Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes. A method includes obtaining a design space for a modeled object, one or more design criteria for the modeled object, and one or more in-use load cases; iteratively modifying a generatively designed three dimensional shape of the modeled object in the design space in accordance with the one or more design criteria and the one or more in-use load cases for the physical structure, comprising: performing numerical simulation of the modeled object in accordance the one or more in-use load cases, computing shape change velocities for an implicit surface in a level-set representation of the three dimensional shape, changing the shape change velocities in accordance with a polynomial function, and updating the level-set representation using the shape change velocities to produce an updated version of the three dimensional shape.