A fast algorithm for periodic structures with general boundary conditions

Abstract

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 <i>N</i> of substructures involved, which is quite inefficient when <i>N</i> 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/<i>N</i> rather than <i>N</i>. 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.