Método penalty versus método de condensación en el cálculo lineal de estructuras con restricciones lineales entre desplazamientos

Penalty method versus condensation method for linear computation of structures with constrained displacements

A penlaty method for linear, static and dynamic, computation of structures under linear constraints in displacements, alternative to the usual condensation or master-slave algorithm, is developed. The theoretical basis of this method is the inclusion of a penalty term, affected bt a scalar coefficient, into definition of the variational principle, followed by the study of the asymptotic behaviour of the system when the above numerical coefficient increases unbounded. Further application of the theorem of minimax, as well as of properties of the hermitian matrices, leads to interesting relations between the eigenvalues of both, unconstrained and constrained structures. Detailed developments are restrained herein to the static and dynamic analysis of structures with nonsingular mass matrix. Criterions in order to necessary cautions associated with numerical application of all penalty methods are also provided. For the static constrained problem, we derive a discrete global solution, avoiding such type of problems, through suitable asymptotic development of the inverse increased stiffness matrix.