A. Y. T. Leung

A Fast Algorithm for Periodic Structures with General Boundary Conditions

A solution algorithm for periodic structures having general boundary conditions is presented. Due to the generally nonperiodic boundary conditions, difference calculus and transformation methods are ineffective. The number of operations for a general solution is directly proportional to the number N of substructures involved, which is quite inefficient when N is large as in the case of space structures. A fast algorithm analogous to the Fast Fourier Transform Method is introduced. The number of operations is proportional to log/N rather than N. Numerical examples are given to illustrate the effectiveness. Due to the general nature of boundary conditions, it can be shown that a periodic structure can be condensed into a substructure of higher level which can then be connected at the boundaries to another structure or supports. The proposed algorithm is suitable for microcomputer environment.