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介绍在结构稳定性分析方面的一些新的发展。提出一种新的Trefftz有限元法和有效算法来计算框架结构的精确数值。使用均匀控制方程的一般解和经过论证的、精确的Trefftz有限元来建立新的形状函数,从而提出以传统的特征值提取法为基础的迭代算法,且通过使用简单的有限元网格可以有效获得精确解。此外,基于新的有限元矩阵和瑞利公式的有效方法可用于后验误差估计和改进。数值分析证明了所提出原理和算法的有效性。最后讨论了该方法在未来的推广问题。
Introduced some new developments in structural stability analysis. A new Trefftz finite element method and an efficient algorithm are proposed to calculate the exact value of the frame structure. A new shape function is built using the general solution of the uniform control equation and the proven, accurate Trefftz finite element, and an iterative algorithm based on the traditional eigenvalue extraction method is proposed and can be validated by using a simple finite element mesh Get the exact solution. In addition, an effective method based on the new finite element matrix and the Rayleigh formula can be used for a posteriori error estimation and improvement. Numerical analysis proves the effectiveness of the proposed principles and algorithms. Finally, it discusses the promotion of this method in the future.