A direct flexibility method

Abstract

We present a Direct Flexibility Method (DFM) for the solution of finite element equations. This method is based on a decomposition of the finite element model into substructures, which may reduce to individual elements. Substructures are preprocessed by the Direct Stiffness Method (DSM) to generate free-free flexibility matrices for floating substructures. The interface problem is solved for the interface forces and the solution recovered over substructure interiors. The DFM shares with the DSM the advantages of being automatic, maintaining locality and sparseness, efficiently handling continuum elements, and requiring only the availability of element stiffness libraries. The new method appears to be advantageous for specific applications. These include: massively parallel processing, inverse problems, treatment of rigid members and inclusions, and use of under-integrated elements without spurious-mode stabilization.

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