摘要
提出了一种截面插值梁模型,利用该模型求解梁在非均匀热载荷作用下的动静态响应,解决了传统梁理论无法处理受不均匀温度场的梁的问题。利用拉格朗日插值函数对梁单元的截面和轴向分别插值,构造梁的位移场。将位移场代入热弹性动力学方程,得到单元应变和应力,再依据虚功原理推导出单元刚度矩阵、质量矩阵以及等效节点载荷列阵,求解得到热应力。利用热应力的横向剪切力更新单元刚度矩阵,计算梁在热载荷作用下的振动特性。计算结果表明,该方法得到的结果与实体单元模型结果吻合,并且更易于处理受非均匀热载荷作用的细长结构,同时能很好地反映截面的形状、受载及响应结果。
Here, a cross-section interpolation beam model was proposed to solve dynamic and static responses of the beam under non-uniform thermal load, and solve the problem of the traditional beam theory being unable to deal with the beam subjected to non-uniform temperature field. Firstly, cross-section and axial direction of beam element were interpolated with Lagrange interpolation function to construct a beam’s displacement field. Then, the displacement field was substituted into the beam’s thermoelastic dynamic equation to obtain element strain and stress. Furthermore, element stiffness matrix, element mass matrix and equivalent node load array were derived according to the virtual work principle, and thermal stress was solved. Finally, element stiffness matrix was updated with transverse shear force obtained with thermal stress, and vibration characteristics of the beam under thermal load were calculated. Calculation results showed that the results obtained using the proposed method are consistent to those obtained with the solid element model;it is easier to deal with slender structures subjected to non-uniform thermal load, and simultaneously, it can well reflect shape, loading and response results of cross-section.
作者
潘成浩
陈国平
何欢
PAN Chenghao;CHEN Guoping;HE Huan(State Key Lab of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Institute of Vibration Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2023年第5期215-222,244,共9页
Journal of Vibration and Shock
基金
国家自然科学基金资助项目(12072153)
机械结构力学及控制国家重点实验室(南京航空航天大学)自主研究课题资助(MCMS-I-0121G01)。
关键词
空间梁模型
截面插值
截面变形
静力计算
热模态分析
spatial beam model
cross-section interpolation
cross-section deformation
static calculation
thermal modal analysis
