1. 1 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Applying Multi-Flexbody Simulation to Non-Linear Joint Analysis Presented by Paul D Fotsch & VPDS Inc

2. 2 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Project overview o Motivation o Approach o Linear Structural Model Preparation o Cut-Surface Load Transformation o Flexbody Simulation / Data Export o Nonlinear Breakout Model o Breakout Model Analysis o Software Involved o Academic Model o Application Model o Questions / Discussion Outline

3. 3 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Employ multi-flexbody simulation to compute quasi-static loads on a reduced Finite Element (FE) Model (FEM). o Convert the reduced FEM loads to a meaningful load distribution on a detailed nonlinear analysis model. o Render from the detailed nonlinear model all pertinent characteristics including load and stress distribution, contact pressure, friction, seal failure, wear, etc. Project Overview

4. 4 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 System & Detail Models Multi-Flexbody Simulation Model Detailed Nonlinear Model Link Arm Frame Spherical Bearing Bolt and Washers

5. 5 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Multi-flexbody simulation has been shown to be effective for computing structural loads for mechanisms. o Flexbody analysis requires a simplified representation at interfaces (joints) and loss of analysis effectiveness there. o Hence, the goal is to employ flexbody simulation’s ability to render loads away from an interface to perform a more effective analysis of a detailed interface model. Motivation

6. 6 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Linear FEM for Flexbodies

7. 7 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Use a breakout model comprised of partial FE models of the interfacing structures for the detailed nonlinear analysis. o Construct the FE models for both the flexbody simulation and nonlinear analysis to have a common boundary mesh. o Compute load transformation matrices that convert flexbody loads to common boundary node loads during the flexbody creation process. Approach

8. 8 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Common Cut-Surfaces Between FEM Non Linear FEM Linear FEM Common Cut-Surface

9. 9 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Each structure involved in the interface is prepared for the flexbody simulation and breakout model analysis as follows: Linear Structural Model Preparation o Cut the FE model at a ‘cut-surface’ some distance from the interface to produce a ‘cut-section’. o Simplify the interfaces using constraints, averaging elements, etc. o Mathematically reduce the model using Guyan reduction for flexbody use. o Perform an inertia relief analysis. o Construct a Force Transformation Matrix (FTM) to recover cut-surface forces from flexbody Degree of Freedom (DOF) forces. o Construct a Displacement Transformation Matrix (DTM) to recover cut- surface displacements from flexbody DOF forces. o Note that the cut-surface is the common boundary mesh.

10. 10 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Full Structure & Cut-Section Models Cut-Surface Cut-Section

11. 11 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Apply unit loads to each simplified interface DOF as individual load cases. o Compute the inertia relief response for each load case. Cut-Surface Load Transformation o Extract cut-surface DOF entries from and and export them for use in loading the breakout model. o Impose the displacement and acceleration results for each load case to the cut-section (partial) model according to:

12. 12 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Import the reduced FE models into the system model. o Simulate desired operating conditions and expected events. o Export the flexbody forces and body positions/orientations for select time points. Flexbody Simulation / Data Export

13. 13 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Academic Model, Double Pendulum

14. 14 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Double Pendulum Simulation

15. 15 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o The breakout model replaces the simplified representation of the interface with one of great detail and refinement. o Detail will generally include contact surfaces with friction and may include seals and other features. o Additional parts may come into play as well. o In short, all features that represent the real hardware may be modeled. Nonlinear Breakout Model

16. 16 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Nonlinear Breakout FEM

17. 17 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o Loads are applied at the cut-surfaces based on the flexbody simulation loads and FTM produced in the FEM preparation step. o Relative deformations are imposed at the cut-surfaces based on the flexbody simulation loads and the DTM produced in the FEM preparation step. o Linear and rotational accelerations, based on the flexbody loads, are imposed on cut-sections and additional parts. o Sufficient DOF are grounded to remove singularities. o A ‘pseudo’ inertia relief analysis is performed. Breakout Model Analysis

18. 18 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Loaded Breakout Model

19. 19 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 o An in-house program, PRASI, processes cut-section NASTRAN models to produce a single structure’s NASTRAN model. o NASTRAN with its Direct Matrix Abstraction Program (DMAP) language creates the reduced flexbody models and transformation matrices. o Dynasty, by Caterpillar Inc., is used for the flexbody simulation. o The detailed nonlinear breakout model is built for ABAQUS. o An in-house program, POASI, adds the forces and imposes the motions to the ABAQUS model. Software Involved o Note: The ‘ASI’ in PRASI and POASI comes from the acronym of the internal process name we call ‘Advanced Structural Interface’

20. 20 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Process Flow Chart NASTRAN Models Modified NASTRAN Models Flexbody Data ABAQUS Model Flexbody Loads Load Transformation Matrices Loaded ABAQUS Model NASTRAN Dynasty Simulation Program FEModeler 1 ABAQUS PRASI Preprocess ASI models POASI Postprocess ASI models FEA Post Processor

21. 21 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Academic Model, Double Pendulum

22. 22 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Academic Model, Double Pendulum

23. Application Model, SUV Linkage

24. 24 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Application Model, SUV Linkage

25. 25 Presented by Paul D Fotsch & VPDS Inc April 13, 2011 Questions / Discussion o Thank you for your attention. o Contact Information: Paul D Fotsch VPDS Inc paul.fotsch@vpds-inc.com