Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy

Area of Science:

• * Computational Mechanics
• * Nonlinear Dynamics
• * Structural Engineering

Background:

• * Nonlinear dynamic analysis of complex engineering structures using finite element (FE) software is computationally intensive.
• * Indirect reduced-order modeling (ROM) strategies reduce computational cost by using FE static solution datasets.
• * Current indirect ROM methods are limited to structures with minimal in-plane displacement, neglecting in-plane kinetic energy.

Purpose of the Study:

• * To develop an enhanced indirect reduced-order modeling strategy that accounts for in-plane kinetic energy.
• * To extend the applicability of indirect ROM to a wider range of structures, including those with free boundary conditions.
• * To maintain accuracy in reduced dynamics for higher deflection amplitudes.

Main Methods:

• * Exploitation of nonlinear manifold theory to incorporate in-plane kinetic energy into reduced dynamics.
• * Development of a novel indirect reduction method that does not require additional FE model information.
• * Validation using a finite element model of a cantilever beam.

Main Results:

• * Demonstrated that neglecting in-plane kinetic energy limits the applicability of existing indirect ROM methods.
• * Showcased that the nonlinear manifold approach effectively accounts for in-plane kinetic energy.
• * Validated the enhanced method's accuracy for a cantilever beam, a structure with significant in-plane displacement.

Conclusions:

• * The proposed nonlinear manifold-based method significantly broadens the scope of indirect reduced-order modeling.
• * This approach enables accurate nonlinear dynamic analysis of structures with substantial in-plane motion.
• * The method offers a computationally efficient alternative for analyzing complex engineering structures with high deflections.