Numerical comparison of two boundary element methods for plane harmonic functions

A direct boundary element method (BEM) has been studied in the paper based on a set of sufficient and necessary boundary integral equations (BIE) for the plane harmonic functions. The new sufficient and necessary BEM leads to accurate results while the conventional insufficient BEM will lead to inaccurate results when the conventional BIE has multiple solutions. Theoretical and numerical analyses show that it is beneficial to use the sufficient and necessary BEM, to avoid hidden dangers due to non-unique solution of the conventional BIE.     

An approximation method to relate the linear viscoelastic functions

A method based on rational approximations is presented to interpolate the data from sinusoidal experiments in linear viscoelasticity. Bounds to the corresponding dynamical function and a discrete approximation to the spectrum are established. From this approximation the related viscoelastic functions can be computed. The method is checked by considering two theoretical models of physical interest and a satisfactory accuracy is achieved.     

Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system, we address the problem of devising a bounded feedback control, which brings the system to the origin in finite time. The construction is based on the notion of a common Lyapunov function. It is shown that the constructed control remains effective in the presence of small perturbations.     

Fitting of simple approximation functions using nonlinear least-squares methods

Least-squares methods are described for fitting of approximation functions which contain two unknown constants. The functions are linear with respect to one of the constants and nonlinear with respect to the other. Linearization is compared to a nonlinear least-squares, algorithm. Advantages of the latter method are discussed and both methods are applied to an example problem.     

Fit regions and functions of bounded variation

Dedicated to James B. Serrin on the occasion of his sixtieth birthday     

BEST APPROXIMATION THEOREM FOR SET-VALUED MAPPINGSWITHOUT CONVEX VELUES AND CONTINUITY

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A new boundary integral equation for plane harmonic functions

In this paper, we propose a new boundary integral equation for plane harmonic functions. As a new approach, the equation is derived from the conservation integrals. Every variable in the integral equation has direct engineering interest. When this integral equation is applied to the Dirichlet problem, one will get an integral equation of the second kind, so that the algebraic equation system in the boundary element method has diagonal dominance. Finally, this equation is applied to elastic torsion problems of cylinders of different sections, and satisfactary numerical results are obtained.     

Suitability of yield functions for the approximation of subsequent yield surfaces

Many consitutive models in the plasticity of metals are based on the existence of a yield function, which is not only used to mark the elastic limit but also as a potential function for the plastic strain rate. The construction of this function therefore deserves the utmost interest. Measurements of the elastic limit show the essential features of how the geometry of the yield function contour lines should change with further straining. Against these typical geometric forms of the yield surface existing proposals for invariant formulations of the yield function taking into account isotropic, kinematic and formative hardening are tested. Even if no evolution equations for the constitutive variables contained in the yield functions are specified, best approximations of measured yield surfaces can be computed by optimisation of a quality function. It can be shown that most of the representations are not even able to describe the experimental results qualitatively. The numeric results show further that the yield function is essentially of grade three in the deviatoric stresses. The evolution of internal variables can be deduced from the approximations of the measurements.     

Imposing nodes for linear structures during harmonic excitations using SMURF method

Vibration absorbers are usually designed using the finite element (FE) model of structures. It is generally believed that the modal models are more accurate than FE models, because in modal testing the model is built by direct measurement of the test structure. In this paper, a method is proposed to design a translational vibration absorber using the measured frequency response functions of a primary structure. The designed vibration absorber imposes a node on the structure when it is excited by a harmonic force. The method is based on the structural modification using experimental frequency response functions technique and determines the required receptance of the absorber at the excitation frequency. Moreover, a procedure is developed to suppress the vibration amplitude of two arbitrary points on a linear structure subjected to harmonic excitations by attaching two sprung mass absorbers. A cantilever beam is considered for the numerical case study, and the sprung masses are designed to suppress the vibration amplitude of the beam at the selected arbitrary points. A U-shape plate was considered for the experimental validation of the method for imposing a node using one absorber. Also, a beam was tested to demonstrate the effectiveness of method for imposing two nodes on the structures. The experimental results show that the designed absorbers can considerably suppress the vibration amplitude at the selected points on the structure.     

Numerical instabilities and convergence control for convex approximation methods

Convex approximation methods could produce iterative oscillation of solutions for solving some problems in structural optimization. This paper firstly analyzes the reason for numerical instabilities of iterative oscillation of the popular convex approximation methods, such as CONLIN (Convex Linearization), MMA (Method of Moving Asymptotes), GCMMA (Global Convergence of MMA) and SQP (Sequential Quadratic Programming), from the perspective of chaotic dynamics of a discrete dynamical system. Then, the usual four methods to improve the convergence of optimization algorithms are reviewed, namely, the relaxation method, move limits, moving asymptotes and trust region management. Furthermore, the stability transformation method (STM) based on the chaos control principle is suggested, which is a general, simple and effective method for convergence control of iterative algorithms. Moreover, the relationships among the former four methods and STM are exposed. The connection between convergence control of iterative algorithms and chaotic dynamics is established. Finally, the STM is applied to the convergence control of convex approximation methods for optimizing several highly nonlinear examples. Numerical tests of convergence comparison and control of convex approximation methods illustrate that STM can stabilize the oscillating solutions for CONLIN and accelerate the slow convergence for MMA and SQP.     

基于调和分析法的全球地形球谐系数模型构建

针对当前全球地形球谐系数模型构建表达精度不高、计算效率较低等问题,研究推导了Gauss-Legendre积分法、矩形离散积分法求解球谐系数公式,提出了联合FFT技术和基于OpenMP多核并行技术的计算优化策略,实现了全球2160阶地形球谐系数模型的高效构建.利用模型Earth2012对两种方法进行了对比分析,结果表明:...     

Improved methods for linear estimation of velocity records

Traditionally, linear mean-square (MS or stochastic) estimation coefficients are calculated using cross-correlations between each of the data at reference and estimation locations. Since the cross-correlation between data at reference and estimation locations typically decreases rapidly with increasing separation distance, the resulting estimated fluctuations diminish away from the reference locations. Two new schemes have been developed to optimally determine estimation coefficients which yield an improved estimated energy representation. One approach involves a non-linear least-square fit toboth the estimation covariance and the cross-correlation between data at reference and estimation locations. By also minimizing the error in the estimation covariance, realistic energy levels can be estimated without significantly altering the correlation between true and estimated velocity signals as given by the traditional MS method. Another scheme, developed for use with a single-point, two-component reference, maximizes the correlation coefficient between the estimate and its measured counterpart. It is shown that for this simple case, the estimated covariance can be setequal to the measured covariance without compromising the correlation coefficientat all. The effectiveness of the proposed techniques is demonstrated by comparing their estimates with those given by the MS method in a plane turbulent mixing layer. In general, the estimation schemes appear to give improved results when references from the edge of the mixing layer are employed. It is also demonstrated how the results of the proposed estimation methods can be used to infer details regarding the mixing layer structure and kinematics. This work was conducted in the Fluid Mechanics Laboratory, NASA Ames Research Center and was supported by the NASA Ames Research Center — Stanford University, Center for Turbulence Research, Postdoctoral Fellowship Program.     

Construction space harmonic functions in polynomial form and spherical functions by complex-functional

In this paper, applying the theory of complex-functional, not only the space harmonic functions in polynomial form, but also the spherical functions are obtained.     

Several solution methods for the generalized complex eigenvalue problem with bounded uncertainties

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the complex eigenvalues of the non-proportional damping structures. By combining the interval mathematics and the finite element analysis, the mass matrix, the damping matrix and the stiffness matrix were represented as the interval matrices. Firstly, with the help of the optimization theory, we presented an exact solution—the vertex solution theorem, for determining the exact upper bounds or maximum values and exact lower bounds or minimum values of complex eigenvalues of structures, where the extreme values are reached on the boundary of the interval mass, damping and stiffness matrices. Then, an interval perturbation method was proposed, which needs less computational efforts. A numerical example of a seven degree-of-freedom spring-damping-mass system was used to illustrate the computational aspects of the presented vertex solution theorem and the interval perturbation method in comparison with Deif’s method.