Optimal Structural Analysis

In this paper a number of topological transformations are proposed for simplifying certain problems in optimal structural analysis. For each case, the main problem is stated and then the transformation is established. Once the required topological analysis is completed, a back transformation results in the solution for the main problem. Expedient transformations studied here employ (1) models drawn on lower dimensional spaces, (2) models embedded onto higher dimensional spaces, (3) interchange models defined which have more suitable connectivity properties than the corresponding original structural model, (4) models studied by their essential components such as their generators. The aim of the present work is two fold. In one hand it shows to mathematicians how the apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. In the other hand it illustrates to engineers the important role of mathematical concepts for the solution of engineering problems.

Keywords:

Optimal structural analysis , embedding , drawing , graph theory , topology , degree of statical indeterminacy , rigidity , force method , ordering , decomposition , finite element