ANCF索梁单元应变耦合问题与模型解耦

索粱结构在土木工程、航空航天等领域有着广泛的应用.在各类索梁动力学建模方法中,由于绝对节点坐标方法(absolute nodal coordinate formulation,ANCF)能够描述柔性体的大变形和大转动问题,因此非常适合大变形索梁结构的动力学建模.对绝对节点坐标索梁单元的应变进行分析可知,弯曲变形会引起单元内部轴向应变的不均匀分布,即单元轴向应变与弯曲应变相互耦合.这种应变耦合效应使单元产生伪应变能,导致单元刚度增大,造成单元失真.分析不同弯曲角下的单元应变及应变能可知,弯曲变形越大,单元失真越严重.通过构造等效一维杆单元重新描述轴向应变,实现了轴向应变与弯曲应变解耦.在此基础上推导广义弹性力,得到了绝对节点坐标索梁单元的应变解耦模型.对解耦前后的两种梁模型进行静力学和动力学仿真,结果表明;解耦模型消除了单元伪应变,相比原模型表现出更好的收敛性和曲率连续性,在相同单元数目下具有更高的精度.同时由于解耦模型降低了单元刚度,因此相比原模型,速度曲线中不再有高频振动.

THE STRAIN COUPLING PROBLEM AND MODEL DECOUPLING OF ANCF CABLE/BEAM ELEMENT 1)

The cable/beam structure has already been widely applied in civil engineering, aerospace engineering, etc. Among various dynamic modeling methods of cable/beam, the Absolute Nodal Coordinate Formulation (ANCF) is very suitable for the modeling of large deformed cable/beam to describe the large deformation and rotation of flexible bodies. According to the strain analysis of ANCF cable/beam element, the bending deformation will cause uneven distribution of axial strain within the element, which means axial and bending strains are coupled with each other. The strain coupling effect brings unrealistic strain energy to the element, resulting in an increased stiffness and element distortion. It is known from the analysis of strain and strain energy at various bending angles that the larger the bending deformation is, the more serious the distortion is. The axial and bending strains are decoupled by redescribing axial strain based on a new constructed equivalent 1D rod element. Then the generalized elastic force is deduced and the strain-decoupled model of ANCF cable/beam element is obtained. The statics and dynamics simulations of two beam models are conducted and the results indicate that the unrealistic strain is eliminated by the decoupled model, and compared with the original model, the decoupled model shows better convergence and curvature continuity and more accurate under same number of elements. Meanwhile, as the stiffness is reduced by the decoupled model, there is no high frequency vibration in the velocity curve any more by compared with the original model.