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首页> 外文期刊>International Journal of Solids and Structures >A new functional perturbation method for linear non-homogeneous materials
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A new functional perturbation method for linear non-homogeneous materials

机译：线性非均质材料的一种新的函数摄动方法

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摘要

A functional perturbation method (FPM), for solving boundary value problems of linear materials with non-homogeneous properties is introduced. The FPM is based on considering the unknown field such as displacements or temperatures, as a functional of the non-uniform property, i.e., elastic modulus or thermal conductivity. The governing differential equations are expanded functionally by Frechet series, leading to a set of differential equations with constant coefficients, from which the unknown field is found successively to any desirable degree of accuracy. A unique property of the FPM is that once the Frechet functions are found, the solution for any morphology is obtained by direct integration, without re-solving the differential equation for each case. The FPM procedure is outlined first for general linear differential equations with non-uniform coefficients. Then, four examples are solved and discussed: a 1D tensile loading of a rod with continuously varying and discontinuous moduli, beam bending, beam deflection on non-uniform elastic foundation and a unidirectional heat conduction problem. FPM results are compared with the exact (if exists) or numerical solution. The FPM accuracy for the bending problem is also compared to the common Rayleigh-Ritz and Galerkin methods. It is shown that the FPM is inherently more accurate, since the convergence rate of the other methods depends on the arbitrarily chosen shape functions, while in the FPM, these functions are obtained as generic results of each order of the solution. The FPM solution is analytical, and is shown to be suitable for large variations in material properties. Thus, a direct insight of each functional perturbation order is possible. Advantages and limitations of the FPM as compared to other existing methods are discussed in detail. (C) 2004 Elsevier Ltd. All rights reserved.
机译：介绍了一种求解非均质线性材料边界值问题的函数摄动方法（FPM）。 FPM基于将诸如位移或温度之类的未知字段视为非均匀特性（即弹性模量或导热率）的函数。控制微分方程在功能上由Frechet级数展开，从而得到一组具有恒定系数的微分方程，从中可以连续发现未知场达到任何期望的精度。 FPM的独特之处在于，一旦找到Frechet函数，就可以通过直接积分获得任何形态的解，而无需为每种情况重新求解微分方程。首先概述了系数不均匀的一般线性微分方程的FPM过程。然后，解决并讨论了四个示例：具有连续变化和不连续模量的杆的一维拉伸载荷，梁弯曲，梁在不均匀弹性基础上的挠度和单向导热问题。将FPM结果与精确（如果存在）或数值解进行比较。还将弯曲问题的FPM精度与常见的Rayleigh-Ritz和Galerkin方法进行了比较。结果表明，FPM本质上更准确，因为其他方法的收敛速度取决于任意选择的形状函数，而在FPM中，这些函数是作为每个解决方案阶数的通用结果而获得的。 FPM解决方案是分析型的，已显示适用于材料特性的较大变化。因此，可以直接了解每个功能扰动顺序。与其他现有方法相比，详细讨论了FPM的优点和局限性。 （C）2004 Elsevier Ltd.保留所有权利。

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