On the evaluation of statical-kinematic stiffness matrix for underconstrained structural systems

Because of singularity of the elastic sti€ness matrix, analysis of underconstrained systems requires the comprehensive sti€ness matrix, comprising both kinds of ®rst-order structural sti€nessÐelastic and statical- kinematic. The latter accounts for the role of the member forces, induced in the system by the equilibrium part of the applied load, as the source of the system resistance to the perturbation part of the same load. Evaluation of the sought member forces using orthogonal load resolution into equilibrium and perturbation components is awkward and computationally expensive. A special modi®cation of the singular elastic sti€ness matrix simpli®es the procedure and makes it amenable to the conventional tools of structural analysis. The eciency and accuracy of the procedure is illustrated by a detailed numerical example