基于广义变分原理和锯齿理论的高精度层合梁模型

A High-accuracy Composite Laminated Beam Model Based on Generalized Variational Principle and Zigzag Theory

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。

A high-accuracy bending and free vibration model of composite laminated beam is developed based on generalized variational principle and zigzag theory.To predict the mechanical behaviors accurately,the following two-step processes are implemented in this paper.Firstly,the linear functions are employed to insure that in-plane displacements through the thickness direction(the direction of z axis)are of the zigzag form.Secondly,the interlaminar stresses which satisfy aprior continuity conditions at the interface and free conditions at the surface are derived with the aid of the Elasticity equilibrium equations.Therefore,the transverse shear correction factors are not required.Moreover,the Reissner's Mixed Variational Theorem is employed to derive the governing equations and the boundary conditions.A simply supported cross-ply beam model is taken as an illustrative example,the problem of static bending and free vibration are analytically solved.Illustrative examples indicate that the displacements,stresses and natural frequencies predicted by present model are accurate which demonstrates the correctness and reliability of present formulation.