自然弯扭梁广义翘曲坐标的求解

提出了自然弯扭梁受复杂载荷作用时静力分析的一种理论方法，重点在于对控制方程的求解，其中考虑了与扭转有关的翘曲变形和横向剪切变形的影响．在特殊的情况下，可以比较容易地得到这些方程的解答，包括各种内力、应力、应变和位移的计算．算例给出了平面曲梁受水平和垂直分布载荷作用时广义翘曲坐标的求解方法．计算结果表明，求得的应力和位移的理论值和三维有限元结果非常接近．此外，该理论不限于具有双对称横截面的自然弯扭梁，同样可推广至具有一般横截面形状的情况．

Solution of Generalized Coordinate for Warping for Naturally Curved and Twisted Beams

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross section, it can also be extended to those with arbitrary cross-sectional shape.