基于样条函数的薄壁曲线箱梁弯扭耦合分析  

Bending-torsion coupling analysis of thin-walled curved box girder based on spline function

作　　者：胡启平[1] 郭新宇 Hu Qiping;Guo Xinyu(Provincial Mechanics Experimental Teaching Demonstration Center,College of Civil Engineering,Hebei University of Engineering,056038,Handan,China)

机构地区：[1]河北工程大学土木工程学院力学实验教学示范中心,邯郸056038

出　　处：《应用力学学报》2021年第3期1169-1175,共7页Chinese Journal of Applied Mechanics

基　　金：河北省自然科学基金(E20164021100)。

摘　　要：为了更加准确地分析薄壁曲线箱梁弯扭耦合问题,放弃了弯曲时的平截面假设和乌曼斯基对扭转时纵向翘曲位移的假定,在标准的三次样条函数基础上推导出了转换后的三次样条函数,利用该函数来模拟弯曲和扭转耦合情况下的纵向位移,考虑了弯曲时剪力滞后、剪切应变,以及翘曲剪应变的影响,并在弯曲和扭转应变能完全耦合的情况下进行了计算。建立了薄壁曲线梁弯扭耦合分析的哈密顿对偶求解体系,导出了哈密顿正则方程。哈密顿正则方程为一阶微分方程组,便于应用高精度的精细积分法来求解。本文将三次样条插值与精细积分相结合,形成了一种半离散半精细积分的新算法,从一定程度上完善了薄壁曲线箱梁的分析理论。将本文算法与相关文献计算结果进行对比,平均相对误差为4.45%,整体吻合良好。In order to improve the computation accuracy of thin-walled curved box girders under bending-torsion coupling deformation together,it abandons the plane section assumption for bending and Umanski’s assumption of longitudinal warping displacement for torsion deformation in this paper,and a transformed cubic spline function is derived based on the standard cubic spline function.The function can be used to simulate longitudinal warping displacement in the bending-torsion coupling problem on the effects of shear lag,shear stress and warping shear stress.The bending and torsional strain energies are fully coupled during computing process.Moreover,a Hamiltonian canonical equations for bending-torsion coupling of thin-walled curved box girders was established and Hamiltonian canonical equations were derived.Hamiltonian canonical equations are first-order differential equations,which is easy to be solved by the precise integration method with high precision.In this paper,a new semi-discrete and semi-precision integral algorithm is developed by combining cubic spline interpolation with precision integral method,which improves the analysis theory of thin-walled curved box girder to a certain extent.The average relative error compared with the results calculated in relevant reference is within 4.45%,which is in good agreement on the whole.

关 键 词：薄壁曲线箱梁 弯扭耦合 三次样条函数 哈密顿正则方程 精细积分法 

分 类 号：TU311[建筑科学—结构工程]