On effective moduli of defective beam lattices via the lattice green’s functions

A method is proposed to analyze the effective moduli of periodically defective beam lattices by using the Lattice Green’s Functions (LGF). The LGF of beam lattices is built to calculate the displacement caused by external nodal forces. We describe the stress redistribution due to defects by applying extra nodal forces. Then, analyzing a defective unit cell is equivalently transformed to that on its perfect counterpart by representing the influence of defects by an equivalent force field based on the superposition principle. Based on the obtained displacement field of the defective unit cell, the elastic moduli of defective lattices can be calibrated based on the equivalence of strain energy, which indicates that the strain energy of the structural energetic expression is equal to its continuum counterpart. By comparing it with finite element simulations, the prediction ability of the proposed method has been demonstrated. Systematic parametric analyses are then carried out to illustrate the effects of element types, defect types, the defect number density, and the slenderness ratio on the effective moduli of defective lattices.