Mathematical Modeling of Networks in Strength of Materials

Abstract

We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity, plasticity, and possibly cracking. The goal is to solve this system and understand how the material responds. Students are asked to start with a simple triangle example and then apply the method to larger structures. The final aim is to solve the full system and justify the results, leading to a possible publication.