Gaussian Ensemble Topology (GET): A New Explicit and Inherently Smooth Framework for Manufacture-Ready Topology Optimization

Abstract: We introduce the Gaussian Ensemble Topology (GET) method, a new explicit and manufacture-ready framework for topology optimization in which design geometries are represented as superpositions of anisotropic Gaussian functions. By combining explicit Gaussian descriptions with a level-set-like Heaviside projection, GET inherently generates smooth, curvature-continuous designs without requiring post-processing steps such as mesh or corner smoothing and feature extraction. The method is validated on standard compliance-minimization and compliant mechanism benchmarks in two and three dimensions. The optimized designs achieve objective values comparable to those obtained with classical Moving Morphable Component (MMC) approaches, but with geometrically consistent, refined boundaries. Numerical examples demonstrate additional advantages of the GET framework, including mesh independence inherent to explicit parameterizations, strong geometric expressiveness, and effective control over smoothness, discreteness, and structural complexity through parameter tuning. As a robust and manufacture-ready approach to explicit topology optimization, GET opens avenues for tackling advanced and complex design problems.