computationally efficient. Its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid‐structure‐electric interaction problems. Copyright © 2012 John Wiley & Sons, Ltd.     

带标志点的LTSA算法及其在轴承故障诊断中的应用

针对非监督式流形学习算法面临的增量式学习问题,提出一种带标志点的增量式局部切空间排列算法.该方法在局部切空间排列算法的基础上,利用最小角度回归算法从原始训练样本中选取标志点,以选取的标志点和新增样本建立所有样本的全局坐标矩阵,利用原始样本低维嵌入坐标和全局坐标矩阵对新增样本的低维嵌入坐标进行估计,并采用全局坐标矩阵特征值迭代方法更新所有样本的低维嵌入坐标.滚动轴承4种不同状态振动数据样本的增量式识别结果表明,本方法在实现局部切空间排列算法增量式学习的基础上,保持了对滚动轴承不同状态样本较高的类别可分性测度.     

A robust adaptive model reduction method for damage simulations

In our opinion, many of complex numerical models in materials science can be reduced without losing their physical sense. Due to solution bifurcation and strain localization of continuum damage problems, damage predictions are very sensitive to any model modification. Most of the robust numerical algorithms intend to forecast one approximate solution of the continuous model despite there are multiple solutions. Some model perturbations can possibly be added to the finite element model to guide the simulation toward one of the solutions. Doing a model reduction of a finite element damage model is a kind of model perturbation. If no quality control is performed the prediction of the reduced-order model (ROM) can really differ from the prediction of the full finite element model. This can happen using the snapshot Proper Orthogonal Decomposition (POD) model reduction method. Therefore, if the expected purpose of the reduced approximation is to estimate the solution that the finite element simulation should give, an adaptive reduced-order modeling is required when reducing finite element damage models.We propose an adaptive reduced-order modeling method that enables to estimate the effect of loading modifications. The Rousselier continuum damage model is considered. The differences between the finite element prediction and the one provided by the adapted reduced-order model (ROM) remain stable although various loading perturbations are introduced. The adaptive algorithm is based on the APHR (A Priori Hyper Reduction) method. This is an incremental scheme using a ROM to forecast an initial guess solution to the finite element equations. If, at the end of a time increment, this initial prediction is not accurate enough, a finite element correction is added to the ROM prediction. The proposed algorithm can be viewed as a two step Newton–Raphson algorithm. During the first step the prediction belongs to the functional space related to the ROM and during the second step the correction belongs to the classical FE functional space. Moreover the corrections of the ROM predictions enable to expand the basis related to the ROM. Therefore the ROM basis can be improved at each increment of the simulation. The efficiency of the adaptive algorithm is checked comparing the amount of global linear solutions involved in the proposed scheme versus the amount of global linear solutions involved in the classical incremental Newton–Raphson scheme. The quality of the proposed approximation is compared to the one provided by the classical snapshot Proper Orthogonal Decomposition (POD) method.     

Concurrent Implementation of the Optimal Incremental Approximation Method for the Adaptive and Meshless Solution of Differential Equations

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, the computational technique is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a posteriori error estimates. Since the basis functions are associated with the nodes only, the method can be viewed as a meshless method. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems. Complicated data structures, expensive remeshing algorithms, and systems solvers are avoided. Computational efficiency is increased by using low-order local basis functions and the parallel direct search (PDS) optimization algorithm. Numerical results are reported for both a linear and a nonlinear problem associated with fluid dynamics. Challenges and opportunities regarding the use of this method are discussed.     

LATIN: A new view and an extension to wave propagation in nonlinear media

The LATIN (acronym of LArge Time INcrement) method was originally devised as a non‐incremental procedure for the solution of quasi‐static problems in continuum mechanics with material nonlinearity. In contrast to standard incremental methods like Newton and modified Newton, LATIN is an iterative procedure applied to the entire loading path. In each LATIN iteration, two problems are solved: a local problem, which is nonlinear but algebraic and miniature, and a global problem, which involves the entire loading process but is linear. The convergence of these iterations, which has been shown to occur for a large class of nonlinear problems, provides an approximate solution to the original problem. In this paper, the LATIN method is presented from a different viewpoint, taking advantage of the causality principle. In this new view, LATIN is an incremental method, and the LATIN iterations are performed within each load step, similarly to the way that Newton iterations are performed. The advantages of the new approach are discussed. In addition, LATIN is extended for the solution of time‐dependent wave problems. As a relatively simple model for illustrating the new formulation, lateral wave propagation in a flat membrane made of a nonlinear material is considered. Numerical examples demonstrate the performance of the scheme, in conjunction with finite element discretization in space and the Newmark trapezoidal algorithm in time. Copyright © 2017 John Wiley & Sons, Ltd.     

A sequential tree approach for incremental sequential pattern mining

“Sequential pattern mining” is a prominent and significant method to explore the knowledge and innovation from the large database. Common sequential pattern mining algorithms handle static databases. Pragmatically, looking into the functional and actual execution, the database grows exponentially thereby leading to the necessity and requirement of such innovation, research, and development culminating into the designing of mining algorithm. Once the database is updated, the previous mining result will be incorrect, and we need to restart and trigger the entire mining process for the new updated sequential database. To overcome and avoid the process of rescanning of the entire database, this unique system of incremental mining of sequential pattern is available. The previous approaches, system, and techniques are a priori-based frameworks but mine patterns is an advanced and sophisticated technique giving the desired solution. We propose and incorporate an algorithm called STISPM for incremental mining of sequential patterns using the sequence tree space structure. STISPM uses the depth-first approach along with backward tracking and the dynamic lookahead pruning strategy that removes infrequent and irregular patterns. The process and approach from the root node to any leaf node depict a sequential pattern in the database. The structural characteristic of the sequence tree makes it convenient and appropriate for incremental sequential pattern mining. The sequence tree also stores all the sequential patterns with its count and statistics, so whenever the support system is withdrawn or changed, our algorithm using frequent sequence tree as the storage structure can find and detect all the sequential patterns without mining the database once again.     

A natural partitioning scheme for parallel simulation of multibody systems

A parallel partitioning scheme based on physical-co-ordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent co-ordinates. Key features of the present scheme include an explicit determination of the independent co-ordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two-stage staggered solution procedure and a Schur complement based parallel preconditioned conjugate gradient numerical algorithm.     

Calibrating color cameras using metameric blacks

Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an ill-conditioned problem that has an infinite number of solutions. We introduce a method to estimate the sensor's spectral sensitivity function based on metamers. For a given patch on the calibration chart we construct numerical metamers by computing convex linear combinations of spectra from calibration chips with lower and higher sensor response values. The difference between the measured reflectance spectrum and the numerical metamer lies in the null space of the sensor. For each measured spectrum we use this procedure to compute a collection of color signals that lie in the null space of the sensor. For a collection of such spaces we compute the robust principal components, and we obtain an estimate of the sensor by computing the common null space spanned by these vectors. Our approach has a number of advantages over standard techniques: It is robust to outliers and is not dominated by larger response values, and it offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional.     

Power distribution network expansion scheduling using dynamic programming genetic algorithm

A genetic algorithm that is dedicated to the expansion planning of electric distribution systems is presented, with incremental expansion scheduling along a time horizon of several years and treated as a dynamic programming problem. Such a genetic algorithm (called dynamic programming genetic algorithm) is endowed with problem-specific crossover and mutation operators, dealing with the problem through a heuristic search in the space of dynamic programming variables. Numerical tests have shown that the proposed algorithm has found good solutions that considerably enhance the solutions found by non-dynamic programming methods. The algorithm has also shown to work for problem sizes that would be computationally infeasible for exact dynamic programming techniques.