基于能量法的变截面层合管整体稳定承载力计算方法

A method for calculating bearing capacity of laminated tube with variable cross section based on energy method

为计算变截面层合管杆件整体稳定承载力,提出一种基于能量法的理论计算模型。采用基于三维梁理论的层合管等效抗弯刚度计算方法,计算了等截面段、变截面段的等效工程弹性系数。在考虑剪切变形的影响以及杆件变截面对轴压挠曲线函数影响的基础上,基于能量法推导了变截面杆整体稳定承载力解析公式。以NASA复合材料变截面杆为算例,进行了理论计算和有限元数值模拟,结果显示:同时考虑上述两因素的理论计算结果与有限元结果最为接近,剪切变形对临界承载力的修正可达10%以上,轴压挠曲线函数的变化对承载力的修正约为1%,可忽略。以锥长和锥角为参数,对变截面杆的承载力、体积和承载效率进行双参数分析,发现变截面对弯曲变形能的影响远大于对剪切变形性能的影响,采用变截面形式能够提高层合管承载效率,且一定锥长下存在承载效率最高对应的最优锥角。

In order to obtain the bearing capacity of laminated tube with variable cross section, an approach based on energy method was presented. A calculation method based on 3D beam theory was adopted. The equivalent engi- neering elastic coefficients of the uniform cross-section part and the variable cross section part were obtained by this method. After considering the influence of shear deformation and the influence of the variable cross section on the deflection curve, the analytical formula of the overall stability bearing capacity of laminated tube was derived based on the energy method. The NASA laminated tube with variable cross section was taken as an example to conduct theoretical calculation and finite element numerical simulation. The modified and unmodified theoretical calculations were compared with finite element result. The result considering the above two factors is mostly close to the finite element result. The influence of shear deformation on the calculation of bearing capacity can be more than 10%, and the influence of deflection curve is about 1% thus can be neglected. The bearing capacity, volume and bearing effi- ciency of laminated tube were analyzed with two parameters of taper length and taper angle. It is found that the vari- ation of cross section has much more influence on bending deformation energy than on shear deformation energy, and this section form can improve bearing efficiency of laminated tube. Besides, under certain taper length, there exists the optimal taper angle corresponding to the maximum bearing efficiency.