# LUT subproject

# Development of generic description of the structural flexibility for real-time multibody simulation

## Demand

Flexible bodies in multibody system applications can be described using the floating frame of reference formulation. In this formulation, body deformation is defined with respect to the reference coordinate system. The body deformation and the motion of the reference coordinate system are coupled together with the descriptions inertia forces in the floating frame of reference formulation. The use of the reference coordinate system in the description of deformation allows for the use of modal reduction techniques. Usage of the modal reduction leads to a computationally efficient approach that makes it possible to describe structural flexibility in the case of real-time simulation.

## Solution

In this project, modal reduction techniques are used to simplify the finite element (FE) model for the usage of real-time simulation.

The main goal of SIMPRO subproject LUT were:

- Develop a procedure to enable real-time or faster-than-real-time simulation with flexible bodies.
- Providing an open source software as a vehicle for modal reduction technique. The general flow of this solver is describe in Figure 1.
- Providing an option to the user to determine most appropriate deformation modes to be used in real-time simulation based on the selected modal reduction technique.

*Figure 1: The general flow of how the solver is functional.*

## Benefits and use cases

The software for modal reduction was developed using an open source software approach. Developed software is able to extract a selective data from commercial finite element software, then process the data which can be used in the real-time simulation software. The solver was developed using several reliable GNU General Public License (GPL) libraries, which are comprehensively used by other well-known software applications, such as Matlab and GNU Octave.

The software based on three numerical methods in model order reduction, which are the Craig-Bampton method, the Guyan reduction method, and the Krylov subspace method as shown in Figure 2. These three methods can be alternated based on user preferences. In order to obtain a correct and accurate results, an experienced user familiar with all three methods is required.

*Figure 2: The working process of the developed solver.*

The solver is tested to compare the results against the commercial software. As summary, introduced procedure offers a versatile way to reduce a finite element model described using in commercial finite element software. The data from FE software is extracted, manipulated, and pull out in form which can be used in the real-time simulation software.

## Subproject deliverables

**Model order reduction solver source code: In Matlab and C**- Mikkola, A.
*et al.***Development of generic description of the structural flexibility for real-time multibody simulation**

Project internal research report - Baharudin, E.
*et al.***Real-time analysis of mobile machines using semi-recursive method with sparse matrix technique**

To be published

## Contacts

- Prof. Aki Mikkola, Lappeenranta University of Technology, aki.mikkola@lut.fi