Concurrent Nullspace Methods for Multibody Systemsby Andrew Kurdila, Georgia Inst of Technology, Atlanta, GA, USA,
Manohar Kamat, Georgia Inst of Technology, Atlanta, GA, USA,
Abstract: This paper presents a new concurrent multiprocessing algorithm for simulating the dynamics of constrained multibody systems. The systems considered are quite general in nature; they may be comprised of any number of rigid and linearly elastic bodies subject to linear, nonholonomic constraints. The method is based upon the recently introduced class of algorithms that generate the nullspace of the constraints. These algorithms are comprised essentially of four computational steps: (i) the calculation of an orthonormal basis for the nullspace of the constraints and its orthogonal complement, (ii) the assembly and factorization of a system coefficient matrix, (iii) the calculation of the product of a right-inverse and a vector, and (iv) the formation and assembly of system vectors. Concurrent multiprocessing implementations of the QR decomposition, singular value decomposition and modified Gram-Schmidt technique are discussed to enable a parallel calculation of the orthonormal bases in step (i) above.
Subject Headings: Algorithms | Vector analysis | Linear functions | Matrix (mathematics) | Decomposition | Structural systems | System analysis | Structural dynamics
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