Coupled finite-element/topology optimization of continua using the Newton-Raphson method

We show that conventional finite element technology can be applied to topology optimization of 2D and 3D continua. Nodal design variables, classical Newton-Raphson solution for the first-order KKT equations and the screened-Poisson equation are sufficient to produce smooth results without the use of level-sets or phase-field technologies. Side-constraints are addressed with variable transformation and a single Lagrange multiplier enforces the volume constraint. We also use our mesh-division Algorithm specialized to topology optimization as a form of producing compatible meshes. By means of 2D and 3D numerical experimentation, we make the case for this approach to density-based compliance minimization. Verification examples are shown, with the corresponding compliance and volume evolution exhibiting a sound behavior.