Hierarchical Free-Form Deformation with Rigid Feature Preservation for Shape-Parameterized Model Order Reduction

Shape-parameterized model order reduction enables rapid analysis of geometrically varying designs, but its application to engineering assemblies is complicated by functional interfaces that must remain geometrically valid under deformation. Examples include revolute joints, whose distortion can compromise the mechanical compatibility of the model. This work presents a feature-preserving geometry transformation framework for shape-parameterized reduced-order modeling. The method combines hierarchical free-form deformation with localized rigidization: a coarse control grid defines low-dimensional global shape variations, while selected fine-grid control points associated with constrained subdomains are moved by a best-fit rigid-body transformation, optionally with uniform scaling, computed from their undeformed and coarse-deformed positions. The resulting composite map provides smooth transitions between constrained and unconstrained regions, admits analytically computable Jacobians, and is verified to remain invertible over the parameter ranges considered. The transformation is integrated into a reference-domain finite element formulation, enabling efficient reduced basis construction and hyperreduction training. The framework is demonstrated on an excavator arm and an automotive suspension rocker. In both cases, the proposed procedure preserves the geometry of the constrained interfaces, and the shape-parameterized reduced-order models achieve rapid error convergence with significant reductions in the number of degrees of freedom and quadrature points relative to the full-order models.