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標題: 具能量拘束方程之多體機械系統使用數值積分穩定法時參數選擇之研究
Parameters Selection of the Constraint Stabilization Method for Numerical Integration of Multibody Mechanical Systems with Energy Constraint
作者: 王文志
Wang, Wen-Chih
關鍵字: Energy constraint;能量拘束方程;Multibody Mechanical Systems;Numerical Integration;Differential -algebraic equation;多體機械系統;數值積分;微分代數方程
出版社: 機械工程學系
本文的目的在解決受拘束(constraint)條件下,多體(multibody)機械系統數值積分的穩定性問題。多體系統之運動方程式是一個包含外力、拘束力、加速度的混合微分、代數方程式(mixed differential-algebraic equations,簡稱DAE)。在使用數值積分法解開微分方程式同時,其位置及速度必須滿足拘束運動方程式及速度運動方程式外尚有能量拘束方程式需被滿足,也就是說積分的變數是相關的。然而一般的數值積分法並不考慮其中的相關性,直接求解而造成數值的偏差。
為了解決此問題,Baumgarte提出拘束穩定方法(constraint stabil-ization method),使得數值積分獲得正確的解。不過此方法唯一的缺點在於係數的選擇,並無規則可循。本文將利用數位控制理論中的系統穩定分析,提供不同數值積分法在使用拘束穩定法時係數的選擇。

The objective of this thesis is to resolve the stability problem for the numerical integration of constrained multibody mechanical systems. The dynamic equations of motion of the constrained multibody mechanical system is a mixed differential-algebraic equation(DAE) which contains external forces, constraint reaction forces as well as acceleration of the generalized coordinates of the system. In applying numerical integration methods to solve the mixed differential- algebraic equation, the constraint equation and its first and second derivatives and energy constraint must be satisfied. That is, the generalized coordinates are dependent. Direct integration methods do not consider this dependency and constraint violation occurs.
This problem was seemingly resolved by Baumgarte's Constraint Violation Stabilization Method. But this solution had some ambiguity in selecting the feedback parameters. In this thesis, the digital stability theory for integration formulas is applied to determine the stability region of the stabilized constraint equations.
Appears in Collections:機械工程學系所

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