Verification of a topology optimization algorithm with geometric nonlinearity

Abstract

The design of optimized structures is becoming increasingly important due to resource scarcity, technological competition and environmental protection issues. By considering various load cases and materials, structural optimization seeks to produce a design that is both economical and safe. Topology optimization has become quite widespread among engineering and is currently applied in many research fields. Most topological optimization studies are carried out under the assumptions of linear elastic behavior, which idealizes the material and imposes equilibrium in relation to the (non-deformed) reference configuration of the structure. However, linearity assumptions are too restrictive for advanced problems. In this context, this work will verify an algorithm based on the topology optimization method with geometric nonlinearity for plane stress problems. The proposed code was developed in MATLAB software. The verification of the code with geometric nonlinearity occurs from the replication of the case of a cantilever beam loaded at the end. The optimization process with non-linearity, in contrast to linear topological optimization, must be dependent on the magnitude of the load. The results obtained demonstrate good stability during the iterative process and asymmetric topologies are generated.