THE CONSTRUCTION OF FREE-FREE FLEXIBILITY MATRICES AS GENERALIZED STIFFNESS INVERSES

We present generalizations of the classical structural flexibility mat rix. Direct or indirect computation of flexibilities as influence coef ficients' has traditionally required pre-removal-of rigid body modes b y imposing appropriate support conditions. Here the flexibility of an individual element or substructure is directly obtained as a particula r generalized inverse of the free-free stiffness matrix. This entity i s called a free-free flexibility matrix. It preserves exactly the rigi d body modes; The definition is element independent. It only involves access to the stiffness generated by a standard finite element program as well as a separate geometric construction of the rigid body modes. With this information, the computation of the free-free flexibility c an be done by solving linear equations and does not require the soluti on of an eigenvalue problem or performing a singular value decompositi on. Flexibility expressions for symmetric and unsymmetric free-free st iffnesses are studied. For the unsymmetric case two flexibilities, one preserving the Penrose conditions and the other the spectral properti es, are examined. The two versions coalesce for symmetric matrices. (C ) 1998 Elsevier Science Ltd. All rights reserved.