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

A method for the general solution of structural semi-definite problems in the presence of zero energy modes is described in this paper. Semi-definite problems are usually associated in Structural Mechanics with floating structures, namely totally unconstrained or partially constrained structures. A general solution of these problems is obtained by the computation of a particular displacement field, 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 field. In particular, it is robust, cost-effective and accounts for all rigid body and mechanism modes, in either floating structures, or semi-definite subdomain problems encountered in domain decomposition methods. Furthermore, it can be combined with any open or closed, serial or parallel solver for symmetric positive definite (SPD) problems, at a very low cost.