A universal parametric nonlinear model order reduction method for complex shell structures

To address constructing nonlinear reduced-order models for perforated shell structures with complex geometries, this paper proposes a universal nonlinear model reduction technique. Utilizing conformal mapping that preserves inherent modal properties, the technique establishes reduction bases for such structures in the mapped plane. The proposed method employs boundary first flattening (BFF) to map non-planar shells to planar domains for global parameterization of complex shells. Within the mapped parametric plane, higher-order elements are employed for high-accuracy computation of parametric modes and modal derivatives, establishing parametric nonlinear reduced-order models for non-planar shells. By exploiting the decoupling of in-plane and out-of-plane deformations in planar structures, the static condensation method (SCM) is employed within the parametric plane to further reduce degrees of freedom (DoFs). The optimal static condensation method (OSCM), which is directly applicable to complex non-planar shells, is developed without the need for additional mathematical modes. The approach is applicable to modal reduction of arbitrarily complex non-planar shells. With computational accuracy maintained, a significant reduction in system DoFs is achieved, providing a solution for real-time analysis and control of complex multibody systems.