任意边界条件下双模量矩形薄板的弯曲

Bending of double modulus rectangular thin plates under arbitrary boundary conditions

将双模量板等效为两个各向同性小矩形板组成的层合板,假定该层合板的中性面即为两个小矩形板的交界面。根据中性面上应力为零且薄板全厚度上应力的代数和为零,推导了双模量矩形薄板的中性面位置。本文采用严宗达[13]提出的带补充项的双重正弦傅里叶级数通解,该通解可以适用于任意边界条件的矩形薄板且不需要叠加或者重新构造。联立边界条件和控制方程,求得通解中的待定系数并代入到通解中,即可得到任意边界条件下双模量矩形薄板的弯曲解析解。与有限元结果比较,本文结果符合工程精度要求。

The dual-modulus plate is equivalent to a laminate composed of two isotropic small rectangular plates.It is assumed that the neutral surface of the laminate is the interface of the two small rectangular plates.According to the fact that the stress on the neutral plane is zero and the algebraic sum of the stress on the full thickness of the plate is zero,the position of the neutral plane of the double-modulus rectangular plate is derived.In this paper,the general solution of a double sine Fourier series with supplementary terms proposed by Yan Zongda is used.This general solution can be applied to rectangular thin plates with arbitrary boundary conditions and does not need to be superimposed or reconstructed.Simultaneous boundary conditions and governing equations are used to obtain the undetermined coefficients in the general solution and bring them into the general solution.Then,the analytical solution of the two-modulus rectangular thin plate under arbitrary boundary conditions can be obtained.Compared with the finite element results,the results obtained in this paper meet the engineering accuracy requirements.