论文部分内容阅读
基于广义变分原理和精化的zigzag理论建立了高精度的层合梁弯曲和自由振动模型。为准确预测层合梁的力学行为做出两个预处理:首先采用线性zigzag函数[1]使面内位移在梁高度方向(z方向)上呈锯齿分布;然后通过弹性平衡方程构造了预先满足层间连续和自由表面条件的层间横向剪力,因此不需要剪切修正因子。另外,基于Reissner混合变分原理推导了该梁模型的控制方程和边界条件,并以正交铺设的两端简支层合梁为例,分析了静弯曲和自由振动行为。算例结果表明,该模型能够准确地预测位移、应力和自振频率,验证了本文方法的精度和可靠性。
Based on the generalized variational principle and refined zigzag theory, a model of bending and free vibration of laminated beams with high precision is established. In order to accurately predict the mechanical behavior of the laminated beam, two pretreatments are made: firstly, the in-plane displacement is zigzag distributed in the direction of the height of the beam (z direction) by linear zigzag function [1]; then, Interlayer shear between layers of continuous and free surface conditions eliminates the need for shear correction factors. In addition, the governing equations and boundary conditions of the beam model are derived based on the Reissner mixed variational principle. The static bending and free vibration behavior are analyzed with the simply supported laminated beams at both ends of the cross-section. The results show that the model can accurately predict displacement, stress and natural frequency, and verify the accuracy and reliability of the proposed method.