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.

中文翻译：

---

通过晶格格林函数对有缺陷的光束晶格进行有效模量


提出了一种使用 Lattice Green's Functions （LGF） 分析周期性缺陷光束晶格有效模量的方法。梁晶格的 LGF 用于计算由外部节点力引起的位移。我们通过施加额外的节点力来描述由于缺陷引起的应力重新分布。然后，通过基于叠加原理的等效力场表示缺陷的影响，分析有缺陷的晶胞与其完美单元的等效元胞进行等效转换。根据获得的缺陷晶胞位移场，可以根据应变能的等价性校准缺陷晶格的弹性模量，这表明结构能表达式的应变能等于其连续体对应物。通过与有限元仿真的对比，证明了所提方法的预测能力。然后进行系统的参数分析，以说明单元类型、缺陷类型、缺陷数密度和长细比对缺陷晶格有效模量的影响。