论文标题
傅立叶系列（基于）科学和工程中计算分析的多尺度方法：V。傅立叶系列多尺度解决方案，用于在pasternak基础上弹性弯曲的弹性弯曲
Fourier series (based) multiscale method for computational analysis in science and engineering: V. Fourier series multiscale solution for elastic bending of Reissner plates on Pasternak foundations
论文作者
论文摘要
傅立叶系列多尺度方法是一种简洁有效的多尺度计算方法，将根据这一系列论文开发。在第五篇论文中，弹性基础上板上的板的常规结构分析扩展到了第四阶线性微分方程（用于板的横向位移）和二阶线性微分方程（对于应力函数）的彻底的多尺度分析（对于一般的边界条件和广泛的模型参数的规定）。为此，解决方案函数每个都表示为角函数的线性组合，两个边界函数和内部函数，以确保获得的串联表达式均匀收敛和术语可区分，最高为第四（或第二）顺序。同时，角函数和内部函数的总和对应于特定的解决方案，两个边界函数对应于满足方程式均匀形式的一般解决方案。借助角功能，两个边界函数和内部函数专门为多项式选择，沿y（或x）方向沿Y（或x）方向的一维半程傅立叶级数以及二维半程傅立叶级数，PASTERNAK基础上的Reissner Plate弯曲板问题的傅立叶系列多尺度解决方案是PASTERNAK基金会上的弯曲问题。然后用数值示例研究了傅立叶级数多尺度解决方案的收敛特性，并证明了pasternak基础上reissner板的弯曲问题的多尺度特征，以用于广泛的模型参数。
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fifth paper, the usual structural analysis of plates on an elastic foundation is extended to a thorough multiscale analysis for a system of a fourth order linear differential equation (for transverse displacement of the plate) and a second order linear differential equation (for the stress function), where general boundary conditions and a wide spectrum of model parameters are prescribed. For this purpose, the solution function each is expressed as a linear combination of the corner function, the two boundary functions and the internal function, to ensure the series expression obtained uniformly convergent and termwise differentiable up to fourth (or second) order. Meanwhile, the sum of the corner function and the internal function corresponds to the particular solution, and the two boundary functions correspond to the general solutions which satisfy the homogeneous form of the equation. With the corner function, the two boundary functions and the internal function selected specifically as polynomials, one-dimensional half-range Fourier series along the y (or x)-direction, and two-dimensional half-range Fourier series, the Fourier series multiscale solution of the bending problem of a Reissner plate on the Pasternak foundation is derived. And then the convergence characteristics of the Fourier series multiscale solution are investigated with numerical examples, and the multiscale characteristics of the bending problem of a Reissner plate on the Pasternak foundation are demonstrated for a wide spectrum of model parameters.
