A review of advances in sensitivity analyses in structural optimization

초록

Design sensitivity analysis plays a pivotal role in structural optimization by providing gradient information critical for efficient and informed design updates. It forms the computational backbone of gradient-based optimization methods, enabling accurate and scalable solutions for a wide range of structural problems. Over the decades, diverse techniques-including finite difference, analytical derivatives, automatic differentiation, and data-driven approaches-have been developed to address increasingly complex scenarios. This review presents a comprehensive overview of sensitivity analysis methods for structural optimization, with emphasis on shape and topology optimization. Sensitivity techniques are categorized into continuum and discrete frameworks and further classified into direct (analytic), adjoint, and hybrid (semi-analytic) methods. The main contribution of this review lies in providing a unified and systematic taxonomy that bridges continuum shape calculus, discrete finite element sensitivity, and topology optimization within a single conceptual framework. The review is based on a systematic survey of the structural optimization literature and adopts this unified classification framework to organize and compare sensitivity formulations across different modeling and computational settings. By unifying state-of-the-art developments across multiple domains and discretization schemes, this review offers insights into the strengths, limitations, and recent progress in the field. Finally, potential research directions are proposed to promote robust, scalable, and uncertainty-aware integration of sensitivity methods into next-generation structural optimization frameworks.

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