摘要
经典的梁板弯曲理论由于未考虑横向剪切变形的影响而只能适用于细长梁和薄板 .传统的多广义位移的深梁理论和中厚板理论由于忽视了转角与挠度之间的内在关系而只能适用于短粗梁和中厚板 .这两种理论存在着转角的独立性与不独立性之间的矛盾 ,因而不相兼容 .本文从基本假设出发 ,既考虑了横向剪切影响 ,又确定了转角与挠度的关系 ,导出了单广义位移的深梁和中厚板解法 ,给出了几种简单梁的解析解 ,并用数值算例验证这一解法的适用性 .
Classical bending theory of beam and plate can only be fit for thin and long beam and thin due to without considering deformed influence of cross shearing. Traditional deep beam and medium\|think plate theory of multi\|generalized displacement can only be fit for short and wide beam and medium\|thick plate due to overlooking the inner relationship of corner and deflection. There is a contradiction of independence and non\|independence of corner between the two kinds of theory, therefore, incompatible. With a basic supposition, the deep beam and medium\|thick plate theory of mono\|generalized displacement were derived, not only having considered the influence of cross shearing, but ascertained the relationship of corner and deflection. A few analytic problems of simple beam were given and the applicability of the theory with mathematical exercise was verified.
出处
《浙江大学学报（理学版）》
CAS
CSCD
2000年第4期409-414,共6页
Journal of Zhejiang University（Science Edition）
关键词
弯曲理论
单广义位移解法
深梁
中厚板
beam
plate
bending theory
influence of cross shearing
general finite unit
