2D TOPOLOGICAL OPTIMIZATION WITH STATIC AND KINEMATIC EFFECTS

Abstract

Topological optimization of linearly elastic 2D structures under static and kinematic effects is presented. As an objective function, the compliance of the structure is considered, which is equal to the work of given external forces and displacements on the displacements and support forces caused by them. The design variables are the thicknesses of 2D finite elements. A constraint in the form of equality on a given volume of distributed material within a given design area is taken into account. The optimization method is based on optimality criteria. The examples consider the topological optimization of a simply supported beam and a cantilever beam under kinematic and static effects.The displacement is given instead of a concentrated force in the middle of simplysupported beam or at the free end of a cantilever beam. The simply supported beam was divided into 150 finite elements along the length and 50 finite elements along the height, the cantilever beam – into 150 finite elements along the lengthand 100 finite elements along the height. Differences between the results of optimization under kinematic effect and the results of optimization under static effect are insignificant. To conduct an experiment on biaxial tensionthe analysis considered a 2D sample consisting of a square test part of constant thickness and a square supporting part, which transmits an external force to the test part. The distribution of thicknesses of the providing part of a given volume was obtained, which minimizes its compliance.Under kinematic effect, the testing machine generates a unit displacement perpendicular to both ends of the specimen and a zero displacement along both edges of the supporting part.Under static effect, the testing machine created a uniform load along the edge of the supporting part in each node. It is shown t hat the sensitivity and the optimization process significantly depend on the type of external effect – static and kinematic.