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A partitioned flexibility (PartFlex) method for structural analysis
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DOI：10.1016/j.cma.2024.117155.png)
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Abstract
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A partitioned flexibility method is presented as a dual to the recently developed displacementonly partitioned (DP) method (Park et al., 2023). The proposed PartFlex method relies on existing FEM software to generate the partitioned block-diagonal mass and flexibility matrices, and associated FEM partitioned nodal topology information. Unlike the classical force method whose formulations are all critically influenced by the choices of indeterminate redundants and how cuts(partitions) are chosen, the present PartFlex method can be constructed as automatic as the construction of displacement FEM equations. That is, the construction of the present flexibility equations does not depends on user's level of expertise. Three key enablers employed in the present PartFlex method are: the use of localized Lagrange multipliers that yields a linearly independent and unique set of interface reaction forces for both determinate as well as indeterminate partitions, the enforcement of Newton's 3rd law along the partition boundaries so that the reaction forces disappear when the partitioned substructures are assembled, and rigid-body modes for floating partitions. The validity of the PartFlex method is demonstrated by analyzing several example problems, and unlike the classical force method that has difficulty in modeling continuum structures such as plates, shells and solids, the present PartFlex method can be efficiently used to model continuum structures.
Keywords:
Partitioned flexibility (PartFlex) method
Flexibility-based equations of motion
Partitioned displacement formulation
Localized Lagrange multipliers
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5.6W
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