An outline of the natural force density method and its extension to quadrilateral elements

摘要

The Natural Force Density Method (NFDM) is a convenient method for ?nding con?gurations of mem-branes and funicular shell structures, providing viable equilibrium geometries in a single linear equilib-rium analysis. It is an extension of the Force Density Method (FDM), ?rst proposed by Linkwitz in 1971, as convenient alternative for ?nding con?gurations of cable nets, which became ubiquitous in the ?eld of membrane design, serving as basis of several successful computer programs. However, the equivalence between a network of force density elements and a continuous membrane is far from obvious, and it may become quite dubious which force densities should be prescribed, to achieve a desired con?guration, comprising a geometric shape and an associate stress ?eld. This is seldom remarked in papers about the method, and even less aware of that might be the general users the of programs based on it. The NFDM, ?rst proposed by Pauletti in 2006, treats directly the continuous problem, overcoming the difficulties of FDM to deal with irregular meshes. Nevertheless, the NFDM was originally proposed considering the tri-angular membrane element introduced by Argyris in 1974, and thus required a fully triangular tessellation of a reference domain. In this paper we present a more concise deduction and systematic outline of the NFDM, as well as a simple extension of the method to quadrangular elements, allowing the use of more general mesh generators for the initial references meshes, and selection of a broader class of membrane or shell ?nite elements, afterwards.