An efficient approximate analysis method based on an exact univariate model for the element loads

Approximate analysis modules for structural design are usually based on a linear Taylor expansion of the nodal displacements in terms of the reciprocals of the design variables. Direct approximations of the member forces have received lesser attention. This paper describes an approach for the direct calculation of the member forces in a truss as a function of the design variables. It is based on the exact expression of the member forces if only one design variable is allowed to vary at a time. In the case of an arbitrary move in the design space the method gives approximate results of a very good quality. This is obtained by enforcing zero order homogeneity of the element loads and by refining the results via a virtual work equation. The method is illustrated with numerical results on previously published test cases for elastic trusses. Preliminary results for an elastic frame are also presented. This new approximate force model is shown to yield excellent results.