Contributions to handle maximum size constraints in density-based topology optimization

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the local constraints are aggregated into a single one by p-mean and p-norm functions, classically used for stress constraints. Moreover, a new test region is investigated which is a ring instead of the classical circle around the element. These developments were implemented for compliance minimization with the MBB beam test case. Results indicate that p-mean performs better in the maximum size field than p-norm, because it underestimates the most violated constraint. This gives some relaxation to the problem that allows stiffer connections. Similar effect has been observed for the ring-shaped region which reduces the amount of holes that are introduced in the structure, specially in the connection of solid members. In addition, it is shown that the maximum size formulation allows the definition of the minimum gap between solid members which gives designers more control over the geometry. The developments have been illustrated and validated with compliance minimization tests of 2D-domains.