[2025] Optimizing load distributions in structural design

Lee, T.U., Lu, H. and Xie, Y.M., 2025. Engineering Structures, 120664. [Link]

Structural performance is highly sensitive to applied loads, where minor changes in the ingredients of load distribution (i.e., locations, magnitudes, and directions) can largely influence the response. Optimizing load distribution, therefore, offers great potential for enhancing structural efficiency and safety. While most techniques focus on probabilistic load distributions to manage uncertainties, optimizing deterministic load distributions for specific scenarios remains relatively underexplored, as it challenges the conventional practice of prescribing fixed loads in structural design.

This paper introduces a new optimization strategy to identify deterministic load distributions of complex structures to maximize or minimize their stiffness, which is particularly relevant and useful for structural design scenarios where applied loads may change their locations

or redistribute their magnitudes (e.g., the traffic loads on a multi-lane bridge). A generalized optimization problem is formulated to consider variable load locations, magnitudes, and directions, enabling infinite possible load distributions. The proposed strategy, however, requires only a single finite element analysis with a small number of load cases to rapidly and inexpensively determine optimized load distributions.

A series of 2D and 3D numerical examples demonstrate the effectiveness and wide applicability of the proposed strategy, including (1) stacking objects on a multi-layer shelf, (2) reinforcing a cantilever, (3) identifying the extremal performance of a cellular beam, and (4) generating elastic energy of a curved-folded bow. The paper also explores combining load and topology optimizations to create innovative, efficient structures with high degrees of design freedom.

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