A smooth evolutionary structural optimization procedure applied to plane stress problem

• Evolutionary topology optimization procedure with smoothing in heuristic removal.
• Comparative analysis of the numerical technique SESO with the ESO method.
• Evolutionary topology optimization procedure with low computational cost.
• Possibility of applying the technique SESO in problems dynamic analysis.
• Possibility of applying the technique SESO in problems geometric nonlinearity.

Topological optimization problems based on stress criteria are solved using two techniques in this paper. The first technique is the conventional Evolutionary Structural Optimization (ESO), which is known as hard kill, because the material is discretely removed; that is, the elements under low stress that are being inefficiently utilized have their constitutive matrix has suddenly reduced. The second technique, proposed in a previous paper, is a variant of the ESO procedure and is called Smooth ESO (SESO), which is based on the philosophy that if an element is not really necessary for the structure, its contribution to the structural stiffness will gradually diminish until it no longer influences the structure; its removal is thus performed smoothly. This procedure is known as “soft-kill”; that is, not all of the elements removed from the structure using the ESO criterion are discarded. Thus, the elements returned to the structure must provide a good conditioning system that will be resolved in the next iteration, and they are considered important to the optimization process. To evaluate elasticity problems numerically, finite element analysis is applied, but instead of using conventional quadrilateral finite elements, a plane–stress triangular finite element was implemented with high-order modes for solving complex geometric problems. A number of typical examples demonstrate that the proposed approach is effective for solving problems of bi-dimensional elasticity.