AN EXTENSION OF THE FORCE DENSITY PROCEDURETO MEMBRANE STRUCTURES

摘要

The force density concept provides a very practical procedure for finding viable shapes for tautrnstructures, such as cable and membrane structures. This work presents the force density procedurernwithin the formalism of structural matrix analysis, yielding an algorithm which can be easilyrnimplemented into a linear structural analysis program, and which is also appropriate to generate goodrninitial guesses for the non-linear analyses required during the thorough design of this type of structures.rnThe paper also discusses the extension of the force densities to membrane structures. In order tornemploy the original force density procedure to membrane structures, membranes have to be assimilatedrnto equivalent cable networks. In this way, the advantage of quick solutions presented by the procedurernmay be overridden by the lack of accuracy of the models.rnTo circumvent this drawback, extensions of the force density to some "stress density" procedures havernbeen proposed in literature. They seem to lack, however, the linear properties shown by the originalrnforce density, requiring therefore some iterative algorithm for solution.rnIn the present work, we propose an extension on the concept of force density to membrane structures,rnwhich makes the stress density concept no longer required. This novel, natural force density conceptrnpreserves the linearity which characterizes the original force densities, at the same time that overcomesrntheir limitations to model continuum membranes, specially in face of irregular finite element meshes.