框架结构稳定分析的泡函数有限元法

寻求一种既有普通杆件有限元的简洁性,又能求解所有框架结构临界载荷的有效方法．根据框架结构杆件失稳变形和泡函数的特点,采用新的基函数系,在普通杆件有限元的形函数中引入泡函数,得到泡函数有限单元法．泡函数是定义在有限单元上的一个模型,其在单元的边界上为零,而在内部非零．它的应用改善了普通杆件有限元法的收敛性,并使其适用于任何框架结构的屈曲分析．算例表明,泡函数有限元法对于框架结构的屈曲分析具有良好的适应性、稳定性、收敛性和求解效率,是一种进行大型结构屈曲分析的有效方法．

Buckling Analysis of Frame Structures using Bubble-Function FEM

This paper attempts to find an effective approach which is as concise as the conventional bar FEM, and can determine the critical loads of all kinds of frame structures also. According to the characteristics of the bar buckling deformation and the bubble-functions themselves, a new basis function series with bubble-functions is taken as the shape function of a bar element, then a bubble-function finite element method (BFEM) is developed. Bubble-function is a kind of FEM model, which is defined within a single element and is zero on boundaries of the element, but nonzero inside. The use of bubble-functions significantly improves the convergence of finite element analysis, and the BFEM is adaptable to the buckling analysis of all kinds of frame structures. Numerical results show that the BFEM is very suitable, convergent and efficient for stability analysis of structures, especially is a valid method for buckling analysis of the large structures.