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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,采用变分渐进法确定梁剖面的任意翘曲,采用平衡方程由二次渐进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。
Based on the generalized Timoshenko beam theory of Hodges, the geometrically accurate nonlinear modeling of the composite beam with arbitrary cross-sectional shape, arbitrary material distribution and large deformation is performed. The strain of any point in the beam is calculated by the method of rotational tensor decomposition. Variational asymptotic method To determine the arbitrary warpage of the beam profile, the generalized Timoshenko strain energy is derived from the quadratic asymptotically accurate strain energy using the equilibrium equation, and the geometrically accurate nonlinear motion equation of the beam is established using the generalized Hamilton principle. The proposed model is applied to the static and dynamic analysis of the composite beam. The accuracy of the modeling method is verified by comparison with the experimental data. The effect of non-classical effects of profile warpage and transverse shear deformation on the composite beam is further studied . The results show that the warpage and natural frequency of composite beams have significant effects on the warpage and natural frequency of the composite beams. The effect of transverse shear deformation on the static deformation and natural frequency of the composite beams is related to the beam length / section height ratio.