A differentiable structural analysis framework for high-performance design optimization

TL;DR

This paper introduces a differentiable analysis framework using Automatic Differentiation to enable efficient gradient-based structural optimization for a wide range of problems, surpassing traditional methods in speed and stability.

Contribution

It develops a general, differentiable structural analysis framework that broadens the applicability of gradient-based optimization beyond simple problems, using AD and custom derivative rules.

Findings

Outperforms existing methods in speed and stability.

Successfully applied to complex structural design problems.

Provides a comprehensive approach for gradient computation in structural optimization.

Abstract

Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions, constraints, and design parameterizations, computing gradients has remained inaccessible, requiring the use of derivative-free algorithms that scale poorly with problem size. This has restricted the applicability of optimization to abstracted and academic problems, and has limited the uptake of these potentially impactful methods in practice. In this paper, we bridge the gap between computational efficiency and the freedom of problem formulation through a differentiable analysis framework designed for general structural optimization. We achieve this through leveraging Automatic Differentiation (AD) to manage the complex computational graph of structural analysis programs, and implementing specific derivation rules for performance critical functions along this graph. This paper provides a complete overview of gradient computation for arbitrary structural design objectives, identifies the barriers to their practical use, and derives key intermediate derivative operations that resolves these bottlenecks. Our framework is then tested against a series of structural design problems of increasing complexity: two highly constrained minimum volume problem, a multi-stage shape and section design problem, and an embodied carbon minimization problem. We benchmark our framework against other common optimization approaches, and show that our method outperforms others in terms of speed, stability, and solution quality.