Minimum norm solutions to linear elastic analysis problems

A basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations. In this regard, the three conventional structural analysis approaches, i.e. the displacement method, the natural factor formulation and the force method, are unified and interpreted in the framework of the minimum norm problem, which is divided into two approaches—the primal formulation and the dual formulation. Numerical comparisons of several computational procedures capable of solving the minimum norm problem are given from computational efficiency and accuracy points of view. Included in the comparisons are the three conventional structural analysis approaches mentioned above, and several alternative approaches.