Inverse and direct projection schemes for topology optimization using polygonal elements

Resumo

Projection schemes are used in topology optimization to provide minimum length scale on structural
members in topology optimization solutions. On the other hand, inverse schemes provide control over the
minimum size of holes in the resultant topology. Literature provide several applications of both schemes associated
to regular meshes using quadrilateral finite elements to discretize the design domain. Besides, in the last decade
polygonal element has been applied to solve topology optimization problems, providing better representation for
the contour of the design domain. This paper applies the concepts of both direct and inverse schemes to
unstructured polygonal finite element meshes. Each projection is made via mesh independent functions based upon
the minimum length scale for either structural members or holes. A linear and a Heaviside projection function are

applied to both schemes. Numerical examples are presented to demonstrate the various features of the projection-
based techniques.