基于结构元的H模糊自适应边界元

针对实际工程系统初始设计阶段经常出现材料的物理特性、结构的几何尺寸以及承受的外来作用等不确定性的问题,研究具有模糊不确定性的边界条件,提出基于模糊结构元（Fuzzy Structure Element,FSE）理论的模糊边界元法.该方法能简便、高效地处理边界条件具有模糊不确定性的系统.数值方法本身具有误差且系统自身具有模糊不确定性,故进一步研究模糊边界元法的H自适应算法,给出实用的误差估计公式;对角点处进行H自适应分析,得到较高精度的解.数值算例验证该方法的有效性和优越性.     

CUDA架构下的三维弹性静力学边界元并行计算

针对传统边界元法计算量大、计算效率低的问题,以三维弹性静力学的边界元法为对象,将基于CUDA的GPU并行计算应用到其边界元计算中,提出了基于CUDA架构的GPU并行算法.该算法首先对不同类型的边界元系数积分进行并行性分析,描述了相关的GPU并行算法,然后阐述了边界元方程组的求解方法及其并行策略.实验结果表明,文中算法较传统算法具有显著的加速效果.     

求解应力强度因子的样条虚边界元交替法

为求解平面裂纹问题的应力强度因子,提出基于Muskhelishvili基本解和样条虚边界元法的样条虚边界元交替法.该方法将平面内带裂纹有限域问题分解成带裂纹无限域问题与不带裂纹有限域问题的叠加.带裂纹无限域问题利用Muskhelishvili基本解法直接得出,不带裂纹有限域问题采用样条虚边界元法求解.利用该方法对复合型中心裂纹方板和I型偏心裂纹矩形板进行分析.数值结果表明该方法精度高且适用性强.     

RBFNN结合自适应边界的机器人手臂轨迹跟踪控制系统设计

针对机器人手臂动态模型中存在动态不确定性问题,提出一种结合径向基函数神经网络(RBFNN)和自适应边界控制的机械臂轨迹跟踪方法;利用RBF神经网络在线学习系统中现有的结构化和非结构化不确定性,近似补偿未知动态部分;利用自适应边界来估计非结构化不确定性上的未知边界和神经网络重建误差;通过加权矩阵产生的李雅普诺夫函数证明了该系统具有渐进稳定性;利用三自由度机械臂进行实验,结果表明,相比FFNN控制器,提出的控制器的跟踪误差改进了3～7倍,稳态误差改进了100～1 000倍.     

线性弹性问题的局部正交分解方法

局部正交分解方法是求解多尺度问题的一种有效算法.该算法不要求介质具有周期性或尺度分离的特点.本文构造了求解多尺度线性弹性问题的局部正交分解方法,并且给出了最佳误差估计.一些数值实验也证实了理论误差结果.     

不确定扰动分数阶混沌系统自适应Terminal滑模同步

针对带扰动不确定分数阶混沌系统的同步问题,基于自适应Terminal滑模控制,设计了一种分数阶非奇异Terminal滑模面,保证误差系统沿着滑模面在有限时间内稳定至平衡点,在系统外部扰动和不确定性的边界事先未知的情况,设计了自适应控制率,在线估计未知边界,使得同步误差轨迹能到达滑模面。最后,以三维分数阶Chen系统和四维分数阶Lorenz超混沌系统为例,利用所设计的自适应Terminal滑模控制器进行同步仿真,验证了所给方法是有效性和可行性。     

求解周期结构中声波传播问题的一种边界元法

本文应用边界积分方程方法(边界元法)求解无限长周期结构中声波的传播问题,根据散射体的周期排布方式,将无限个散射体对应无限个边界积分方程的求解问题转化为在某一个单位块中有限个边界积分方程的求解,从而使得该问题的数值求解变得简单可行.然后将该方法应用于声子晶体能量禁带的预测中,通过对数值算例的求解以及与其他方法求解结果的比较,验证了本文所提出方法的可行性和准确性.     

Buck型变换器输出跟踪的自适应动态规划算法

本文采用自适应动态规划算法研究了Buck型DC–DC变换器系统的输出跟踪问题.首先构造一个误差系统,并定义含跟踪误差和控制代价的性能指标;然后,利用自适应动态规划算法得到Buck型变换器系统的最优控制,使得含有跟踪误差和控制代价的性能指标达到最优.接着,利用该算法研究了网络环境下的Buck型DC–DC变换器系统的输出跟踪问题.该算法避免了代数求解Riccati方程,求解简洁快速.最后,仿真实验验证了该算法的有效性.     

二维线性弹性问题的等几何边界元分析

引入基于推广B样条的等几何分析方法对二维弹性问题进行边界元分析.首先使用推广B样条表示待分析的问题域,可以精确地表示待求域的圆弧边界;然后使用边界积分方程对边界未知量求解,将求得的位移通过细分方法插值到边界上;最后通过重心坐标法求得域内解,减少计算复杂度,提高了计算的精确度.分片测试及其他实例结果证实了该方法的有效性.     

多目标环境下分布未知的系统误差估计方法研究

针对多传感器多目标跟踪过程中分布未知的系统误差估计问题,对于系统误差在均匀分布和非均匀分布之间保持不确定假设下的估计方法进行了研究,提出了两种不同的误差估计方法,推导出相应误差估计方法的误差计算公式.针对两种方法在不同的系统误差分布假设下所表现出的估计性能和特点,提出了一种将两种方法结合起来的系统误差估计算法:通过合理选择阈值门限η,能够在多传感器多目标且系统误差分布未知的复杂环境下对两种误差估计方法自适应的进行切换,从而充分发挥两种方法各自的优点.同时可以对算法中估计方法模块进行扩充,以适应更复杂的误差分布情形下的多传感器系统误差自适应估计.     

Adaptive finite element procedures in elasticity and plasticity

The paper discusses error estimation and h-adaptive finite element procedures for elasticity and plasticity problems. For the spatial discretization error, an enhanced Superconvergent Patch Recovery (SPR) technique which improves the error estimation by including fulfillment of equilibrium and boundary conditions in the smoothing procedure is discussed. It is known that an accurate error estimation on an early stage of analysis results in a more rapid and optimal adaptive process. It is shown that node patches and element patches give similar quality of the postprocessed solution. For dynamic problems, a postprocessed type of error estimate and an adaptive procedure for the semidiscrete finite element method are discussed. It is shown that the procedure is able to update the spatial mesh and the time step size so that both spatial and time discretization errors are controlled within specified tolerances. A time-discontinuous Galerkin method for solving the second-order ordinary differential equations in structural dynamics is also presented. Many advantages of the new approach such as high order accuracy, possibility to filter effects of spurious modes and convenience to apply adaptive analysis are observed. For plasticity problems, some recent work that improved plastic strains and plastic localization is discussed.     

Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques

Summary  The paper discusses error estimation and adaptive finite element procedures for elasto-static and dynamic problems based on superconvergent patch recovery (SPR) techniques. The SPR is a postprocessing procedure to obtain improved finite element solutions by the least squares fitting of superconvergent stresses at certain sampling points in local patches. An enhancement of the original SPR by accounting for the equilibirum equations and boundary conditions is proposed. This enhancement improves the quality of postprocessed solutions considerably and thus provides an even more effective error estimate. The patch configuration of SPR can be either the union of elements surrounding a vertex node, thenode patch, or, the union of elements surrounding an element, theelement patch. It is shown that these two choices give normally comparable quality of postprocessed solutions. The paper is also concerned with the application of SPR techniques to a wide range of problems. The plate bending problem posted in mixed form where force and displacement variables are simultaneously used as unknowns is considered. For eigenvalue problems, a procedure of improving eigenpairs and error estimation of the eigenfrequency is presented. A postprocessed type of error estimate and an adaptive procedure for the semidiscrete finite element method are discussed. It is shown that the procedure is able to update the spatial mesh and the time step size so that both spatial and time discretization errors are controlled within specified tolerances. A discontinuous Galerkin method for solving structural dynamics is also presented.     

A methodology for adaptive mesh refinement in optimum shape design problems

This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.     

Quasi-Optimal Convergence Rate of an Adaptive Weakly Over-Penalized Interior Penalty Method

We analyze an adaptive discontinuous finite element method (ADFEM) for the weakly over-penalized symmetric interior penalty (WOPSIP) operator applied to symmetric positive definite second order elliptic boundary value problems. For first degree polynomials, we prove that the ADFEM is a contraction for the sum of the energy error and the scaled error estimator between two consecutive loops of the adaptive algorithm. After establishing this geometric decay, we define a suitable approximation class and prove that the adaptive WOPSIP method obeys a quasi-optimal rate of convergence.     

An Adaptive Finite Element Method for the Wave Scattering with Transparent Boundary Condition

Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions. The model is formulated as a boundary value problem for the Helmholtz equation with a transparent boundary condition. Based on a duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated Dirichlet-to-Neumann boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of boundary operator which decays exponentially with respect to the truncation parameter. A new adaptive finite element algorithm is proposed for solving the acoustic obstacle scattering problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are marked through the finite element discretization error. Numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method.     

Application of a posteriori error estimation to finite element simulation of compressible Navier-Stokes flow

In this paper, we discuss how to improve the adaptive finite element simulation of compressible Navier-Stokes flow via a posteriori error estimate analysis. We use the moving space-time finite element method to globally discretize the time-dependent Navier-Stokes equations on a series of adapted meshes. The generalized compressible Stokes problem, which is the Stokes problem in its most generalized form, is presented and discussed. On the basis of the a posteriori error estimator for the generalized compressible Stokes problem, a numerical framework of a posteriori error estimation is established corresponding to the case of compressible Navier-Stokes equations. Guided by the a posteriori errors estimation, a combination of different mesh adaptive schemes involving simultaneous refinement/unrefinement and point-moving are applied to control the finite element mesh quality. Finally, a series of numerical experiments will be performed involving the compressible Stokes and Navier-Stokes flows around different aerodynamic shapes to prove the validity of our mesh adaptive algorithms.     

A p-adaptive three dimensional boundary element method for elastostatic problems using quasi-Lagrange interpolation

An adaptive method for the determination of the order of element (or element order) was developed for the boundary element analysis of 3D elastostatic problems using quasi-Lagrange interpolation. Here the order of element means the highest order of polynomial function, which interpolates the displacement distribution in element. This method was based on acquiring the desired accuracy for each boundary element. From the numerical experiments, the relation ξ=k(1/p)^β was deduced, where ξ is the error of the result of the boundary element analysis relative to the exact value, p is the order of element, and k and β are constants.Applying this relation to the two results of computations with different orders of element, the order of element for the third computation was deduced. A computer program using this adaptive determination method for the order of element was developed and applied to several 3D elastostatic problems of various shapes. The usefulness of the method was illustrated by these application results.     

涡流检测系统仿真分析的自适应算法

该文针对电磁场有限元计算的特点,深入研究了涡流检测系统中电磁场有限元后验误差估计的误差模选择问题,并在分析Zienkiewicz-Zhu方法在电磁场有限元后验误差估计应用中存在局限性的基础上,提出了一种适合于涡流检测系统中电有限元分析的后验误差估计新方法。在此基础上,结合James R.Stewart和Thomas J.R.Hughes所提出的简单实用的有限元算法,提出了一种适合于涡流检测系统中电磁场有限元分析的hp 自适应新算法。     

On an h-type mesh-refinement strategy based on minimization of interpolation errors

An adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre-assigned limit. The estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives. Applications to several two-dimensional model problems are discussed. The results indicate that the method can be very effective for both regular problems and problems with strong singularities.     

Error analysis and adaptive refinement of boundary elements in elastic problem

The adaptive boundary element mesh generation based on an error analysis scheme called ‘sample point error analysis’ developed previously for the potential problem is extended and applied to the two-dimensional static elastic analysis. The errors on each element are determined as the required modification so aa to enforce the boundary integral equation to hold on the points other than the assumed initial nodes, which are referred to as the sample points. Boundary elements refinement, h-version in this study, is performed with the aid of the extended error indicator defined by the above-mentioned errors multiplied by the corresponding fundamental solutions. Two-dimensional simple problems are analysed to validate the utility of the proposed method.