图像扭曲
数学
背景(考古学)
有限元法
计算
不稳定性
旋转(数学)
质心
数学分析
几何学
应用数学
牙石(牙科)
算法
结构工程
计算机科学
工程类
物理
机械
人工智能
生物
古生物学
医学
牙科
作者
Jean‐Marc Battini,Costin Pacoste
标识
DOI:10.1016/s0045-7825(01)00352-8
摘要
The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and it is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed. This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements.
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