许功明, 沈大荣. 用加权残数法分析各向异性层合薄板的几何非线性问題[J]. 工程力学, 1985, 2(3): 20-29.
引用本文: 许功明, 沈大荣. 用加权残数法分析各向异性层合薄板的几何非线性问題[J]. 工程力学, 1985, 2(3): 20-29.
Xu Gong-Ming, Shen Da-Rong. Geometrically Nonlinear Analysis of Laminated Anisotropic Plates by Weighted - Residual Method[J]. Engineering Mechanics, 1985, 2(3): 20-29.
Citation: Xu Gong-Ming, Shen Da-Rong. Geometrically Nonlinear Analysis of Laminated Anisotropic Plates by Weighted - Residual Method[J]. Engineering Mechanics, 1985, 2(3): 20-29.

用加权残数法分析各向异性层合薄板的几何非线性问題

Geometrically Nonlinear Analysis of Laminated Anisotropic Plates by Weighted - Residual Method

  • 摘要: 各向异性层合薄板的几何非线性问题,由于控制方程和边值问题求解的复杂性,历来解法繁杂,工作量大且存在较大局限性。本文利用加权残数法简捷,有效的特点,提出以具有良好拟合性和对边界条件灵活可适性的五次B—样条基函数的组合作为试函数基底,然后采用阻尼最小二乘法,应用于解决这类复杂问题。本文在计算时编制了较为通用的程序,若干具体算例表明,本方法收敛稳定,结果准确,且解法简捷,统一,便于程序标准化与推广应用。

     

    Abstract: Geometrically nonlinear problems of laminated anisotropic plates have always been tedious, complicated ones which causes a lot of laboure, and there is considerable limitation in various previous solving method, owing to the complex nature of the governing equations and the boundary value problem.This paper suggest that a simple, direct and effective method——weighted-residual method be applied to solve this kind of Complicated problem,by taking the combination of quintic B-Spline functions, which have fine fitness and flexible adaptability to boundary conditions, as the basis of try-function, and then using the damping least square method. A comparative universal program has been organized.As shown by some concrete examples, the presented method possesses those advantages,such as stability in convergence and accuracy in results. Furthermore tho solving process is simple, direct and integrative, and convenient for standardizing programes and extending application.

     

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