An integrated geometric–algebraic method for solving semi-definite problems in structural mechanics

✍ Scribed by M. Papadrakakis; Y. Fragakis

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 270 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00234-1

✦ Synopsis

A method for the general solution of structural semi-de®nite problems in the presence of zero energy modes is described in this paper. Semi-de®nite problems are usually associated in Structural Mechanics with ¯oating structures, namely totally unconstrained or partially constrained structures. A general solution of these problems is obtained by the computation of a particular displacement ®eld, which ensures the equilibrium of the structure, and of the zero energy modes of the structure. The proposed method combines geometric and algebraic concepts and goes beyond the restrictions of existing methods in this ®eld. In particular, it is robust, cost-eective and accounts for all rigid body and mechanism modes, in either ¯oating structures, or semi-de®nite subdomain problems encountered in domain decomposition methods. Furthermore, it can be combined with any open or closed, serial or parallel solver for symmetric positive de®nite (SPD) problems, at a very low cost.