自然弯扭梁的非线性分析

研究了两端边界均为完全约束的自然弯扭梁在小应变，大位移和大转动情况下的非线性性质，并考虑了横向剪切变形和扭转翘曲变形的影响，分析中还包括了拉伸，弯曲和扭转的各种弹性耦合。由最小势能原理可以导出所给问题的平衡方程。这里欧拉角可以用来表示任意大的转动。该方法还可方便地推广到其他各种不完全约束边界的情况。此外，利用上述结果还可以得到该梁在小位移理论中的基本方程和有关公式。

Nonlinear Analysis of Naturally Curved and Twisted Beams

The nonlinear behavior of naturally curved and twisted beams undergoing small strains, large displacements and rotations was investigated for these beams with complete constrained boundaries at two ends, and the transverse shearing deformations and torsion-related warping were taken into account. The various elastic couplings of extension-twisting or bending-twisting were included in the analysis. The equilibrum equations were deduced from the minimum potential energy principle. The Euler angles could be expressed with arbitrarily large rotations. The above-mentioned method can also be extended to the various incomplete constrained boundaries conveniently. In additon, the geverning equations and concerning formulas in. the small displacement theory of the beams can be derived by means of above results.