Unimodal beam elements

Abstract

A uniform prismatic elastic element in small displacements theory can be modeled as consisting of extension, torsion and flexural elements acting in parallel. The extension and torsion elements are unimodal, whereas the flexural elements are bimodal, due to the combined action of bending moments and shear forces. This dissimilarity between the elements is the source of inconsistency between the analysis of a truss and a framed structure, especially in a force approach. It is shown that by an appropriate change of basis, one can uncouple the flexural element into a unimodal moment element which carries the average moment of the element, and a unimodal shear element which carries the shear force and related moment. As a result any framed structure can be viewed as a generalized truss and analyzed accordingly in a standard form.It is further shown that it is possible to physically construct a moment element and a shear element, both exhibiting unimodal deformation patterns. Consequently one can replace a classical beam element by a moment element and a shear element assembled in parallel. The approach is tested numerically in the case of beams of constant height subjected to several loading conditions. Preliminary results indicate that in theory, substantial weight reductions can be obtained when designing structures composed of parallel unimodal elements.