General solution of the problem of design of laminated plates possessing the given stiffnesses

The paper deals with the problem of design laminated plates possessing the given stiffnesses. The following two design problems are considered: (1) th e continuous design problem (when one can use materials with any elastic ch aracteristics to manufacture the plate); (2) the discrete design problem (w hen one can use a finite set of materials). It is known that design problem s are closely related with convex analysis problems. It is shown that the l aminated plate design problems are related with the convex combinations pro blem (CCP). Using the CCP technique, one can analyze the laminated plate design problem s in detail. This paper is concentrated on the general solution of the desi gn problem (i.e. the set of all solutions of the problem). The general solu tions are constructed for both the continuous and the discrete design probl ems. The methods developed in the paper can be used to solve the design pro blem numerically. (C) 2001 Elsevier Science Ltd. All rights reserved.