Projection-Based Topology Optimization Using Discrete Object Sets

We look to expand the reach of continuum topology optimization to include the design of ‘structures’ that gain functionality or are specifically manufactured from discrete, non-overlapping objects. While significant advancements have been made in restricting the geometric properties of topology-optimized structures, including restricting the minimum and maximum length scale of features, continuum topology optimization is still largely limited to monolithic structures. A wide variety of structures and materials, however, gain their stiffness or functionality from discrete objects, such as fiber-reinforced composites. This work examines a recently developed method for optimizing the distribution of discrete objects (2d inclusions) across a design domain and extends the approach to variable shape and variable sized objects that must be selected from a designer-defined set. This essentially enables simultaneous optimization of object sizes, shapes, and/or locations within the projection framework, without need for additional constraints. As in traditional topology optimization, gradient-based optimizers are used with sensitivity information estimated via the adjoint method, solved using finite element analysis. The algorithm is demonstrated on benchmark problems in structural design for the case where the objects are stiff inclusions embedded in a compliant matrix material.