A VON MISES STRESS-BASED TOPOLOGY OPTIMIZATION OF CONTINUUM ELASTIC STRUCTURES THROUGH THE PROGRESSIVE DIRECTIONAL SELECTION METHOD

Resumo

This work presents a study applying the von Mises equivalent stress as a performance parameter for
topological optimization of two-dimensional continuous elastic structures employing the Progressive Directional
Selection (PDS) method. A typical objective to achieve the ideal topology of a structure is to define the best
material distribution of the design domain, considering an objective function and mechanical constraints. In
general, most studies deal with minimizing the compliance of structures. Numerical methods for optimizing the
topology of continuous structures have been widely investigated. Most of these methods are based on finite element
analysis, where the design domain is discretized into a fine mesh of elements. Evolutionary Structural Optimization
(ESO) is one of these methods based on the simple concept of gradually removing inefficient finite elements from
a structure. This method was formulated from the engineering point of view that the topology of the structures is
naturally conservative for safety reasons and contains an excess of material. In such a context, the optimization
consists of finding the optimal topology of a structure and determining whether there should be a solid or void
element for each point in the design domain. ESO's algorithms are easy to understand and implement. The stress
level of each element is determined by comparing the von Mises stress of the element and the maximum von Mises
stress of the entire structure. After each finite element analysis, elements that present a stress level below the
defined rejection ratio are excluded from the model. However, the ESO is a heuristic method, and there is no
mathematical proof that an optimal solution can be achieved by eliminating elements. In addition, the original
approach is inefficient because it needs to find the optimal topology comparing several solutions generated
intuitively, adjusting the rejection ratio and evolutionary rate. To avoid this problem, but taking advantage of the
simplicity of applying ESO, a new approach using the PDS method is proposed, inspired by the natural directional
selection observed in biology. In the first work using PDS, the optimization problem was the minimization of the
strain energy of a structure analyzed through the Finite-Volume Theory (FVT). This investigation discusses a
scheme to minimize the von Mises equivalent stress of a discretized domain with a volume constraint. One example
of topological optimization of 2D continuous elastic structure inspired by a classic literature problem is
investigated.