Inverse acoustic scattering by solid obstacles: topological sensitivity and its preliminary application

A to pological sensitivity approach is developed for the imaging of penetrable solid obstacles embedded in a fluid background medium by way of inverse acoustic scattering. To this end, an asymptotic form for the scattered field caused by a nucleating spherical solid obstacle in the reference fluid medium is derived within the boundary integral equation framework, where the required limiting behaviour of the acceleration field inside the perturbation is established based on solutions of two simplified fluid–solid interaction problems. With this result, the equivalence of acoustic scattering by fluid and solid scatterers in terms of asymptotic behaviour is observed and numerically validated. The direct and adjoint-field topological sensitivity expressions for transient and time-harmonic excitations are obtained accordingly. The utility of the proposed method as a tool for preliminary obstacle reconstruction and bulk modulus characterization is illustrated through numerical examples and an exploratory experimental study. On the basis of adjusted topological sensitivity formulas for fluid reference domains containing pre-existing solid inhomogeneities, an iterative 3D obstacle reconstruction approach is established and its performance with synthetic data is demonstrated.     

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.     

三维障碍物形状近场反演的一种快速算法

文章研究了从点声源散射场的有限孔径近场测量信息来再现多个三维障碍物形状的反问题。指出了数值求解这类反问题的一种简单快速逄。数值结果表明了该算法是有效和实用的。     

Topological derivatives for fundamental frequencies of elastic bodies

In this article a new method for topological optimization of fundamental frequencies of elastic bodies, which could be considered as an improvement on the bubble method, is introduced. The method is based on generalized topological derivatives. For a body with different types of inclusion the vector genus is introduced. The dimension of the genus is the number of different elastic properties of the inclusions being introduced. The disturbances of stress and strain fields in an elastic matrix due to a newly inserted elastic inhomogeneity are given explicitly in terms of the stresses and strains in the initial body. The iterative positioning of inclusions is carried out by determination of the preferable position of the new inhomogeneity at the extreme points of the characteristic function. The characteristic function was derived using Eshelby's method. The expressions for optimal ratios of the semi-axes of the ellipse and angular orientation of newly inserted infinitesimally small inclusions of elliptical form are derived in closed analytical form.     

Shape optimization of unsteady natural convection fields

This paper presents a numerical method for two shape optimization problems, namely, prescribing the temperature history distribution on sub-boundaries and maximizing the discharged heat on sub-boundaries of unsteady natural convection fields. The square error integral between the actual temperature distribution and the target temperature distribution on the sub-boundaries during a specified period of time was used as the objective functional for the prescribed temperature history distribution. The shape gradients of these shape determination problems were derived theoretically using the Lagrange multiplier method, adjoint variable method, and the material derivative formulae. Reshaping was performed by the traction method, which was proposed as an approach for solving shape optimization problems. Numerical programs for the shape determination problems are developed based on FreeFem++ in order to verify the proposed method.     

Multivariate numerical derivative by solving an inverse heat source problem

A method for approximating multivariate numerical derivatives is presented from multidimensional noise data in this paper. Starting from solving a direct heat conduction problem using the multidimensional noise data as an initial condition, we conclude estimations of the partial derivatives by solving an inverse heat source problem with an over-specified condition, which is the difference of the solution to the direct problem and the given noise data. Then, solvability and conditional stability of the proposed method are discussed for multivariate numerical derivatives, and a regularized optimization is adopted for overcoming instability of the inverse heat source problem. For achieving partial derivatives successfully and saving amount of computation, we reduce the multidimensional problem to a one-dimensional case, and give a corresponding algorithm with a posterior strategy for choosing regularization parameters. Finally, numerical examples show that the proposed method is feasible and stable to noise data.     

基于有限元法的正交各向异性复合材料结构材料参数识别

以大型商用有限元软件ABAQUS为计算平台,提出了正交各向异性复合材料结构材料参数的识别方法。将材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与有限元计算的相应位移之差的平方和。采用Levenberg-Marquardt方法极小化目标函数,其中灵敏度的计算基于复合材料的有限元离散结构的求解方程对识别的材料参数求导。数值算例表明本文中提出的方法是有效的。在识别参数过程中,参数的初值以及搜索范围的确定对于识别结果有着重要影响。因此必须充分利用材料参数的先验信息。ABAQUS是高效可靠的商用有限元软件,提出的参数识别方法基于这类商用软件,因而该方法有很强的实用性。     

Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures

This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi‐scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element. The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectiveness of the proposed methodology is illustrated in a set of finite element‐based numerical examples.Copyright © 2010 John Wiley & Sons, Ltd.     

基于形状导数和水平基函数的复合材料层合结构拓扑优化

首次利用水平基物质分布函数推出域内积分与边界积分泛函的形状导数 , 建立了复合材料刚性连续结构拓扑优化设计理论的新模型。通过将形状导数和增广的 Lagrangian 乘子法相结合 , 提出了复合材料结构拓扑优化敏度分析的新方法。设计边界的进化是通过人为掌握目标函数下降的速度来控制。水平基函数的曲面在不改变拓扑结构的前提下上下运动 , 从而通过边界的合并与分离改变嵌入其中的零水平基面上设计构件的拓扑结果。广泛的 2D复合材料悬臂梁研究验证了本文中方法的有效性。      

半埋目标低频声波散射反演的一种新算法

半埋目标低频声波散射在数学上归纳为求解带有混合边界的不可穿透的散射体外声场问题,是一个公认的理论难题。本文首次将区域导数法引入边界条件为混合边界不可穿透的散射体的外声场问题中,数值结果证明算法是可行的、正确的,为解决半埋目标低频声波散射物形状识别提供了一种新方法,这在工程实际及军事上均有重要的应用价值。     

Identification of cracks and cavities using the topological sensitivity boundary integral equation

The purpose of this communication is to present a novel approach to compute the so called Topological Sensitivity (TS) of any variable or functional in elasticity using Boundary Integral Equations (BIEs), and its use as a tool for identification of defects, by itself or in conjunction with zero-order methods, like Genetic Algorithms. The TS of a cost functional provides a measure of the susceptibility of a defect being at a given location. The main contributions are summarized in the following points:     

导数光谱法在药物分析中的应用进展

本文综述了导数光谱法在药物分析中的应用进展。简述了方法的基本原理,详述了在复方药物制剂方面、中药方面以及计算机导数光谱法、比值导数光谱法和差示导数光谱法的具体应用,对于药物质量控制和临床药学检测都有参考意义。     

基于Melnikov方法的分数阶Duffing振子混沌阈值解析研究

研究了含有分数阶微分项的Duffing振子的分岔与混沌行为,利用等效刚度和等效阻尼的概念对分数阶微分项进行处理,将分数阶微分项等效成三角函数与指数函数的形式,用Melnikov方法分析了分数阶Duffing振子产生分岔与混沌的必要条件,得到了其解析结果.进行了解析解和数值解的比较,证明了解析结果的精确度,并通过仿真计算...     

缺陷识别中的逆Born近似方法

利用平面简谐纵波对二维散射远场Ｂｏｒｎ近拟解，给出了二维Ｆｒｏｕｒｉｅｒ变换法建立散射体（缺陷）的特征函数与形状因子的关系式，对钛合金中正方形铝夹杂和圆形孔穴分别进行计算机模拟识别，结果表明这种方法对定量无损检测技术有理论和应用价值。     

Mixed-dimensional modeling by means of solid and higher-order multi-layered plate finite elements

Abstract

Solid and higher-order plate finite elements are coupled for the analysis of composite structures by means of the Arlequin method. Plate and solid elements are derived by a unified formulation and they do not depend on the number of nodes. Higher-order and zig-zag plate elements are easily formulated regardless the approximation order along the through-the-thickness direction. Composite and sandwich plates are investigated. Multi-model solutions are assessed towards equivalent mono-model ones and commercial finite element software results. The numerical investigation shows that higher-order plate finite elements and solid ones are successfully coupled.     

A topological optimization approach for structural design of a high‐speed low‐load mechanism using the equivalent static loads method

In high‐speed low‐load mechanisms, the principal loads are the inertial forces caused by the high accelerations and velocities. Hence, mechanical design should consider lightweight structures to minimize such loads. In this paper, a topological optimization method is presented on the basis of the equivalent static loads method. Finite element (FE) models of the mechanism in different positions are constructed, and the equivalent loads are obtained using flexible multibody dynamics simulation. Kinetic DOFs are used to simulate the motion joints, and a quasi‐static analysis is performed to obtain the structural responses. The element sensitivity is calculated according to the static‐load‐equivalent equilibrium, in such a way that the influence on the inertial force is considered. A dimensionless component sensitivity factor (strain energy caused by unit load divided by kinetic energy from unit velocity) is used, which quantifies the significance of each element. Finally, the topological optimization approach is presented on the basis of the evolutionary structural optimization method, where the objective is to find the maximum ratio of strain energy to kinetic energy. In order to show the efficiency of the presented method, we presented two numerical cases. The results of these analyses show that the presented method is more efficient and can be easily implemented in commercial FE analysis software. Copyright © 2011 John Wiley & Sons, Ltd.     

Parametric design sensitivity analysis of high‐frequency structural–acoustic problems using energy finite element method

A design sensitivity analysis of high‐frequency structural–acoustic problems is formulated and presented. The energy finite element method (EFEM) is used to predict structural–acoustic responses in the high frequency range, where the coupling between structural junctions and the structural–acoustic interface are modelled using power transfer coefficients. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural–structural and structural–acoustic coupling matrices. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and numerical sensitivity results show excellent agreement as compared to analytical finite difference results. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity analysis and design optimization of three‐dimensional non‐linear aeroelastic systems by the adjoint method

We consider the problem of optimizing a non‐linear aeroelastic system in steady‐state conditions, where the structure is represented by a detailed finite element model, and the aerodynamic loads are predicted by the discretization of the non‐linear Euler equations. We present a solution method for this problem that is based on the three‐field formulation of fluid–structure interaction problems, and the adjoint approach for coupled sensitivity analysis. We discuss the computational complexity of the proposed solution method, describe its implementation on parallel processors, and illustrate its computational efficiency with the aeroelastic optimization of various wings. Copyright © 2002 John Wiley & Sons, Ltd.     

Shape optimization of flow guides in three‐dimensional extrusion processes by an approximation scheme based on state variable linearization

A new scheme of shape optimization is applied to the design of a flow guide in flat‐die extrusion processes. In general, tremendous time is inevitably required for the optimization of large‐scale three‐dimensional extrusion processes. This is because the finite element analysis requires large computation time owing to the complexity of the die geometry and flow behaviour. The proposed scheme effectively reduces the computation time for the optimization process by approximating the objective function. This is achieved by introducing a transformed equation of the state variables. The scheme is then applied to the practical extrusion processes to produce ‘l’, ‘H’ and ‘L’ sections. The objective of the optimization is to make a balanced flow of the material in the exit region. Control points of a Bezier curve describing the outline of the flow guide are regarded as the design variables. Through application to large‐scale problems, the effectiveness and usefulness of the proposed scheme is demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.     

An analytical stiffness derivative extended finite element technique for extraction of crack tip Strain Energy Release Rates

An analytical approach combined with the extended finite element method (XFEM) is proposed to extract the Strain Energy Release Rates within the classical stiffness derivative technique. The proposed idea hinges on the following two XFEM properties: (i) the crack is mesh independent, i.e. there is no need for mesh perturbations in the vicinity of the crack and (ii) the asymptotic crack tip field is embedded in the mathematical formulation of the stiffness matrix. By employing these properties we show that the derivative of the stiffness matrix with respect to the crack extension can be computed in a closed form and on the fly during the analysis. Thus the virtual crack extension, and the error inherent in the finite difference scheme of the classical stiffness derivative technique is completely avoided. Numerical results on few benchmark problems show that this method is comparable to the J-integral method.