[Paper Review] Multiphysics model reduction of thermomechanical vibration in a state-space formulation

Jun-Geol Ahn, Hyun-Ik Yang+1 more|arXiv (Cornell University)|May 4, 2021

Structural Health Monitoring Techniques31 references4 citations

TL;DR

This paper proposes a two-step multiphysics model reduction (MMS) method for thermomechanical vibration problems using a symmetric state-space formulation that includes displacement, velocity, and temperature shift. By first reducing structural modes and then updating the thermal domain while preserving coupling effects via residual flexibility, the method achieves improved accuracy and computational efficiency, validated through numerical examples with parallel solver compatibility.

ABSTRACT

The aim of this work is to propose a new multiphysics mode synthesis (MMS) for the thermomechanical vibration problem. The present thermomechanical model is based on a state-space formulation, which consists of displacement, velocity, and temperature shift. The state-space based thermomechanical formulation is symmetric unlike a conventional non-symmetric formulation. In the proposed MMS, the structural variables are first reduced, which is then applied to the coupling term in the thermal parts. A term of the thermal domain is then reduced while preserving the multiphysics coupling effects, resulting in improved accuracy. The proposed two-step MMS with the thermal physics domain update can be implemented with the coupling term derived by using the residual flexibility. The proposed MMS strategy can be also applied to accelerate the computational speed by using independent parallel solvers. The performance of the proposed MMS method is evaluated through numerical examples.

Motivation & Objective

• To address the challenge of high computational cost in simulating thermomechanical vibration in coupled systems.
• To develop a model reduction strategy that preserves multiphysics coupling effects between structural and thermal domains.
• To improve accuracy in reduced-order models by applying a two-step reduction process with thermal domain update.
• To enable efficient computation using independent parallel solvers through the proposed formulation.
• To establish a symmetric state-space formulation that avoids non-symmetric formulations common in prior methods.

Proposed method

• The method employs a symmetric state-space formulation incorporating displacement, velocity, and temperature shift as state variables.
• Structural degrees of freedom are reduced first using a modal truncation approach.
• The coupling term in the thermal domain is derived using residual flexibility to maintain multiphysics interaction.
• A second reduction step is applied to the thermal domain while preserving the coupling effects from the structural reduction.
• The two-step MMS strategy is implemented with independent parallel solvers to accelerate computation.
• The formulation ensures symmetry, improving numerical stability and accuracy compared to conventional non-symmetric approaches.

Experimental results

Research questions

• RQ1 How can model reduction be effectively applied to thermomechanical vibration problems while preserving coupling between mechanical and thermal fields?
• RQ2 Can a symmetric state-space formulation improve the stability and accuracy of multiphysics model reduction?
• RQ3 What is the impact of a two-step reduction strategy—first structural, then thermal—on the accuracy of the reduced-order model?
• RQ4 How does the use of residual flexibility in the coupling term affect the preservation of multiphysics effects?
• RQ5 To what extent can the proposed method be accelerated using independent parallel solvers?

Key findings

• The proposed two-step MMS method achieves higher accuracy than conventional model reduction techniques by preserving multiphysics coupling effects.
• The symmetric state-space formulation ensures better numerical conditioning compared to non-symmetric formulations.
• The use of residual flexibility in the coupling term effectively maintains interaction between structural and thermal domains during reduction.
• The method enables efficient parallel computation by decoupling structural and thermal solvers after model reduction.
• Numerical examples demonstrate the method's effectiveness in reducing computational cost while maintaining solution fidelity.