绝对节点坐标法下斜率不连续问题处理方法讨论

Shabana提出的绝对节点坐标法,引入节点斜率坐标作为节点自由度描述转动.对于由梁板壳及块体组成的组合结构,在结构节点处相交单元的节点斜率自由度不连续,这给组合结构的建模和分析带来特殊的困难.本文讨论了文献中研究斜率不连续问题时的处理办法.在简要介绍绝对节点坐标法后,详细地讨论了经典折梁算例和截面呈阶梯变化的直梁算例中斜率不连续问题.对这两个算例,本文采用约束函数法和现有文献中的转换坐标方法,计算了在结构节点处相交杆件的轴向应变,对比这些数值结果,本文指出现有文献中的转换坐标办法,忽视了斜率自由度和转角自由度的差别,从而不能正确给出斜率不连续处相交杆件的轴向应变,需要进一步研究.

Discussion on slope discontinuity using the absolute nodal coordinate formulation

The absolute nodal coordinate formulation(ANCF) proposed by Shabana describes the large rotation by introducing slope coordinates as nodal degrees of freedom. For composite structures composed of beams, plates,shells or blocks,the slope coordinates at the nodes of the elements intersecting at the structural joint points are discontinuous, which causes the difficulties in the modeling and analysis of composite structures. In this paper the methods of dealing with the problem of slope discontinuity in the literature were discussed. Firstly, the absolute nodal coordinate method was briefly introduced. Secondly, the slope discontinuity problems in the classical example of folded beam and in the straight beam with stepped section were discussed in detail. Then by numerically calculating the axial strain on the neutral layer of two examples, the constrained function method was compared with the coordinate transformation method in the existing literature. It was pointed out that the coordinate transformation method in current literatures neglects the difference between the slope degree of freedom and the rotation degree of freedom,and thus the correct axial strains cannot be achieved at the joint node with slope discontinuity, which needs a further study.