Topology optimization of arbitrary-size blocks using a bivariate formulation

The paper analyses the various optimization strategies and analytical formulations for the topology-optimization problem, and presents an improved solution. Using the 'actual-shaped module' formulation with a 'bivariate' optimization strategy, single blocks are moved one at a time in the direction of steepest descent. This method of solution offers a compromise between the univariate approach, in which only one design variable is varied at a time, and the method of feasible direction, in which all the design variables are varied at the same time. The mechanics of block movement for obtaining the optimal position, avoiding overlaps with other blocks, are described, and the equations are presented. The technique allows computer implementation for fully automated design without user interaction.