PLATES WITH A DOUBLY-PERIODIC PATTERN OF CIRCULAR HOLES LOADED IN PLANE STRESS OR IN BENDING.

The doubly-periodic stress distribution in a plate with a doubly-periodic pattern of equal circular holes is expressed in terms of two quasiperiodic stress functions, which can be expanded in derivatives of the zeta function of Weierstrass. The coefficients of the expansions are obtained by satisfying a functional equation along the hole boundaries and certain periodicity requirements. Numerical results have been restricted to a rectangular and a rhombic penetration pattern. Effective elastic constants are shown for practically the whole parameter field of the two parameters that describe the pattern geometry.