Parametric-ROM of Structures with Varying Geometry using Direct Parameterization of Invariant Manifolds

TL;DR

This paper introduces a parametric reduced-order modeling framework for structures with varying geometry, utilizing direct parameterization of invariant manifolds to efficiently handle geometric changes without altering material properties.

Contribution

It develops a novel method that incorporates geometry parameters as additional variables in the reduced-order model using invariant manifolds, enabling efficient parametric analysis in structural dynamics.

Findings

Efficient parametric reduction for geometrically varying structures.

Explicit power series expansion of inverse determinant in weak form.

Enhanced capability for parametric studies in structural dynamics.

Abstract

This work presents a framework for parametric reduction in FEM, where geometry is controlled by a parameter without altering material properties or stress states. The inverse determinant in the weak form is expanded as a power series, with explicit expressions for the zeroth and first-order terms. External forcing and parameter dependence are incorporated into an enlarged autonomous system, reduced via the direct parameterization of invariant manifolds method and homological equations. The parameter is treated as an additional variable with trivial dynamics, isolated for inclusion in the ROM. This approach enables efficient parametric studies and advances reduced-order modeling in structural dynamics.