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

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

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