THE COMPLETED FORM OF ELASTIC MODEL FOR ANCF THIN PLATE ELEMENT AND ITS APPLICATION ON DYNAMIC MODELING OF THE LEAF SPRING
摘要: 绝对节点坐标方法已在多体系统动力学研究中广泛应用, 但常用来描述板壳类结构的薄板单元, 由于梯度不完备而无法直接用于带有初始弯曲参考构型的柔性体变形描述. 为避免全参数板单元建立车辆钢板弹簧模型时存在的严重截面闭锁问题, 拟采用薄板单元用于板簧建模. 为此, 探索了将现有绝对节点坐标薄板单元纳入一般连续介质力学弹性力表达的方法, 采用中面上单位法向量作为单元厚度方向的梯度向量, 从而得到了完备化的薄板单元及其描述初始弯曲构型时消除初应变的方法. 在此基础上通过定义簧片的未变形构型, 在钢板弹簧中引入可控的预应力, 实现对钢板弹簧装配过程的准确模拟. 通过数值算例验证了本方法的正确性. 建立了车辆钢板弹簧模型, 通过建立在簧片上的局部坐标系实现接触点的跨单元搜索, 并采用惩罚函数法和平滑化的库伦摩擦模型施加簧片间的接触力. 引入参考节点的概念建立了整合车身与吊耳及其机构运动关系的刚柔耦合模型.}}Abstract: The absolute nodal coordinate formulation(ANCF) was widely used in the research of multi-body dynamics. But the thin plate element which designed for modeling thin shell structure couldn't be adopted for initial curved structure directly because of its deficiency of position vector gradient. Thin plate element was chosen for modelling the leaf spring to avoid the troublesome locking problem when using fully parameterized ANCF element. One explored the way to express the elastic force of existing thin plate element via common continuum mechanics system by adopting the unitized normal vector on the centroid plane as the added position vector gradient for thickness direction. So as to modify its elastic force formulation. The completed form of the element was given which could eliminated the introduced initial stress when describing initially curved leaf using the standard procedure which could only be performed on fully parameterized ANCF element. The modification for elastic force would not affect the element property. By setting undeformed structure which differs from initial one, the controlled initial stress could be introduced into the model for describing the assemble process. Numerical results were given to verify the validity of this modification. An initial curved double-leaf spring model was built. In order to specify the exact contact region, a cross element search strategy using a local material coordinate system built on the entire leaf was developed. Introduced a more precise calculation procedure for contact and friction force using penalty method and smooth Coulomb law. The rigid-flexible coupled leaf spring model combined with ANCF reference nodes was built, integrated with shackle, chassis and their mechanism movement.
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