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Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb's friction

机译:具有单边接触和库仑摩擦的非光滑机械系统的预计事件捕获时间步长方案

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This work addresses the problem of the numerical time-integration of nonsmooth mechanical systems subjected to unilateral contacts, impacts and Coulomb's friction. The considered systems are the space-discretized continuous systems obtained by using a Finite Element Method (FEM) approach or the multi-body systems, or a mix of them as in flexible multibody dynamics. Up to now, two main numerical schemes are available for this purpose: the Moreau-Jean scheme which solves the constraints at the velocity level together with a Newton impact law and the Schatzman-Paoli scheme which directly considers the constraints at the position level. In both schemes, the position and velocity constraints are not both satisfied in discrete time. A first attempt to improve the time simulation is made by directly using the Gear-Gupta-Leimkuhler (GGL) approach for Differential Algebraic Equations (DAE), that solves, in discrete time, the constraints on both position and velocity levels. This obtained direct projection scheme succeeds in solving in discrete time both position and velocity constraints, but introduces some chattering at contact after a finite accumulation of impacts. A second new scheme is proposed that improves the direct projected scheme by combining several steps of activation and projection to avoid the chattering effect. The stability and the local order of the scheme will be discussed. The usefulness of the scheme is demonstrated on several academic examples and is illustrated on an industrial application: the modeling and simulation of an electrical circuit breaker.
机译:这项工作解决了非光滑机械系统在单边接触,冲击和库仑摩擦作用下的数值时间积分问题。所考虑的系统是通过使用有限元方法(FEM)方法或多体系统或在柔性多体动力学中将它们混合而获得的空间离散连续系统。到目前为止,有两个主要的数值方案可用于此目的:Moreau-Jean方案和牛顿冲击定律一起求解速度级的约束,而Schatzman-Paoli方案直接考虑位置级的约束。在这两种方案中,位置和速度约束都不能在离散时间内同时满足。直接使用Gear-Gupta-Leimkuhler(GGL)方法求解微分代数方程(DAE)的第一项尝试是改进时间仿真的方法,该方法可在离散时间内解决对位置和速度水平的约束。这种获得的直接投影方案成功地解决了离散时间的位置和速度约束,但是在有限的冲击积累之后会在接触时产生一些震颤。提出了第二种新方案,该方案通过组合激活和投影的多个步骤来避免抖动效应,从而改进了直接投影方案。将讨论该方案的稳定性和局部顺序。该方案的有效性在几个学术实例中得到了证明,并在工业应用中得到了说明:电路断路器的建模和仿真。

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