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Stability analysis of frame structures by bubble-function method

机译：气泡函数法分析框架结构的稳定性

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In the stability analysis of frame structures, the results by conventional finite element method (FEM) in which one member is taken as one element are sometimes unavailable. This paper took a new basic function system with bubble functions as the shape function of a bar element to develop a bubble function finite element method (BFEM), in which the bending and the geometric stiffness matrices were derived from the principle of virtual work. Bubble functions are finite element modes that are located entirely within a single element and are zero on boundaries of the element, but are nonzero at the other points. BFEM is as concise as conventional bar FEM but has better accuracy, and is adaptable to the buckling analysis of all kinds of frame structures. The use of bubble functions significantly improves the convergence of finite element analysis, and efficiently reduces the computation cost for the buckling analysis of frame structures. Numerical results show that using bubble functions in finite element for the stability analysis of structures is very efficient, especially for high-rise and large-scale frame structures.
机译：在框架结构的稳定性分析中，有时无法获得通过传统的有限元方法（FEM）得出的结果，其中以一个构件为一个构件。本文以气泡函数为棒状单元的形状函数为基础，开发了一种新的气泡函数有限元方法（BFEM），该方法基于虚功原理推导了弯曲和几何刚度矩阵。气泡函数是有限元模式，它们完全位于单个元素内，并且在元素边界处为零，而在其他点处不为零。 BFEM与传统的杆式FEM一样简洁，但精度更高，并且适用于各种框架结构的屈曲分析。气泡函数的使用大大改善了有限元分析的收敛性，并有效降低了框架结构屈曲分析的计算成本。数值结果表明，在有限元中使用气泡函数进行结构稳定性分析非常有效，特别是对于高层和大型框架结构而言。

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