Model Order Reduction for Temperature-Dependent Nonlinear Mechanical Systems: A Multiple Scales Approach
This work addresses the computational challenge of simulating thermo-mechanical systems with disparate time scales, offering a more efficient model reduction technique for engineers.
The authors use the method of multiple scales to reduce thermo-mechanical structural models with slowly-varying temperature, constructing an adaptive reduction basis that yields better accuracy and fewer unknowns than standard Galerkin projection on linear and nonlinear beam examples.
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a slowly-varying temperature distribution in a systematic manner. In the process, we construct a reduction basis that adapts according to the instantaneous temperature distribution of the structure, facilitating an efficient reduction in the number of unknown. As a proof of concept, we demonstrate the method on a range of linear and nonlinear beam examples and obtain a consistently better accuracy and reduction in the number of unknowns than standard the Galerkin projection using a constant basis.