Periodic Lattice Structures

This book presents novel efficient methods for the static analysis of periodic lattice structures using a semi-analytical discrete functional approach. The governing equation of equilibrium is written in a compact convolution operator form by analyzing only one repetitive lattice element. This approach admits fast solution procedures with the discrete Fourier and z-transform inversion schemes and leads to a numerical lattice Green’s function formulation. The lattice Green’s function solution encapsulates all the fundamental response behavior of the periodic structure arising from the static external loading. Another strategy is presented for the analysis of beam-like lattices, where the solution is given by a number of characteristic static modes of structural deformation. Load distribution, boundary conditions and the number of repetitive elements in the structure do not affect the basic solution forms and are taken into account on a subsequent stage of the analysis. The lattice Green’s function approach is also demonstrated for the problems with arbitrary boundary shapes and for the probabilistic analysis of pre-load member stress in mismatched redundant truss structures.