Least square methods in structural analysis

摘要

A new approach to structural analysis is presented. The method uses equilibrium and deformation geometry field relations directly without resorting to an energy formulation. A matrix vector of errors in the field relations is minimized first with respect to the internal quantities, e.g., the moments. Subsequently the error is minimized with respect to the external forces and displacements. In the latter formulation, the internal quantities have been eliminated by back substitution. The least-square method for minimizing functional forms is the precedent for this work. The method is tested on beam and plate problems. The development of the pertinent matrices is interesting and depends on the trial functions used to represent the internal quantities.