Bending Theories for Beams and Plates With Single Generalized Displacement
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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。鉴于此从基本假设出发,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理论和中厚板理论,给出了几种简单梁的解析解,并用数值算例验证了这一理论的适用性。Abstract: Classical bending theories for beams and plates can not be used for short,stubby beams and thick plates since transverse shearing effect is excluded,and ordinary theories with multiple generalized displacements can not be used for long,slender beams and thin plates since the innate relation between rotation angle and deflection is ignored.These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle.Based on several basic assumptions,a new type of theories which not only include the transverse shearing effect is presented, but also the relation between rotation angle and deflection is obtained.Analytical solutions of several simple beams are given.It has been testified by numerical examples that the new theories can be used for either long,slender beams and thin plates or short,stubby beams and thick plates.
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Key words:
- beam /
- plate /
- bending theory /
- transverse shearing effect /
- universal finite element
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