任意阶梯型截面Timoshenko梁的弯曲

doi:10.12066/j.issn.1007-2861.1974

摘要/Abstract

摘要：

研究边界弹性支承任意阶梯型截面Timoshenko梁的弯曲变形, 利用Heaviside函数给出了在横向载荷作用下阶梯型截面Timoshenko梁弯曲挠度和转角的解析闭合解, 避免了经典解析方法应用分段函数导致的繁琐. 在此基础上, 数值分析了固支和悬臂单、双阶梯型截面Timoshenko梁的弯曲变形, 考察了变截面位置、截面大小、梁高跨比以及边界支承刚度等对Timoshenko梁弯曲的影响. 结果表明, 阶梯型截面Timoshenko梁的挠度和转角与等截面Timoshenko梁的挠度和转角有较大的差异, 虽然阶梯型截面Timoshenko梁挠度光滑, 但在截面变化位置处, 阶梯型截面Timoshenko梁转角斜率存在明显的跳跃.

关键词: 阶梯型截面 Timoshenko 梁, 弯曲变形, 弹性支承, 广义函数, 解析闭合解

Abstract:

Bending deformation of a Timoshenko beam with arbitrary stepped cross-section and elastic support on boundaries was investigated. Based on the Heaviside function, analytical closed-form solutions of the deflection and rotational angle of the Timoshenko beam with arbitrary stepped cross-section subject to transverse load was derived. On this basis, the bending behavior of clamped and cantilever Timoshenko beams with single and double stepped cross-sections was analyzed numerically. Influences of location and quantity of the cross-section change, span-height ratio of the beam as well as stiffness of the boundary supports on the bending of the Timoshenko beam were examined. It is shown that there exist major differences of deflections and rotational angles between a Timoshenko beam with stepped cross-section and a Timoshenko beam with constant cross-section. Although deflection of the Timoshenko beam with stepped cross-section is smooth, there exists evident jump of the slope of the rotational angle of a Timoshenko beam with stepped cross-section at the location of the cross-section change.

Key words: Timoshenko beam with stepped cross-section, bending deformation, elastic support, generalized function, analytical closed-form solution

中图分类号:

TU223
TU317

杨骁, 钱程, 钱雪薇. 任意阶梯型截面Timoshenko梁的弯曲[J]. 上海大学学报(自然科学版), 2019, 25(5): 786-795.

Xiao YANG, Cheng QIAN, Xuewei QIAN. Bending of Timoshenko beam with arbitrary stepped cross-section[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(5): 786-795.

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