基于位移控制新法的结构非线性有限元数值模拟
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华东交通大学

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TU311.4

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国家自然科学基金项目(51878275)


Nonlinearly Numerical Simulation of Finite Element Based on A New Displacement Control Method for Structures
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    摘要:

    在材料、构件和结构的非线性问题的有限元数值模拟过程中,当需要模拟达到或通过荷载-位移空间中平衡路径的极值点以及软化下降段时,荷载增量控制法一般是无能为力的。为了克服这个困难,本文利用杜修力等人提出的位移控制新理论,对有限元求解方程中的刚度矩阵的主对角元素乘以大数,并将边界条件引入到有限元求解方程中,使得新的刚度矩阵依然具有对称性和带状性,因此仅需要对经典的荷载控制法程序做少量的修补,而且运算过程简单、迭代计算量少。论文最后采用MATLAB编制程序,并结合实际算例进行分析,结果表明:本文建立的方法不但有效、可行,而且简单。

    Abstract:

    In the nonlinearly numerical simulation of finite element for materials, components and structures, during the simulation it is in general impossible for the load increment control method to simulate the peak point and the softening decent segment of special equilibrium path for load-displacement relation. In this paper, a new theory of displacement control proposed by Du Xiuli et al. was used to overcome this problem. To make a new stiffness matrix to be symmetric and banded, the main diagonal elements of stiffness matrix in the conventional finite element incremental equation were multiplied by a huge number, and the boundary conditions were also introduced to the finite element equation. Therefore, only a little modification is needed for the program of traditional load control method which can simplify the iterative process of calculation. Finally, it was programmed by MATLAB. As applications, some practically numerical examples were given. It was shown by the analysis that the method presented in the paper is not only effective, feasible, but also simple.

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历史
  • 收稿日期:2020-07-23
  • 最后修改日期:2020-07-23
  • 录用日期:2020-08-28
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