建立基于力的变截面梁单元质量矩阵的新方法  

A new method of formulating the consistent mass matrices for force-based beam elements

作　　者：左占宣[1] 李爽[1] 翟长海[1] 谢礼立[1,2] 

机构地区：[1]哈尔滨工业大学土木工程学院,哈尔滨150090 [2]中国地震局工程力学研究所,哈尔滨150080

出　　处：《计算力学学报》2013年第5期744-748,共5页Chinese Journal of Computational Mechanics

摘　　要：基于位移的有限梁单元中三次Hermite插值函数不能有效地描述变截面梁单元内部位移变化,只能通过加密网格增加单元数解决,会造成计算量增大。基于力的有限梁单元由于使用的力插值函数不受截面形状变化的影响,在处理变截面梁时有很大优势,可以得到精确的位移插值函数,利用较少的单元可以达到很高的精度,解决了基于位移的有限梁单元在处理变截面梁时的不足。本文得到了考虑剪切变形的位移插值函数和考虑转动惯量的一致质量矩阵。利用算例验证了本文理论的正确性和高效性。The displacement-based beam elements can not effectively describe the internal displacement field for variable cross section beams. The only method to solve this problem is to use more elements, which will increase the computational cost. Force-based beam elements, which use the force interpolation functions and can get the accurate displacement interpolation functions, have advantages of dealing with the variable cross-section beams and have higher accuracy than the displacement-based beam elements. This paper derives the consistent mass matrices considering moment of inertia and shear deformation. The accuracy and efficiency of the mass matrices is verified by numerical examples.

关 键 词：梁单元 剪切变形 一致质量矩阵 

分 类 号：O316[理学—一般力学与力学基础]