GREENS TENSORS AND LATTICE SUMS FOR ELASTOSTATICS AND ELASTODYNAMICS

We present expressions for the Green's tensors in terms of lattice sum s for general two-dimensional arrays in both elastostatics and elastod ynamics. We represent the lattice sums in rapidly convergent forms by Fourier transform methods. We compare the static lattice sums with rec ently published highly accurate values for square arrays. We also esta blish Rayleigh identities for elastostatic and elastodynamic problems, generalizing previous work in electrostatics and electromagnetism. Th e Rayleigh identities may be used in studies of phononic band gaps.