Image reconstruction for in-line holography with the Yang-Gu algorithm

A new approach to the numerical reconstruction of wave fronts stored by in-line holography is presented. The new algorithm can achieve good reconstructed results in both unitary and nonunitary systems. The influences of recording distance and noise as well as of digitalization errors on the quality of reconstruction are numerically investigated. The experimental results demonstrate the validity of this new approach.     

Design of microlenses with long focal depth based on the general focal length function

A general focal length function is proposed to design microlenses with long extended focal depth and high lateral resolution. The focal performance of the designed microlenses, including the actual focal depth, the focal spot size, and the diffraction efficiency, is calculated by rigorous electromagnetic theory and the boundary-element method for several f-numbers. In contrast to conventional microlenses, the numerical results indicate that the designed microlenses can exhibit long extended focal depth and good focal performance. It is expected that the long focal length function will be widely used to design microlenses with long focal depth characteristics.     

基于贝叶斯法的复杂有限元模型修正研究

从概率思维角度出发,证明基于最大熵原理的贝叶斯反分析准则函数法和解不适定问题的正则化方法是一致的,提出一种基于信息融合和贝叶斯理论的模型修正方法。该方法采用试验设计构造样本,采用二次响应面作为快速运行模型,通过响应面自身的特性和精度要求进行收敛判断,在响应面迭代中确定信息融合系数（设计规范、有限元计算信息、实测信息）和待修正的设计参数值。该方法充分利用先验信息,迭代计算量较小,可推广至大型复杂非线性结构。某抽水蓄能电站地下厂房结构的有限元模型修正结果验证了该方法的有效性     

弯张换能器的有限元设计

IV型弯张换能器是水声领域中一类低频、大功率换能器，其理论分析通常采用有限元法。利用ANSYS软件建立了800Hz的IV型弯张换能器的有限元模型，进行结构分析与设计。根据分析的结果制作出样机，测试的结果与理论分析基本符合。     

Mixed finite element method for generalized convection-diffusion equations based on an implicit characteristic-based algorithm

Summary A mixed finite element method for generalized convection-diffusion equations is proposed. The primitive variable with its spatial gradient and the diffusion flux are interpolated as independent variables. The variational (weak) form of the governing equations is given on the basis of the extended Hu-Washizu three-field variational principle. The mixed element is formulated with stabilized one point quadrature scheme and particularly implicit characteristic-based algorithm for eliminating spurious numerical oscillations. The numerical results illustrate good performances in accuracy and efficiency of the proposed mixed element in comparison with standard finite element.     

基于有限元法的柔性铰链力学模型和性能分析

为了精确描述柔性铰链力学性能,提出一种通用的基于有限元法的力学模型,并基于该模型分析其静态和动态性能．柔性铰链采用欧拉-伯努利梁模拟其力学行为,将其划分为3个三自由度的结点、2个变截面单元．采用最小势能原理建立与柔性铰链结构参数相关的封闭形式刚度矩阵,采用拉格郎日方程建立铰链的质量矩阵和动力学方程．为了验证所推导的力学模型的精确性,与 ANSYS分析结果进行比较分析,两者的结果差值在1.1％～5.6％范围之内,说明理论模型与ANSYS分析结果吻合,所建立的模型能精确反映其静态和动态性能．基于柔性铰链有限元模型,可精确分析铰链参数与其精度和固有频率的关系、应力分布和频率响应,为正圆型柔性铰链应用于柔顺机构设计提供了一种精确的力学模型．     

有限元模型修正的虚拟拉直算法

在拉直算法的基础上,提出了一种新的有限元模型修正方法.拉直算法主要适合于模型修正模型中的约束方程不出现矛盾方程的情况,而对于出现矛盾的约束方程,修正效果可能会很差,其主要原因是修正变量较少,这也导致了拉直算法不适合于含高阶实验模态数据的修正.因此,为了避免矛盾方程的出现和获得可行的修正模型,提出增加带宽的方式(即附加虚拟元素)以增加未知变量的个数,并提出了虚拟拉直修正方法,该方法可有效地修正含高阶模态的实验模态数据.最后以一个平面框架结构为例来说明本文方法的可行性.     

基于SVR 方法的有限元模型确认中不确定性建模研究

针对模型确认中结构有限元模型不确定性建模问题,采用D最优实验设计方法生成无明显分布规律的样本空间,提出用支持向量机回归（Support Vector Regression）方法建立结构响应和不确定参数之间的映射关系,给出了基于SVR方法进行不确定建模的一般步骤,引入了三级检验对支持向量机响应面模型的精度和泛化能力进行全面评价,以GARTEUR模型为仿真算例,比较了向量机响应面模型和幂多项式响应面模型,结果证明了该方法对模型的不确定性建模问题具有较高的精度,具有较好的推广性。     

基于小波有限元的悬臂梁裂纹遗传优化辨识

利用小波有限元法求解了裂纹悬臂梁的前三阶固有频率,并将其拟合成以裂纹位置和深度作为变量的频响函数曲面。将裂纹识别中的匹配追踪问题转化为多维优化问题,以实测固有频率作为输入,利用遗传算法寻优求解出与输入值相差最小的样本点,进而预测出裂纹的位置和深度。试验研究表明,所提出的裂纹识别方法具有较好的精度和鲁棒性,且易于推广到诸如转子、叶片等复杂结构的裂纹监测诊断场合。     

相控阵超声全聚焦成像算法的有限元仿真研究

基于超声相控阵基本理论和全聚焦成像算法(Total Focus Method,TFM),以30 mm厚的Q235钢板中的孔缺陷检测为研究对象,使用ABAQUS有限元软件,建立了相控阵TFM有限元检测模型。根据模拟结果,在MATLAB软件中编写了相控阵TFM成像算法。同时,采用超声多通道实验平台,对构建的TFM有限元检测模型和编写的相控阵TFM算法进行实验验证。实验结果与有限元模拟结果有较好的一致性。     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

一种基于改进MCMC算法的模型修正方法

标准马尔可夫链蒙特卡罗(MCMC)算法不易收敛、拒绝率高,使其应用受到限制。在贝叶斯方法中引入最大熵值法来估计参数的后验概率密度函数最大值,进而将布谷鸟算法中新鸟巢更新的思想融入Metropolis-Hasting(MH)抽样算法得到改进的MH抽样算法,同时使用支持向量机(SVM)建立待修正参数与有限元模型输出之间的代理模型,以提高模型修正的计算效率。分别使用三自由度线性系统和平面桁架模型来验证本文方法的有效性,结果表明:修正后样本的马尔可夫链混合性能好,停滞概率低,修正后参数相对误差均小于2%。     

On the finite element method for calculating stress intensity factors with a modified elliptical model

A finite element method based on the modification of the elliptical displacement function model developed earlier by the authors is presented for the determination of stress intensity factors in cracked bodies. The modified elliptical model not only retains the simplicity of the original method in describing stress conditions at the crack tips but also extends the application of the method to cases where the elliptical shape of the crack surface is not entirely preserved. The present method avoids the need for successive computations of several strain energies in a cracked body as required by the strain energy approach and of high concentration of very fine elements at the crack tip by the conventional stress approach.

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Résumé On présente une méthode par éléments finis basée sur la modification du modèle de la fonction de déplacements elliptiques développée précédemment par les auteurs, pour déterminer les facteurs d'intensité des contraintes dans des solides fissurés. Le modèle modifié conserve la simplicité de la méthode originale pour décrire les conditions de contraintes aux extrémités d'une fissure. En outre, il permet d'étudier son application à des cas où la forme de la surface de la fissure n'est pas rigoureusement elliptique.La méthode proposée évite de devoir procéder à des calculs en série de plusieurs énergies de déformation dans le corps fissuré, ainsi que le requiert l'approche basée sur l'énergie de déformation. Elle permet aussi de ne pas devoir calculer des concentrations importantes d'éléments à très petites mailles à l'extrémité de la fissure, ainsi que l'exige l'approche concentionnelle basée sur les contraintes.

     

Hyperelastic analysis based on a polygonal finite element method

In this contribution, we present a novel polygonal finite element method applied to hyperelastic analysis. For generating polygonal meshes in a bounded period of time, we use the adaptive Delaunay tessellation (ADT) proposed by Constantinu et al. [1 A. Constantinu, P. Steinmann, T. Bobach, G. Farin, and G. Umlauf, The adaptive Delaunay tessellation: A neighborhood covering meshing technique., Comput. Mech., vol. 42, no. 5, pp. 655–669, 2008.[Crossref], [Web of Science ®] , [Google Scholar]]. ADT is an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. In this work, we have extended the ADT to nonconvex domains using concepts from constrained Delaunay triangulation (CDT). The proposed method is thus based on a constrained adaptive Delaunay tessellation (CADT) for the discretization of domains into polygonal regions. We involve the metric coordinate (Malsch) method for obtaining the interpolation over convex and nonconvex domains. For the numerical integration of the Galerkin weak form, we resort to classical Gaussian quadrature based on triangles. Numerical examples of two-dimensional hyperelasticity are considered to demonstrate the advantages of the polygonal finite element method.     

A contact algorithm for cohesive cracks in the extended finite element method

Cracks with quasibrittle behavior are extremely common in engineering structures. The modeling of cohesive cracks involves strong nonlinearity in the contact, material, and complex transition between contact and cohesive forces. In this article, we propose a novel contact algorithm for cohesive cracks in the framework of the extended finite element method. A cohesive-contact constitutive model is introduced to characterize the complex mechanical behavior of the fracture process zone. To avoid the stress oscillations and ill-conditioned system matrix that often occur in the conventional contact approach, the proposed algorithm employs a special dual Lagrange multiplier to impose the contact constraint. This Lagrange multiplier is constructed by means of the area-weighted average and biorthogonality conditions at the element level. The system matrix can be condensed into a positive definite matrix with an unchanged size at a very low computational cost. In addition, we illustrate solving the cohesive crack contact problem using a novel iteration strategy. Several numerical experiments are performed to illustrate the efficiency and high-quality results of our method in contact analysis of cohesive cracks.     

A contact algorithm for 3D discrete and finite element contact problems based on penalty function method

A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.     

A fully nonlinear multi-parameter shell model with thickness variation and a triangular shell finite element

This work presents a fully nonlinear multi-parameter shell formulation together with a triangular shell finite element for the solution of static boundary value problems. Our approach accounts for thickness variation as additional nodal DOFs, using a director theory with a standard Reissner-Mindlin kinematical assumption. Finite rotations are exactly treated by the Euler-Rodrigues formula in a pure Lagrangean framework, and elastic constitutive equations are consistently derived from fully three-dimensional finite strain constitutive models. The corresponding 6-node triangular shell element is presented as a generalization of the T6-3i triangle introduced by the authors in [3].Fellowship funding from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) and CNPq (Conselho Nacional de Pesquisa), together with the material support and stimulating discussions in IBNM (Institut für Baumechanik und Numerische Mechanik), are gratefully acknowledged in this work.Received December 2003     

Implementation of a constitutive model in finite element method for intense deformation

Since the constitutive information is one of the most important aspects of material deformation analysis, here a new constitutive model is proposed that can investigate the behavior of material during intense deformation better than existent models. The model that is completely based on physical mechanisms can predict all stages of flow stress evolution and also can elucidate the effects of strain and strain rate on flow stress evolution of material during intense plastic deformation. Here as an application, implementation of the constitutive model in finite element method (FEM) is used to compare two methods of sever plastic deformation (SPD) processes of copper sheet; repetitive corrugation and straightening (RCS) and constrained groove pressing (CGP). The modeling results are in good agreement with the experimental data and show that the hardness uniformity and its magnitude for RCSed sheet are higher than that for CGPed sheet. However, the prominence of these processes in strain uniformity depends on pass number.     

Design of a wavelength multiplexer-demultiplexer by the use of planar microlenses

The ray-tracing method is applied to design a wavelength multiplexer-demultiplexer by the use of planar microlenses as focusing and collimating elements. By simulating both uniform and Gaussian intensity distributions of the input sources, we find the position of the input-output components of the wavelength multiplexe-rdemultiplexer, which maximizes the coupling efficiency in each channel. Losses are also evaluated.     

A RBF based finite difference method for option pricing under regime-switching jump-diffusion model

Abstract

In this article, we presented a method for option pricing problem under regime-switching jump-diffusion models. We have proposed a numerical method for solving a partial integro-differential equation (PIDE) for pricing European option and for solving linear complementarity problem (LCP), to evaluate the price of American options. We use implicit explicit method for time semi discretization, followed by radial basis function based finite difference (RBF-FD) method for spatial discretization to solve PIDE. The proposed method is further extended to solve the LCP by coupling it with operator splitting method. Numerical simulation is done for European and American option to demonstrate efficiency and accuracy of the proposed method.