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

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.