Analysis of Mixed Discrete—Continuous Structures

Abstract

A flat plate reinforced by a series of parallel beams, sometimes called an orthotropic plate, is a highly efficient load carrying unit and is a good first example of a mixed discrete-continuous structure for analysis by a discrete field method (see Fig. 5). Many mixed discrete-continuous structures are multidimensional lattices with multimensional elements and so are intractable by the micro discrete field technique. With a single set of beams, however, the ribbed plate is a one dimensional lattice with two dimensional elements and so can be analyzed by either the micro or the macro field approach. A broad class of ribbed plate problems have been solved via the micro stiffness approach(*). If there are several simultaneous interactive forces between the ribs and the plates, the micro approach is attractive as the number of unknown node line displacements is independent of the number of interactive forces considered; for example, solutions that include torsional interaction between the rib and plate are now only available by the micro or difference equation approach. On the other hand, the necessity of getting an exact general boundary solution(**) for the plate strips between rib lines makes the algebra and derivation unattractive for systems with only one or two types of rib-plate interactive forces.