集中载荷作用下双模量矩形截面梁的弹性解  

Elasticity Solution of Bimodulous Rectangular Beam under Concentrated Load

作　　者：李政 肖珍 吴晓 LI Zheng;XIAO Zhen;WU Xiao(School of Intelligent Building,Changde College,Changde,415000,China)

机构地区：[1]常德学院智能建筑学院,常德415000

出　　处：《湖南师范大学自然科学学报》2023年第6期143-148,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(52008164);湖南省教育厅科学研究项目(22C0939)。

摘　　要：利用弹性理论的半逆解法研究了双模量矩形截面梁的弯曲变形,推导出了集中载荷作用下双模量简支矩形截面梁的应力及位移表达式。研究分析表明:对于集中载荷作用下双模量简支矩形截面梁,弹性理论给出了集中载荷作用下双模量简支矩形截面梁拉伸区、压缩区的轴向位移及弯曲挠度表达式,这说明双模量梁截面任意点的弯曲挠度都不相同,而材料力学方法仅能推导出集中载荷作用下双模量简支矩形截面梁的中性轴挠曲线表达式。双模量简支矩形截面梁中性轴处弯曲挠度对当模量比变化很敏感,原则上建议计算双模量简支矩形截面梁中性轴处弯曲挠度应采用弹性理论。The bending deformation of bimodulous rectangular cross-section beam was studied by using the semi-inverse method of elastic theory.The expressions of stress and displacement of bimodulous simply supported rectangular cross-section beam under concentrated load are derived.The analysis shows that the expressions of axial displacement and bending deflection in tension and compression zones of simply supported rectangular beams with bimodulous under concentrated load are given by elastic theory.It shows that the bending deflection at any point of the double mode beam section is different.However,the material mechanics method can only derive the expression of the neutral axial deflection curve of a simply supported rectangular beam with bimodulous under concentrated load.The bending deflection at the neutral axis of a simply supported bimodulous rectangular beam is sensitive to the change of the equivalent modulus ratio.In principle,the elastic theory is suggested to calculate the bending deflection at the neutral axis of a simply supported bimodulous rectangular beam.

关 键 词：集中载荷 双模量 矩形 梁 弹性理论 应力 挠曲线 

分 类 号：O341[理学—固体力学]