chap94 - 1 Reduction in number of dofs Reduction in the...

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Unformatted text preview: 1 Reduction in number of dofs Reduction in the number of dof to represent a structure reduces the size of matrices and, hence, computational cost. Because a subset of the original dof represent the whole set of dof, some error is introduced. The retained dof are called master dof (masters) and the eliminated ones slave dof (slaves) . The number of masters is the size of the reduced system . Masters can be chosen to minimize the loss of accuracy Guyan reduction is a commen method of reduction. 2 Guyan Reduction Assumption : inertia forces on the slave dof are negligible compared to elastic forces on them. This implies that the terms in the mass matrix (multiplied by 2 ) corresponding to the slaves are negligible compared to the terms in the stiffness matrix. Considering the equilibrium equation of an undamped system under free vibration: [ ] (*) . Eq 2 D M K = Partitioning the matrices according to masters D m and slaves D s , = D D M M M M K K K K s m ss T ms ms mm ss T ms ms mm 2 3 Master-Slave Transformation Implementing the assumption in the partitioned equation, = D D M M K K K K s m ms mm ss T ms ms mm 2 The second row then gives where over-bars have been omitted since master-slave transformation is not restricted to free vibration. transformation is not restricted to free vibration....
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chap94 - 1 Reduction in number of dofs Reduction in the...

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