拉压不同模量矩形板的双向弯曲问题

doi:10.3969/j.issn.1007-2861.2015.02.003

上海大学学报(自然科学版) ›› 2017, Vol. 23 ›› Issue (1): 128-137.doi: 10.3969/j.issn.1007-2861.2015.02.003

拉压不同模量矩形板的双向弯曲问题

张良飞, 姚文娟

上海大学土木工程系, 上海200444

收稿日期:2015-01-03 出版日期:2017-02-28 发布日期:2017-02-28
通讯作者: 姚文娟(1957—), 女, 教授, 博士生导师, 博士, 研究方向为结构工程. E-mail: wenjuan@mail.shu.edu.cn
作者简介:姚文娟(1957—), 女, 教授, 博士生导师, 博士, 研究方向为结构工程. E-mail: wenjuan@mail.shu.edu.cn

Biaxial bending of rectangular plates with different modulus

ZHANG Liangfei, YAO Wenjuan

Department of Civil Engineering, Shanghai University, Shanghai 200444, China

Received:2015-01-03 Online:2017-02-28 Published:2017-02-28

摘要/Abstract

摘要：

拉压不同模量矩形板的双向弯曲的中性轴可以从两个弯曲方向考虑. 基于不同模量理论, 利用静力平衡方程推导了不同模量矩形板的中性轴位置, 再利用Kantorovich变分法求解了不同模量矩形板的挠曲线方程, 并将得到的数值解和有限元解进行比较, 二者较为吻合. 计算结果表明, 当拉压不同模量的差异较大时, 不同模量弯曲矩形板的挠度不宜采用相同模量经典板壳理论. 该方法为分析不同模量矩形板和其他结构形式的板的弯曲问题提供了求解思路,并为其在工程中的应用提供了一定的理论参考.

关键词: 不同模量, 双向弯曲, Kantorovich变分法

Abstract:

An eutral axis can be considered from two bending directions to solve the biaxial bending problem of rectangular plates with different modulus. Based on the different modulus theories, an equation of the neutral axis location is derived using the static equilibrium equation of rectangular plates with different modulus. The deflection curve equation is solved with the Kantorovich method. Its solution agrees well with the finite element solution. The result shows that the classical shell theory is not applicable in calculating deflection of a rectangular plate when tensile and compressive modulus are quite different. The proposed method provides an approach to analyze the bending problem of other structure forms of plate with different modulus, and theoretical reference for engineering applications.

Key words: biaxial bending, different modulus , Kantorovich variational method

张良飞, 姚文娟. 拉压不同模量矩形板的双向弯曲问题[J]. 上海大学学报(自然科学版), 2017, 23(1): 128-137.

ZHANG Liangfei, YAO Wenjuan. Biaxial bending of rectangular plates with different modulus[J]. Journal of Shanghai University（Natural Science Edition）, 2017, 23(1): 128-137.

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拉压不同模量矩形板的双向弯曲问题

Biaxial bending of rectangular plates with different modulus

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