The construction of free–free flexibility matrices as generalized stiffness inverses

✍ Scribed by C.A. Felippa; K.C. Park; M.R. Justino Filho

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 451 KB
• Volume: 68
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(98)00068-6

✦ Synopsis

We present generalizations of the classical structural ¯exibility matrix. Direct or indirect computation of ¯exibilities as `in¯uence coecients' has traditionally required pre-removal of rigid body modes by imposing appropriate support conditions. Here the ¯exibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free±free stiness matrix. This entity is called a free±free ¯exibility matrix. It preserves exactly the rigid body modes. The de®nition is element independent. It only involves access to the stiness generated by a standard ®nite element program as well as a separate geometric construction of the rigid body modes. With this information, the computation of the free±free ¯exibility can be done by solving linear equations and does not require the solution of an eigenvalue problem or performing a singular value decomposition. Flexibility expressions for symmetric and unsymmetric free±free stinesses are studied. For the unsymmetric case two ¯exibilities, one preserving the Penrose conditions and the other the spectral properties, are examined. The two versions coalesce for symmetric matrices.