This study presents an efficient beam formulation for static and vibration analysis of 2D non-prismatic beams with the kinematic assumptions of the Timoshenko beam theory. Beams having complex configurations can be straightforwardly constructed by using B-spline basis functions, which are used for descriptions of the beam axis and the sectional height. This feature enables analysis of free-form non-prismatic beams with strong curvatures to be performed conveniently and accurately, and is not virtually found in any existing formulations that are related to non-prismatic beams. The concept of isogeometric analysis is adopted by discretizing the kinematic unknowns, i.e., the translational displacements of the beam axis and the sectional rotation, using B-spline basis functions. A procedure for the recovery of stress components is also presented. The accuracy and performance of the developed approach are assessed through several numerical examples which cover several types of beam, e.g., sinusoidal beam, tapered beam and Tschirnhausen's beam representing free-form beams. Furthermore, convergence tests are also performed to demonstrate convergence properties of the proposed formulation.

这项研究提出了一种有效的梁公式，用于二维非棱柱梁的静力和振动分析。 季莫申科梁理论的运动学假设。可以使用B样条基函数直接构造具有复杂配置的梁，该函数用于描述梁的轴和截面高度。此功能可以方便，准确地分析具有强曲率的自由形式非棱柱光束，而在与非棱柱光束相关的任何现有配方中都找不到这种特征。等几何分析的概念是通过使用B样条基函数离散化运动学未知量（即束轴的平移位移和截面旋转）来采用的。还介绍了一种恢复应力成分的程序。通过几个数值示例，可以评估所开发方法的准确性和性能，这些示例涵盖了几种类型的光束，例如正弦光束，锥形光束和Tschirnhausen的代表自由形式光束的光束。此外，还进行了收敛测试以证明拟议配方的收敛性。