On Analysis of Discrete Systems With Variable Structure

In many applications a discrete system undergoes structural (or connectivity) changes when subjected to loads or deformations. Each time the connectivity between the discrete elements changes a new system of equations must be generated and solved. In the paper a new method based on the numerically generated inverse matrix for the entire system allows the updating of the latter after each change in connectivity instead of generation and recalculation of the new system of equations. The method is symmetrical with respect to addition and elimination of links. The presented algorithm is based on recursive relationships between the inverse matrices for two systems differing by one element. The method is demonstrated for plane granular clusters, i.e. systems of particles bound together and having zero internal degrees of freedom, which is equivalent to any overconstrained system comprising the two-node finite elements. The problems of numerical efficiency and accuracy of the method are discussed and demonstrated on numerical examples.