固体力学中的统一分析梁与有限节线法

针对现有梁理论不能解决的杆状类工程结构构件和结构体系，本文提出了一种新的梁模型——统一分析梁与一种新的数值分析方法——有限节线法。利用统一分析梁和有限节线法不仅可以解决任意杆状类结构构件或结构体系的力学分析问题，而且当问题的性质与传统梁理论的前提条件一致时，会得出同样精度的解答。算例计算结果证明了统一分析梁的合理性与有限节线法的正确性。

A unified analytical beam & a finite nodal-line method in solid mechanics

In view of the mechanics problems of beam-like structural members or systems that cannot be dealt with by existing beam theories, a unified analytical model for all beam-like members or structural systems, known as a Unified Analytical beam or a UA beam, and a novel computational methodology named Finite Nodal-Line (FNL) method are presented. By means of the UA beam theory and the FNL method, the analyses of arbitrary stocky shaped members and structural systems will be readily carried out. Furthermore, when the properties of a mechanics problem are consistent with the application conditions of a traditional classical beam, both the UA beam and traditional classical beam will possess an identical precision solution for the problem. The comparison study among different examples of beams is performed to verify the rationality of the UA beam theory and the validity of the FNL method.