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.
ZHOU Ke-jian, GONG Ke. A triangular finite element with 9-DOF in common use for thin and thick plate vibration problems[A]. In: DU Qing-hua Ed:Proceedings of the ICVPE-Xian[C]. Xi'an: Xi'an Jiaotong University Press,1986,214-219.