基于旋转场曲率的二维剪切梁单元建模

发布时间：2018-11-22 08:19

【摘要】：对二维剪切梁单元进行研究,利用平面旋转场理论推导了精确曲率模型.采用几何精确梁理论构建了剪切梁单元弹性力矩阵.通过绝对节点坐标方法建立了系统的非线性动力学方程,提出基于旋转场曲率的二维剪切梁单元,并分别引入经典二维剪切梁单元和基于位移场曲率的二维剪切梁单元进行比较研究.首先,静力学分析证明了所提模型的正确性;其次,特征频率分析验证了模型可与理论解符合,收敛精度高,并且能准确地预测单元固有频率对应的振型;最后,在非线性动力学问题上,通过与ANSYS结果对比分析,证明了该模型可有效处理柔性大变形问题,并且与经典二维剪切梁单元相比具有缓解剪切闭锁的优势.因此,本文提出的基于旋转场曲率的二维剪切梁单元在处理几何非线性问题中具有较大的应用潜力.
[Abstract]:The two-dimensional shear beam element is studied and the exact curvature model is derived by using the plane rotation field theory. The elastic force matrix of shear beam element is constructed by using the geometric accurate beam theory. The nonlinear dynamic equations of the system are established by using the absolute nodal coordinate method. A two-dimensional shear beam element based on the curvature of the rotation field is proposed. The classical two dimensional shear beam element and the two dimensional shear beam element based on displacement field curvature are introduced respectively. Firstly, the model is proved to be correct by statics analysis. Secondly, the characteristic frequency analysis verifies that the model can agree with the theoretical solution, has high convergence accuracy, and can accurately predict the mode shape corresponding to the natural frequency of the unit. Finally, on the nonlinear dynamics problem, by comparing with the ANSYS results, it is proved that the model can effectively deal with the problem of large flexible deformation, and it has the advantage of relieving the shear locking compared with the classical two-dimensional shear beam element. Therefore, the two-dimensional shear beam element proposed in this paper based on the curvature of rotation field has great application potential in dealing with geometric nonlinear problems.
【作者单位】： 西北工业大学航天学院航天飞行动力学技术重点实验室;武汉理工大学机电工程学院;
【基金】：国家自然科学基金重大项目(批准号:61690210,61690211);国家自然科学基金(批准号:61603304,11472213)资助的课题~~
【分类号】：O316
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本文编号：2348666