Structures of all types are subject to dynamic loads that affect them and potentially alter their integrity. The field of structural dynamics is concerned with predicting and discovering how physical structures behave under such applied loads. Finite element modeling is often used for these tasks. It is a computational process in which a structure is broken down into small pieces, assumptions on how these pieces deform are made, and then the structure is reassembled.
This technique allows for tremendous flexibility of shape and materials, but the major drawback is that it involves a very large system of equations when the structure is complex and can involve hundreds of thousands to millions of unknowns. If the problem is dynamic, these unknowns change with time and thus the equations must be solved repeatedly a large number of times. That can be a very expensive request with days and weeks of computations needed.
Marc Mignolet, professor of aerospace and mechanical engineering in the Ira A. Fulton Schools of Engineering at Arizona State University, is working with his graduate students and Xiaoquan (Julian) Wang, a Fulton Schools research scientist, to research the vibration, or dynamic response, of structures, particularly panels and wings of aircraft.
“Our focus is on developing what is referred to as reduced order models, ROMs for short,” Mignolet says. “They are small size models, with less than 100 unknowns, that are extracted from the finite element model, approximating it based on the physics of the response. The benefit is that the ROMs run much faster than the finite element models but they conserve very accurately the spatial resolution of these models.”
Mignolet’s work was recognized by the European Association for Structural Dynamics at the EURODYN 2020 Conference that was held virtually with a Senior Research Prize “for his outstanding developments in the field of nonintrusive reduced-order modeling methods for the nonlinear geometric response of structures.”
“The award recognizes the cumulative work we have carried out in the last 19 years,” Mignolet says. “We demonstrated that these ROMs can be used for real structures in a broad set of conditions, with or without heat, aerodynamics and uncertainty. We have demonstrated how to build them reliably and these ROMs can now address real problems and dramatically reduce analysis time.”
When a structure has “small” deformations, the equations that need to be solved are linear with respect to the unknowns and there is a standard way of building the ROM. However, when these deformations become larger, the equations become nonlinear and the standard approach no longer works.
A notable momentum to study these nonlinear geometric problems has come from the aerospace community.
“Going faster tends to increase the aerodynamic forces and being lighter may imply being overall softer,” Mignolet says. “The net result is then that the deformations are likely to increase. A similar situation also occurs when heating takes place on future hypersonic vehicles in which heat not only softens the structure but the heating in itself may lead to large forces or deflections.”
This has meant that Mignolet’s work is more specifically focused on developing and validating ROM methodologies for nonlinear geometric structural problems, with or without heating.
“One specificity of our work is that the structure is first modeled in a commercial finite element software, then the ROM is obtained from the finite element model. That allows great flexibility on modeling but also ease of transition to industrial designers and analysts,” Mignolet says.
Mignolet’s vision is for engineers in the field to use this work, not just researchers.
“We have grown by studying new structures and by evolving and fine-tuning our methodology to successfully treat them,” Mignolet says. “Having the methodology used ‘out there’ will bring new opportunities and cases for us to make the approach more robust as well as serving the engineering community.”