Structure-Aligned Geometric Compensation for Additive Manufacturing Warpage via Vibrational Modal Analysis

Additively manufactured parts can deviate from their nominal design due to residual-stress-induced deformation during thermal cycling, reducing dimensional accuracy. Geometric compensation seeks to correct this deviation by pre-deforming the design so that the printed part recovers its intended shape. Most existing approaches construct compensation by directly reversing the measured geometric deviation. This work shows that geometric compensation is fundamentally a representation problem rather than purely an inversion problem. Direct inversion of the measured deformation field may propagate non-structural components and therefore fail to recover the underlying structural deformation. To address this, compensation is reformulated within a reduced vibration-mode subspace obtained from modal analysis of the nominal structure. The reduced modal representation restricts compensation to deformation patterns consistent with the structural behavior of the part. Finite-element simulations show that the proposed formulation effectively compensates warpage in additive manufacturing when the deformation is governed by dominant structural response, and remains robust to measurement and reconstruction errors.