摘要
A reciprocal theorem for the effective conductivities of two-dimensional (2D) rectangular arrays of multiply coated cylinders of arbitrary cross section is derived. The theorem is expressed as: [formula omitted] where [formula omitted] and [formula omitted] are the reduced effective conductivities of the array in the x and y directions, respectively, and [formula omitted] and [formula omitted] [formula omitted] are the reduced conductivities of the cylinder and coating layer i, respectively, with the matrix assigned the reduced conductivity of one. This theorem is also valid for a class of 2D composites containing aligned, randomly distributed, multiply coated cylinders of arbitrary cross section, whose heat conduction behavior can be described by an equivalent inclusion model. © 1999, American Institute of Physics. All rights reserved.