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

受单边约束的复杂刚体动态系统的高效仿真与分析

• 批准号: 0555174
• 负责人: Kurt Anderson
• 金额: $ 23.55万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555174&HistoricalAwards=false
• 关键词: Efficient; Simulation; Analysis; Complex; Rigid

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.

这项研究与最近开发的 RCR 和 ODCA 动力学仿真和分析算法的扩展相关，以处理涉及互补理论背景下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为关节体系统形成相关的互补性问题方面与更传统的方法显着不同。具体来说，所提出的公式有效地分解了质量矩阵，并在形成运动方程时直接将约束嵌入到运动方程中。因此，这些方法消除了与生成系统质量和约束雅可比矩阵及其后续分解相关的成本，并且另外将单边（不等式）约束载荷与许多其他分析解耦。因此，所得方程应该以通常与制定、操纵和求解系统运动以及互补问题中的约束方程相关的成本的很小一部分来强制执行约束。具有 mU 单边约束的系统面临 2 mU 可能性组合问题，对于可能不存在一致的解决方案。通常需要获得一致的解决方案的组合搜索可以通过使用莱姆克方法等方法同时满足运动方程和单边约束互补条件（即西格诺里尼定律）来消除（或至少大大减少）。所开发方法的性能将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。问题解决的唯一性和物理正确性问题也将受到严格调查。