Topology design of plane bar systems based on polygonal discretization

Structural mechanics

A topology formation method for frame and truss structures, which is relevant for use in computer-aided design, is proposed. A flat figure discretized into polygonal primitives is used as a basic structure. This structure is presented in the form of a finite element model and is assumed redundant. Its elements are excluded using the principle of maximizing the intensity of the force flow during the initial calculation and the shortest path of this force flow between the points that reflect force and kinematic connections. At the same time, the heuristic principle implemented in the ACO algorithms was used. Registration of geometrically variable systems is performed based on an estimate of the infinite norm of the stiffness matrix of the finite element model. For flat trusses and frames, examples of the formation of rational topologies under given force and kinematic constraints are considered. Comparison with the method of redundant structure, which implements the exclusion based on the genetic algorithm, is performed. It has been shown that the proposed technique allows one to effectively select both one and several alternative variants of the topology of bearing systems.