Joining of complex substructures by the matrix force method.

A new method of matrix force analysis is described for the calculation of stresses and deflections in complex structures partitioned into a number of structural components (substructures). Each substructure first is analyzed separately assuming that all common joints with the adjacent substructures are disconnected and the joint internal forces on the common boundaries are replaced by the substructure interaction forces. The magnitudes of the interaction forces are determined from the external and internal equilibrium equations and the displacement compatibility equations. The selection of the redundant interaction forces for the compatibility equations is carried out automatically using Jordanian elimination technique. Once the magnitudes of the interaction forces are known, the internal forces (or stresses) and deflections are then determined from the analysis of individual substructures. All steps in the analysis are suitable for a fully automatic computer program. A numerical example is included to show the details of the analysis.