空间曲梁单元的扭转修正系数研究  

Torsional shear correction factors for 3D curved beam elements

作　　者：宋泰宇 李国平[2] SONG Tai-yu;LI Guo-ping(Tongji Architectural Design(Group)Co.,Ltd.,Shanghai 200092,China;Department of Civil Engineering,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学建筑设计研究院(集团)有限公司,上海200092 [2]同济大学土木工程学院,上海200092

出　　处：《计算力学学报》2021年第1期84-89,共6页Chinese Journal of Computational Mechanics

基　　金：中国博士后科学基金(2020M671237);同济大学建筑设计研究院(集团)有限公司科研项目(2020KY07)资助项目.

摘　　要：三维空间曲梁有限单元模型是模拟曲梁结构的有效数值方法,可以考虑曲梁的弯扭耦合特性,最为符合曲梁的几何和受力特征。由于有限元法采用梁理论的平截面假定,空间曲梁单元上的扭转剪应力分布与实际曲梁截面上的扭转剪应力不同,从而会导致扭转刚度和扭转变形的计算失真。本文基于剪切应变能等效原理,推导了不同长宽比的矩形截面空间曲梁单元的扭转刚度修正系数η和截面边中点处扭转剪应力的修正系数λ,并采用曲线悬臂梁进行了验证。验证结果表明,根据本文提出的η作为校正因子的空间曲梁单元模型,对任意矩形截面曲梁计算的扭转变形均与实体单元模型的结果吻合良好;且只有截面为正方形时,扭转剪应力修正系数η才恰好与弯曲剪应力修正系数(1.2)一致。Using a 3D curved beam element is an accurate and efficient numerical method to model curved beam structures,because this type of elements take the coupling effect of bending and torsion into account and in accordance with the actual geometrical and structural characteristics of curved beam structures.As a result of the plain section assumption adopted by the classic beam theory,the torsional shear stresses calculated by a 3D curved beam element model have a different sectional distribution from the actual torsional shear stresses in curved beams,leading to an incorrect torsional stiffness and torsional deformation of curved beams.Based on the principle of shear energy equivalence,the correction factors of torsional stiffness (η) and torsional shear (λ) for rectangular cross-section 3D curved beam elements are derived out.The validity of the proposed correction factors is illustrated with a curved cantilever beam example.The results indicate that the torsional deformations calculated by the 3D curved beam element model with the proposed correction factors with those from solid element models.The results also reveal that the torsional shear correction factor equals to the transverse shear correction factor (1.2) only in the case when the beam cross-section is square.

关 键 词：有限单元法 弹性力学 曲线梁 空间曲梁单元 扭转剪应力 扭转刚度 

分 类 号：U441[建筑科学—桥梁与隧道工程] O343[交通运输工程—道路与铁道工程]