应用于薄壁矩形板和明德林矩形板的匹配截面法

Kirill Danylenko, Igor Orynyak
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引用次数: 0

摘要

本文阐述了应用于板材问题的有限元法的主要新变体。它与经典的有限元方法至少有三点不同。首先,它使用强微分公式而不是弱微分公式,并假设所有微分方程都是近似解析解。其次,它在求解过程中明确使用了所有几何和物理参数,而不是像有限元方法中通常所做的那样,选择一些参数,例如位移和旋转角度。第三,相邻元素之间的共轭发生在相邻截面之间,而不是多边形顶点。这些条件要求位移、角度、力矩和力的连续性。矩形元素的每个边有 6 个主要参数,因此每个矩形元素共有 24 个参数。右侧和上侧的参数被视为输出参数,它们通过矩阵方程与下侧和左侧的参数相关联,因此可以采用传递矩阵法来编制整个板的方程组。薄壁板和 Mindlin 板的数值示例显示了该方法的高效性和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Method of matched sections in application to thin-walled and Mindlin rectangular plates
The paper elaborates the principally new variant of finite element method in application to plate problem. It differs from classical FEM approach by, at least, three points. First, it uses the strong differential formulation rather than the weak one and suppose the approximate analytical solution of all differential equations. Second, it explicitly uses all geometrical and physical parameters in the procedure of solution, rather than some chosen ones, for example, displacement and angles of rotation as usually done in FEM formulation. Third, the conjugation between adjacent elements occurs between the adjacent sections rather than in polygon vertexes. These conditions require the continuity of displacements, angles, moments and forces. Each side of rectangular elements is characterized by 6 main parameters, so, at whole there are 24 parameters for each rectangular element. The right and upper sides’ parameters are considered as output ones, and they are related with lower and left sides ones by matrix equations, which allows to apply transfer matrix method for the compilation of the resulting system of equations for the whole plate. The numerical examples for the thin-walled and Mindlin plates show the high efficiency and accuracy of the method.
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