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

本研究扩展了最近开发的RCR和ODCA动力学仿真和分析算法，以在互补理论的背景下处理涉及双边和单边约束的复杂铰接多体系统。所提出的方法在如何处理约束以及如何形成铰接体系统的相关互补性问题方面与传统方法明显不同。具体来说，所提出的公式有效地分解了质量矩阵，并在运动方程形成时直接将约束嵌入到运动方程中。因此，该方法消除了与生成系统质量和约束雅可比矩阵相关的成本，以及它们随后的分解，并且另外将单边（不等式）约束负载与许多其他分析解耦。因此，所得到的方程应该以非常小的成本来执行约束，通常与系统运动的表述、操作和求解以及互补问题中的约束方程相关。具有mU个单边约束的系统面临2mU个可能性组合问题，该问题可能不存在一致解。通常需要获得一致解的组合搜索，可以通过使用Lemke方法等方法同时满足运动方程与单边约束互补条件（即西格里尼定律）来消除（或至少大大减少）。将所开发方法的性能与使用更传统的互补方法对相同系统进行建模和仿真所获得的性能进行比较。问题解的唯一性和物理正确性也将被严格地研究。

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.