从优化设计理论谈材料力学中的等强度超静定梁  

DISCUSSION ON STATICALLY INDETERMINATE BEAM OF EQUAL STRENGTH IN MECHANICS OF MATERIALS FROM OPTIMAL DESIGN THEORY

作　　者：孟增[1] 王选 周焕林[1] MENG Zeng;WANG Xuan;ZHOU Huanlin(College of Civil Engineering,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《力学与实践》2022年第6期1394-1398,共5页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11972143)。

摘　　要：工程中常用的梁结构因各横截面上的弯矩不同,采用等截面梁时,材料不能得到充分利用,经济性较差。若采用等强度梁,可以使所有截面上的最大应力同时达到材料的许用值,充分挖掘梁结构的承载潜能,提高材料利用率。本文从优化设计角度出发,求解等强度梁截面几何尺寸沿轴线变化的情况,有助于在一般情况下深化对等强度梁设计的理解。The beam commonly used in engineering has different bending moments on different cross-sections.The material in a beam with uniform cross-section cannot be fully utilized,which is not economical.However,if equal-strength beams are used,the stress on all sections can simultaneously reach the maximum allowable value of the materials so as to fully exploit the load-bearing potential.Accordingly,the material utilization rate is promoted.From the perspective of optimization design,this paper solves the stress on each cross-section along the axis,which is helpful to deepen the understanding of the equal-strength beam design from a general viewpoint.

关 键 词：等强度梁 结构优化设计 材料力学 弯曲变形 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]