Fuzzy Heuristic Gradient Projection for frame topology optimization

In this paper, a new methodology to obtain an optimal structure size considering geometries nonlinearity is presented. This method makes use of Heuristic Gradient Projection method in addition to Fuzzy Logic. The Heuristic Gradient Projection (HGP) method, a previously developed method for 3D-frame design and optimization, utilizes mainly bending stress relations in order to simplify the process of iterations. HGP is based on comparing the resulting equivalent stress with the allowable stress value. The proposed Fuzzy Heuristic Gradient Projection (FHGP) approach incorporates both bending stress and axial stress when processing with the allowable stress value. The weighting factors of both axial and bending stresses are found using a Fuzzy Logic controller. Fuzzy logic is incorporated to reach an optimal solution with lesser number of function evaluations. A simple cantilever example, subjected to axial force and bending moment, is presented to illustrate this approach in addition to a 10-member planar frame that is used to prove the efficacy of the new method. FHGP approach generally results in faster convergence.