Structural topology optimization with implicit design variable—optimality and algorithm

This paper presents a novel formulation for structural topology optimization in which both cost function and constraints are expressed in terms of an implicit design variable—the iso-line/surface threshold of a characteristic response function, such as a strain or mutual strain energy density function. A new material representation model is developed to implicitly describe material usage in a given design domain in terms of one implicit design variable. Based on the Karush–Kuhn–Tucker (KKT) necessary conditions, optimality criteria for finding solutions are established and then employed to develop a simple algorithm for one-material minimum mean compliance and compliant mechanism problems. The algorithm consists of sequentially moving iso-surface threshold (MIST) of chosen characteristic response function. Numerical examples are then presented to validate the proposed algorithm MIST for the minimum mean compliance, compliant mechanism, and fully stressed design problems.