基于交互模式的柔性体接触碰撞动力学建模方法

目前对于任意形状的柔性体接触碰撞问题,一般采用有限元离散,通用的建模方法有两类:罚函数法和附加约束法.罚函数法将接触作用视为弹簧阻尼力元,无需求解约束方程,但依赖于碰撞力参数的选取;附加约束法可严格满足接触约束条件,但数值求解更为复杂.针对两类接触模型各自的优缺点,提出基于交互模式的建模方法.该方法将整个模型分为局部静力学模块和主体动力学模块,在每个积分步内,局部静力学模块求解接触力,主体动力学模块求解运动学变量,两个模型之间进行位移和力的交互.该方法综合了附加约束法和罚函数法各自的优点,既无需人为选取碰撞参数,又满足局部区域互不嵌入的约束条件,同时数值求解方便.通过杆-板碰撞的实验算例及滑块-滑槽多点碰撞的数值算例,验证了该方法的有效性.

Dynamic modeling method of flexible bodies with contact/impact based on interactive mode

To solve the contact/impact problem of flexible bodies in arbitrary shape, the finite element method is widely used to discretize the contact bodies. In the finite element method, two contact models are mainly used to compute the contact force, i.e., penalty function method and additional constraint method, which are different in constraint imposition strategy. The penalty function method regards the contact effect as a force function of local penetration at the contact point and its rate. This method has gained significant popularity because it does not bring extra dimensions to the dynamic equations and does not need to solve constraint equations either. However, as the non-penetration constraint is not precisely satisfied in the contact process when using the penalty function method, the accuracy of the numerical simulation depends on the choice of the penalty parameter. On the other hand, the additional constraint method can strictly satisfy the contact constraint condition by introducing the Lagrange multipliers into the dynamic equations, but the method poses some numerical difficulties due to the additional effort required to solve the multipliers. Considering the advantages and disadvantages of the two contact methods, the interactive mode method is proposed. This method divides the whole model into local static module and main dynamics module. The static module establishes a local finite element model of the contact region to compute the contact force, and the main dynamics module is used to obtain the kinematic variables of the whole body. In the simulation, the two modules are coupled by exchanging displacements and forces in each time step. In the current integration step, the main dynamics module provides the displacements of the boundaries of the local contact region at first, the values are transferred to the local finite model to compute the contact force next, and then the contact force is fed back to the dynamics module for the calculation of the next step. The proposed method combines the advantages of both the additional constraint method and the penalty function method, in which not only the artificial selection of penalty parameter is avoided, but also the non-penetration constraint of local contact region is satisfied and the numerical solution is convenient. The validity of the proposed method is verified by the comparison between simulation results and experimental results of a rod-plate impact case. Furthermore, a multi-point impact problem of a slider sliding in the gap chute is presented to validate the proposed method of dealing with the general impact problem.