基于板-梁理论的功能梯度材料蜂窝梁组合扭转分析  

Combined Torsion Analysis of Functionally Graded Material Honeycomb Beams Based on Plate-beam Theory

作　　者：张文福[1,2] 杨立繁 黄鸿杰 ZHANG Wenfu;YANG Lifan;HUANG Hongjie(School of Architectural Engineering,Nanjing Institute of Technology,Nanjing 211167,China;School of Mechanical Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院建筑工程学院,江苏南京211167 [2]南京工程学院机械工程学院,江苏南京211167

出　　处：《洛阳理工学院学报（自然科学版）》2024年第4期24-31,共8页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

基　　金：国家自然科学基金项目(1578143).

摘　　要：以端部作用有集中扭矩的功能梯度材料工字形蜂窝梁为研究对象,基于Vlasov刚周边假设、kirchhoff板力学模型与板-梁理论,通过金属与陶瓷体积分数的幂律分布,得出功能梯度梁的力学性能在厚度方向上呈连续变化,并通过能量变分法推导出蜂窝梁扭转的总应变能。根据作用于端部的集中扭矩,建立总势能方程,通过求解微分方程得出蜂窝梁组合扭转最大扭转的理论解。采用ANSYS软件对理论进行检验,利用shell181单元的分层模拟材料特性,计算了17组不同尺寸的蜂窝梁在端部集中扭矩下的最大扭转角,与理论解进行对比误差在1.61%~3.47%之间。Taking the functional gradient material I-beam with concentrated torque acting on the end as the research object,based on the Vlasov rigid perimeter assumption,the kirchhoff plate mechanics model and the plate-beam theory,it is concluded that the mechanical properties of the functional gradient beams vary continuously in the thickness direction through the power-law distribution of the volume fractions of metals and ceramics,and the total strain energy for the torsion of the honeycomb beams is derived through the energy-variable-division method.Based on the concentrated torque acting on the end,the total potential energy equation is established,and the theoretical solution for the maximum torsion of the combined torsion of the honeycomb beam is derived by solving the differential equation.ANSYS software is used to check the theory,and the layered simulation of material properties using shell181 cells is used to calculate the maximum torsion angles of 17 groups of honeycomb beams of different sizes under the concentrated torque at the ends,and the errors are between 1.61%-3.47%when compared with the theoretical solutions.

关 键 词：板-梁理论 组合扭转 功能梯度材料 蜂窝梁 有限元分析 

分 类 号：TU391[建筑科学—结构工程]