复合材料梁的几何精确非线性建模及非经典效应

Geometrically exact nonlinear modeling and non-classical effect influence of composite beams

基于Hodges的广义Timoshenko梁理论对具有任意剖面形状、任意材料分布及大变形的复合材料梁进行几何精确非线性建模,采用旋转张量分解法计算梁内任意一点的应变,采用变分渐近法确定梁剖面的任意翘曲,采用平衡方程由二次渐近精确的应变能导出广义Timoshenko应变能,采用广义Hamilton原理建立梁的几何精确非线性运动方程。将所建模型用于复合材料梁的静动力分析,通过与实验数据的对比,验证了建模方法的准确性,并进一步研究了剖面翘曲及横向剪切变形非经典效应对复合材料梁的影响。研究表明,剖面翘曲对复合材料梁的静变形和固有频率有显著影响,横向剪切变形对复合材料梁的静变形和固有频率的影响与梁的长度/剖面高度比有关。

The geometrically exact nonlinear modeling of composite beam with arbitrary cross sectional shape,generally anisotropic material behavior and large deflection had been presented,based on the generalized Timoshenko beam theory of Hodges.The concept of decomposition of rotation tensor was used to calculate the strains in the beam.The variational asymptotical method was used to determine the arbitrary warping of the beam cross section.The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy.The geometrically exact nonlinear equations of motion were established by the Hamilton＇s generalized principle.The established modeling was used for the static and dynamic analysis of composite beams and was verified by the comparisons with experimental data.The influences of the non-classical effects such as the cross sectional warping and the transverse shear deformation on the composite beams were investigated.The results indicate that the cross sectional warping has significant influences on the static deformation and the natural frequencies of the composite beams,and the influences of the transverse shear deformation on the static deformation and the natural frequencies of the composite beams are related to the length to depth ratio of the beam.