Flexibility Method on Coupling Redundant Complex Structures

An analysis method is developed for calculating the flexibility matrix, the deflections, and the internal forces of complex structures by coupling the constituent redundant component structures. The flexibility matrix of each redundant component structure is calculated individually, referred to its own datum; then statically determinable force influence matrices are described, which are used to couple these structures. Their elements are the forces sustained by each component structure as a unit external force is applied, or as a unit redundant existing between component structures is considered. Specialized formulations are also shown for statically determinate components, statically determinate coupling, or both. Support settlement and thermal distortion effects are also evaluated. This method makes it possible to analyze physically separate structures and to recombine them at once, or in several stages, using the statically determinable coupling matrices, so that no inversions will have to be performed of matrices of larger order than those for which adequate precision can be guaranteed.