Analytical transport network (ATN) theory is extended to account for static, structural mechanics. The extension provides a consistent, computationally economical, and interpretable formalism for examining morphological/topological trade-offs relevant to the design of multi-functional materials. The approach is demonstrated through application to over 100,000 computationally-generated lattice structures consisting of non-uniform channels. It is orders of magnitude faster and less memory intensive than finite element analysis. This, along with its compact mathematical formalism, present the opportunity for future integration into multi-functional characterization/design frameworks (e.g., topology optimization and machine learning).

分析运输网络（ATN）理论已扩展为考虑静态结构力学。该扩展为检查与多功能材料设计相关的形态/拓扑折衷提供了一致，计算经济且可解释的形式主义。通过将其应用到100,000多个由非均匀通道组成的计算生成的晶格结构中，对该方法进行了演示。与有限元分析相比，它的速度快而且数量级少。这与其紧凑的数学形式主义一起，为将来集成到多功能特征/设计框架（例如拓扑优化和机器学习）中提供了机会。