基于“板-梁”理论的FGM三角形截面梁组合扭转研究  

Combined Torsion of FGM Triangular Section Beams Based on the"Plate-Beam"Theory

作　　者：张文福 邵琰皓[1] ZHANG Wenfu;SHAO Yanhao(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215009,China;School of Civil Engineering and Architecture,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215009 [2]南京工程学院建筑工程学院,南京211167

出　　处：《建筑钢结构进展》2024年第12期62-70,共9页Progress in Steel Building Structures

基　　金：国家自然科学基金(51578120、51178087、52178143)。

摘　　要：三角形截面梁因其优异的力学性能,在工程领域得到了广泛应用。功能梯度材料(FGM)也因其可根据材料功能来设计材料性质单向或双向变化的特点,表现出优异的性能,具有广阔的应用前景。以FGM性质沿板件宽度变化的三角形截面悬臂梁为例,当其受到端部集中扭矩作用时,基于“板-梁”理论及相关假设,推导了该悬臂梁组合扭转的总势能和总应变能表达式,给出了三角形截面的翘曲刚度和自由扭转刚度;建立了能量变分模型,并依据能量变分原理,进一步得到了能量微分模型,最后求解得到了三角形截面悬臂梁在端部扭矩作用下的最大扭转角表达式;采用有限元软件ANSYS建立了相应的有限元模型并进行了求解,将有限元结果与理论结果进行对比,验证了“板-梁”理论的正确性。Triangular section beams have been widely used in the engineering field due to their excellent mechanical properties.Functionally gradient materials(FGMs)also exhibit excellent performance and broad application prospects due to their ability to design materials with unidirectional or bidirectional changes in material properties based on material functionality.Taking the case of a triangular section cantilever beam with FGM properties varying along the width of the plate as an example,when subjected to a concentrated torque at the end,the total potential energy and total strain energy expressions for the combined torsion of the cantilever beam were derived based on the"plate-beam"theory and relevant assumptions.The warping stiffness and free torsional stiffness of the triangular section were provided,and an energy variational model was established,and according to the principle of energy variation,an energy differential model was further obtained.The expression for the maximum torsion angle of a triangular section cantilever beam under the action of end torque was finally solved.A corresponding finite element model was established using the finite element software ANSYS and solved.The finite element results were compared with the theoretical results,and the correctness of the"plate-beam"theory was verified.

关 键 词：功能梯度材料 三角形截面 “板-梁”理论 组合扭转 

分 类 号：TU31[建筑科学—结构工程]