Читать книгу Rethinking Prototyping - Группа авторов - Страница 50

To calculate the internal forces in beam elements, we need to define additional orientations of the beam-ends. In this paper, we consider only rigid joints. That means each beam end will rotate simultaneously with the corresponding node and maintain their relative difference in orientations. The Euler-Bernoulli beam element, which has 12 DOF each, is used to calculate internal forces in beams. The axial force, bending moments and torque are determined by the corresponding positions and orientations of the two beam-ends of the beam element. The formulations for calculating internal forces are listed as follows:

Where θ is the included angle that is defined by the orientation of the beam end and the axial direction of the beam. Its geometric definition is shown in Fig. 2.