Topology optimization with variable loads and supports using a super-Gaussian projection function

This work presents a new method for efficiently designing loads and supports simultaneously with material distribution in density-based topology optimization. We use a higher-order or super-Gaussian function to parameterize the shapes, locations, and orientations of mechanical loads and supports. With a distance function as an input, the super-Gaussian function projects smooth geometric shapes which can be used to model various types of boundary conditions using minimal numbers of additional design variables. As examples, we use the proposed formulation to model both concentrated and distributed loads and supports. We also model movable non-design regions of predetermined solid shapes using the same distance functions and design variables as the variable boundary conditions. Computing the design sensitivities using the adjoint sensitivity analysis method, we implement the technique in a 2D topology optimization algorithm with linear elasticity and demonstrate the improvements that the super-Gaussian projection method makes to some common benchmark problems. By allowing the optimizer to move the loads and supports throughout the design domain, the method produces significant enhancements to structures such as compliant mechanisms where the locations of the input load and fixed supports have a large effect on the magnitude of the output displacements.