Efficient Simulation and Analysis of Complex Rigid Body Dynamic Systems Subject to Unilateral Constraints

这项研究是与最近开发的RCR和ODCA动力学仿真和分析算法的扩展，以处理复杂的铰接多体系统，涉及双边和单边约束的互补性理论的背景下。 所提出的方法显着不同于更传统的方法，在如何处理约束和相关的互补性问题形成的铰接机构系统。具体而言，所提出的配方有效地分解的质量矩阵，并直接嵌入的运动方程中的约束，因为它们正在形成。该方法从而消除了与产生系统质量和约束雅可比矩阵以及它们的后续分解相关联的成本，并且另外从许多其他分析中消除了单边（不等式）约束载荷。因此，由此产生的方程应该强制执行的约束，在一个非常小的部分的成本通常与制定，操纵和解决系统的运动，和约束方程内的互补problem.Systems拥有mU单边约束面临的2mU的可能性组合问题，其中一个一致的解决方案可能不存在。组合搜索，通常需要获得一个一致的解决方案，可以消除（或至少大大减少），通过满足运动方程的同时与单边约束互补条件（即Signorini的法律）使用的方法，如Lemke的方法。所开发的方法的性能进行比较，在建模和仿真相同的系统，使用更传统的互补方法。问题的解决方案的唯一性和物理正确性的问题也将严格调查。

This research is associated with the extension of recently developed RCR and ODCA dynamics simulation and analysis algorithms to deal with complex articulated multibody systems involving both bilateral and unilateral constraints in the context of complementarity theory. The proposed method differs markedly from more traditional approaches in how constraints are treated and the associated complementarity problem is formed for an articulated body system. Specifically, the proposed formulation effectively decomposes the mass matrix and directly embeds the constraints within the equations of motion as they are being formed. The methods thereby removes the costs associated with producing the system mass and constraint Jacobian matrices, as well as their subsequent decompositions, and additionally decouples the unilateral (inequality) constraint loads from much of the other analysis. Thus, the resulting equations should enforce the constraints at a very small fraction of the cost usually associated with formulating, manipulating and solving the system motion, and constraint equations within a complementarity problem.Systems possessing mU unilateral constraints face a 2mU possibility combinatorial problem, for which a consistent solution may not exist. The combinatorial search, generally needed to obtain a consistent solution, may be eliminated (or at least drastically reduced) through the satisfaction of the equations of motion simultaneously with the unilateral constraints complementarity conditions (i.e. Signorini's law) using approaches such as Lemke's method. The performance of the developed method will be compared with that obtained in modeling and simulation the identical systems using a more traditional complementarity approaches. The issue of problem solution uniqueness and physical correctness will also be rigorously investigated.