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

2025-10-07

AI Summary

Existing topology optimization methods rely on post-processing—such as mesh smoothing and feature extraction—to obtain manufacturable, smooth boundaries, thereby increasing computational cost and workflow complexity. This paper proposes a Gaussian Function Integration (GFI) topology optimization framework: structural geometry is explicitly represented via superposition of anisotropic Gaussian functions, coupled with a Heaviside-type level-set projection for mesh-independent parametric modeling. To the best of our knowledge, this is the first work to introduce explicit Gaussian function integration into topology optimization; the representation inherently ensures curvature continuity and manufacturing compatibility, while enabling flexible control over smoothness, discreteness, and geometric complexity through tunable parameters. Numerical experiments—including 2D/3D stiffness maximization and compliant mechanism design—demonstrate performance competitive with state-of-the-art Moving Morphable Components (MMC) methods, while yielding designs with sharper boundaries and superior geometric consistency—entirely eliminating the need for post-processing.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Developing a manufacture-ready topology optimization framework using Gaussian functions
• Generating smooth curvature-continuous designs without post-processing steps
• Achieving mesh independence and geometric control through explicit parameterizations

Innovation

• Uses anisotropic Gaussian functions for geometry representation
• Combines explicit descriptions with level-set-like Heaviside projection
• Generates smooth designs without post-processing steps