On the implicit integration of differential-algebraic equations of multibody dynamics

The topic of the thesis is implicit integration of the differential-algebraic equations (DAE) of Multibody Dynamics. Methods used in the thesis for the solution of DAE are based on state-space reduction via generalized coordinate partitioning. In this approach, a subset of independent generalized coordinates, equal in number to the number of degrees of freedom of the mechanical system, is used to express the time evolution of the mechanical system. The second order state-space ordinary differential equations (SSODE) that describe the time variation of independent coordinates are numerically integrated using implicit formulas. Efficient means for acceleration and integration Jacobian computation are proposed and numerically implemented.; Methods proposed for numerical solution of the index 3 DAE of Multibody Dynamics are the State-Space Reduction Method, the Descriptor Form Method, and the First Order Reduction Method. Algorithms based on the State-Space Reduction and Descriptor Form Methods employ the extensively used family of Newmark multi-step formulas for implicit integration of the SSODE. More refined Runge-Kutta formulas are used in conjunction with both First Order Reduction and Descriptor Form Methods. Rosenbrock-Nystrom and SDIRK formulas of order 4 that are employed are L-stable methods with sound stability and accuracy properties. All integration formulas are provided with robust error control mechanisms based on integration step-size selection.; Several algorithms are developed, based on the proposed methods for numerical solution of index 3 DAE of Multibody Dynamics. These algorithms are shown to be robust and accurate. Typically, two orders of magnitude speed-up is achieved when these algorithms are compared to previously used, well established, explicit numerical integration algorithms for simulation of a stiff model of the High Mobility Multipurpose Wheeled Vehicle (HMMWV) of the US Army.; Computational methods developed in this thesis enable efficient dynamic analysis of systems containing bushings, stiff subsystem compliance elements, and high frequency subsystems that heretofore required tremendous amounts of CPU time, due to limitations of the previously employed numerical algorithms.