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求解一元非线性方程的埃特金算法是一种线性化自动迭代算法,其每次迭代需要计算两次函数值。将其推广到结构优化非线性准则方程组的迭代求解,可实现结构优化迭代求解的完全自动化。为克服其每次迭代需要两次结构分析的缺点,构造了一种新型线性化迭代解法,称为Atiken Chen算法,该算法利用前次结构分析信息,每次迭代只需一次结构分析,从而大大提高了结构优化迭代计算的效率与自动化程度。算例验证了该算法的可行性和优越性。 相似文献
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考虑翘曲效应的薄壁曲梁几何非线性分析 总被引:7,自引:2,他引:7
利用UL法研究了开口薄壁曲线梁几何非线性分析问题。采用多项式插值函数表示位移场。考虑了翘曲自由度及曲率效应模拟开口薄壁曲梁的结构行为。所有位移参数定义于截面形心以便在弹性应变能中包括弯扭耦合项。利用修正的弧长法求解非线性方程,跟踪荷载位移曲线。用算例对提出的方法进行了验证,表明了薄壁曲梁的分析中翘曲变形不可忽略。 相似文献
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以摄动法将层合板的非线性振动偏微分方程线性化,从摄动方程中分离出时域函数并求解。将场函数设定为含时域函数的待定函数,通过微分求积法对空间域的摄动方程进行离散,将其转化成一系列的线性方程并通过编程求解。算例结果分析说明算法精度良好且效率高。 相似文献
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张力膜结构的找形分析 总被引:16,自引:2,他引:14
张力膜结构的形状不能随意选择,设计时首先要确定满足平衡条件和建筑要求的表面形状。本文根据大位移理论,得出了适合于张力膜结构的几何非线性有限元方程,给出了采用几何非线性有限元法确定张力膜结构的初始形状的方法,对预张应力的确定及找形问题的非线性方程求解收敛准则提出了建议。文中给出了几个找形算例,算例表明本文的找形方法是有效、正确的。 相似文献
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Bioluminescence tomography (BLT) aims at the determination of the distribution of a bioluminescent source quantitatively. The mathematical problem involved is an inverse source problem and is ill-posed. With the Tikhonov regularization, an optimization problem is formed for the light source reconstruction and it is usually solved by gradient-type methods. However, such iterative methods are often locally convergent and thus the solution accuracy depends largely on initial guesses. In this paper, we reformulate the reduced regularized optimal problem as a nonlinear equation and apply a homotopy method, which is a powerful tool for solving nonlinear problem due to its globally convergent property, to it. Numerical experiments show that the application of the homotopy technique is feasible and can produce satisfactory approximate solutions for a very large range of initial guesses. 相似文献
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M. Moghaddam W. C. Chew M. Oristaglio 《International journal of imaging systems and technology》1991,3(4):318-333
Two methods of solving the nonlinear two-dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born-type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers. 相似文献
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We present a numerical approach to estimating the effective diffusion coefficients of drug diffusion from a device into a container with a source and sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate this estimation problem as a continuous, nonlinear, least-squares problem subject to a set of constraints containing a partial differential equation system. The nonlinear optimization problem is then discretized by applying a finite volume scheme in space and an implicit time-stepping scheme to the equation system, yielding a finite-dimensional, nonlinear, least-squares problem. An algorithm is proposed for the resulting finite-dimensional, constrained, nonlinear optimization problem. Numerical results using experimental data are presented to demonstrate the usefulness and accuracy of the method. 相似文献
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A consistent grayscale‐free topology optimization method using the level‐set method and zero‐level boundary tracking mesh
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Shintaro Yamasaki Atsushi Kawamoto Tsuyoshi Nomura Kikuo Fujita 《International journal for numerical methods in engineering》2015,101(10):744-773
This paper proposes a level‐set based topology optimization method incorporating a boundary tracking mesh generating method and nonlinear programming. Because the boundary tracking mesh is always conformed to the structural boundary, good approximation to the boundary is maintained during optimization; therefore, structural design problems are solved completely without grayscale material. Previously, we introduced the boundary tracking mesh generating method into level‐set based topology optimization and updated the design variables by solving the level‐set equation. In order to adapt our previous method to general structural optimization frameworks, the incorporation of the method with nonlinear programming is investigated in this paper. To successfully incorporate nonlinear programming, the optimization problem is regularized using a double‐well potential. Furthermore, the sensitivities with respect to the design variables are strictly derived to maintain consistency in mathematical programming. We expect the investigation to open up a new class of grayscale‐free topology optimization. The usefulness of the proposed method is demonstrated using several numerical examples targeting two‐dimensional compliant mechanism and metallic waveguide design problems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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We consider a Robin inverse problem associated with the Laplace equation,
which is a severely ill-posed and nonlinear. We formulate the problem as a boundary
integral equation, and introduce a functional of the Robin coefficient as a regularisation
term. A conjugate gradient method is proposed for solving the consequent regularised
nonlinear least squares problem. Numerical examples are presented to illustrate the
effectiveness of the proposed method. 相似文献
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系统非线性参数识别的松驰法 总被引:11,自引:2,他引:9
研究了非线性参数系统模型的识别问题,通过引入求解线性方程的松驰法思想,构造了一类新的迭代识别算法。算例表明此方法具有很好的参数识别精度,并且具有概念清楚,易于编程等特点,为非线性系统模型参数的识别问题提供了新的思路。 相似文献
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In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method. 相似文献
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遗传算法在工程爆破参数优化中的应用 总被引:4,自引:0,他引:4
工程爆破中的参数优化问题是个复杂的非线性规划问题。以矿山爆破参数优化数学模型为例,采用遗传算法实现了爆破参数的优化。结果证实了利用遗传算法进行爆破参数优化的可行性与高效性,为求解该问题提供了一个有效的新途径。 相似文献
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Accelerating PDE constrained optimization by the reducedbasis method: application to batch chromatography
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Yongjin Zhang Lihong Feng Suzhou Li Peter Benner 《International journal for numerical methods in engineering》2015,104(11):983-1007
In this work, we show that the reduced basis method accelerates a partial differential equation constrained optimization problem, where a nonlinear discretized system with a large number of degrees of freedom must be repeatedly solved during optimization. Such an optimization problem arises, for example, from batch chromatography. To reduce the computational burden of repeatedly solving the large‐scale system under parameter variations, a parametric reduced‐order model with a small number of equations is derived by using the reduced basis method. As a result, the small reduced‐order model, rather than the full system, is solved at each step of the optimization process. An adaptive technique for selecting the snapshots is proposed, so that the complexity and runtime for generating the reduced basis are largely reduced. An output‐oriented error bound is derived in the vector space whereby the construction of the reduced model is managed automatically. An early‐stop criterion is proposed to circumvent the stagnation of the error and to make the construction of the reduced model more efficient. Numerical examples show that the adaptive technique is very efficient in reducing the offline time. The optimization based on the reduced model is successful in terms of the accuracy and the runtime for acquiring the optimal solution. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献