改进的绝对节点坐标平面梁有限元传递矩阵法

IMPROVED FINITE ELEMENT TRANSFER MATRIX METHOD OF PLANE BEAM ELEMENTS USING THE ABSOLUTE NODAL COORDINATE FORMULATION

针对大运动柔性梁的动力学问题,采用绝对节点坐标有限元法建立了非线性单元动力学方程。在单元动力学方程中节点广义加速度和节点广义内力之间呈线性关系,基于此并结合结构力学传递矩阵法,提出了全新的绝对节点加速度平面梁有限元传递矩阵法。与传统有限元传递矩阵法相比,方法的传递矩阵和时程积分方法无关,便于不同常微分方程数值方法的引入。最后通过大运动小变形梁算例验证了此法。

For the dynamics problems of flexible beams with large overall motion,nonlinear element dynamic equations are established,adopting the absolute nodal coordinate formulation（ ANCF）. Since the relationship of generalized accelerations and generalized forces is linear in the equations,a new absolute nodal acceleration finite element transfer matrix method（ TMM） for plane beam is proposed,combining the idea of TMM. Compared with traditional finite element transfer matrix method,transfer matrixes of the proposed method are derived without time-integration methods. Here ordinary differential equation numerical methods can be applied conveniently. Finally,the method is verified correct by an example,the beam with large overall motion and small deformation.