Flexible Body Simulation in MBDyn

Transcription

1 Flexible Body Simulation in MBDyn Pierangelo Masarati FRAME Lab Department of Aerospace Science and Technology Politecnico di Milano, Italy MAGIC Machine Ground Interaction Consortium 2014 Univ. of Wisconsin, Madison, WI, December 9, 2014

2 Outline 2 Introduction Flexibility Interaction with C::E Conclusions

3 3 Introduction

4 Introduction 4 Politecnico di Milano Italy: Largest engineering school in Italy, with best international rankings Aerospace Eng. graduates about 250 BS, 180 MS, 10 PhD per year Home of MBDyn MultiBody Dynamics < Significant research in rotorcraft (helicopters, tiltrotors, ) also space (e.g. Rosetta & Philae) Basics of multibody dynamics taught at all levels Specific class at PhD level (Dan Negrut teaches HPC every year) Research groups in other departments work at vehicle dynamics, ground-vehicle interaction, granular dynamics and multibody dynamics in general

5 Introduction 5 MBDyn (in 10 points): 1) 2) 3) 4) 5) 6) 7) 8) One of the first general-purpose free multibody software Project started in 1990s Released as free software in 2001 < Monolithic Multidisciplinary Customization via user-defined modules (plus full access to source) Mainly solves initial-value DAE problems (but also more than that!) Mechanics: Newton-Euler EoM of unconstrained rigid bodies Direct enforcement of kinematic constraints with Lagrange mult. 9) Implicit integration; supports several multi-step schemes 10)Several direct linear solvers Masarati, Morandini, Mantegazza, An Efficient Formulation for General-Purpose Multibody/Multiphysics Analysis, ASME J. Comput. Nonlinear Dyn., 2014, doi: /

6 Introduction 6 MBDyn driving problem: rotorcraft dynamics Smooth dynamics problem Multidisciplinary modeling: kinematics, structural dynamics, aerodynamics, systems (up to biomechanics! as shown later) Fluid-structure interaction Flexibility is a key aspect e.g. for aeroelasticity Trade-off between detail and complexity calls for coarse meshes and simple flexible elements (e.g. beam elements for rotor blades and component synthesis for airframe) Special applications may require more...

7 Introduction 7 Other problems: Fluid-structure interaction (several cooperations, mainly UWyo) Wind energy (with REPower, Uwyo,...) Space robotics (direct and inverse dynamics, motion planning, SMEs) Insect-motion (cooperation with CrabLab, GATech) Pilot-in-the-loop (mainly flight) simulation Real-time hardware-in-the-loop simulation Vehicle dynamics (with Hutchinson CdR) Industrial process simulation (with Hutchinson CdR, SMEs)

8 8 Flexibility

9 Flexibility 9 Supported flexible elements: Lumped: 1, 3 and 6-D deformable elements 1-D: beam elements 2-D: shell and membrane elements Component Mode Synthesis (CMS) modal joint element Note: most elements exploit the notion of constitutive law, a function that maps generalized strain and strain rate into generalized force f =f (u, u ) f / u f / u the meaning of f and u is context-dependent. Element connectivity is independent of the CL Several CL's are implemented; user-defined CL's can be added

10 Flexibility: Lumped Elements 10 Lumped: 1, 3 and 6-D lumped deformable elements: Belong to the joint family 1-D: the rod joint (force along line between bodies) the deformable axial joint (moment about a specified axis) 3-D: the deformable displacement (linear) joint (force) the deformable hinge (angular) joint (moment) 6-D: The deformable (linear & angular) joint (force & moment)

11 Flexibility: Lumped Elements 11 Lumped: 1, 3 and 6-D lumped deformable elements: Worth mentioning: the invariant joint family Most formulations of lumped joints (e.g. ADAMS, ABAQUS, DYMORE) depend on connectivity: exchanging bodies 1 & 2 changes the behavior for non-infinitesimal strain Our invariant joint does not suffer from this issue. Masarati, Morandini, Intrinsic Deformable Joints, Multibody System Dynamics, doi: /s y. Bauchau, Li, Masarati, Morandini, Tensorial Deformation Measures for Flexible Joints, ASME J. Comput. and Nonlinear Dyn., 2011 doi: /

12 Flexibility: 1-D Beam Elements 12 1-D beam elements: MBDyn supports the so-called finite-volume beam element Ghiringhelli, Masarati, Mantegazza, A Multibody Implementation of Finite Volume Beams, AIAA Journal, 2000, doi: /2.933 f I, mi f 2, m2 f II, m II f 3, m3 f 1, m1 point I point II node 3 node 2 node 1 Geometrically Exact Beam Formulation (GEBF) Arbitrary cross-section properties (e.g. 6 x 6 section stiffness matrix) Recently participated in joint benchmarking effort (results follow) Bauchau et al., Validation of Flexible Multibody Dynamics Beam Formulations using Benchmark Problems, IMSD 2014, Busan, Korea, Bauchau et al., Validation of Flexible Multibody Dynamics Beam Formulations using Benchmark Problems", Multibody 2015, Barcelona, Spain, 2015

13 Flexibility: 1-D Beam Elements Benchmark #1: Princeton beam Straight, uniform beam subjected to transverse tip load causing large displacement Geometric nonlinearity dominates the solution 7 approaches compared; MBDyn was among the closest to experiment 13

14 Flexibility: 1-D Beam Elements Benchmark #2: 4-Bar Mechanism Non-ideal flexible 4-bar mechanism (hinge C misaligned) Snap-thru 14

15 Flexibility: 1-D Beam Elements Benchmark #3: Lateral buckling Clamped beam subjected to transverse load that causes bending-torsion buckling 15

16 Flexibility: 1-D Beam Elements 16 Static analysis required the development of pseudo-arc length load increment strategy (implemented as a user-defined module) P. Masarati, Robust Static Analysis Using General-Purpose Multibody Dynamics, Journal of Multi-Body Dynamics, 2015, doi: / A general approach has been formulated and implemented as a userdefined component that supports arbitrary static problems analysis Augment state with load parameter Add overall state increment (weighted) normalization equation Apply load increment accordingly Jacobian matrix of augmented problem no longer singular (for singularity of multiplicity 1)

17 Flexibility: 1-D Beam Elements Benchmark #4: Rotating Shaft Rotating shaft with misaligned disk, passing through critical speed 17

18 Flexibility: 1-D Beam Elements 18 Beam benchmark effort with C::E (Corotational) beam implemented in C::E (by Alessandro Tasora) Tasora, Masarati, Analysis of Rotating Systems Using General-Purpose Multibody Dynamics, IFToMM ICORD 2014, Milan, Italy, Benchmarking in progress Static benchmarks are fine Open points: C::E needs 2nd-order accurate DVI-capable algorithms 2nd-order A/L stable multistep scheme already tested in DVI problems Fancello, Morandini, Masarati, Helicopter Rotor Sailing by Non-Smooth Dynamics Co-Simulation, Archive of Mechanical Engineering, 2014, doi: /meceng C::E needs API refactoring to use this type of methods

19 Flexibility: 2-D Shell Elements 19 2-D: shell and membrane elements 4-node C0 shell element implemented in MBDyn Based on formulation proposed by Witkowski (Comp. Mech. 2009) Includes a combination of Enhanced Assumed Strain (EAS, applied to membrane) Assumed Natural Strain (ANS, applied to shear) Main differences: Angular strains directly computed from definition (no need for corotational derivatives) Consistent linearization of internal work (second-variation of angular strain)

20 Flexibility: 2-D Shell Elements Static Validation 25 Cantilever subjected to end shear force (Example 3.1 from Sze 2004, [1]) [1] Sze, Liu, Lo, Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elements in Analysis and Design,

21 Flexibility: 2-D Shell Elements Static Validation Slit annular plate subjected to lifting line force (Example 3.3 from Sze 2004) B A 26

22 Flexibility: 2-D Shell Elements Static Validation Pullout of an open-ended cylindrical shell (Example 3.5 from Sze 2004) A C B 27

23 Flexibility: 2-D Shell Elements Static Validation snapthru Pinched cylindrical shell mounted over rigid diaphragms (Example 3.6 from Sze 2004) A B 28

24 Flexibility: 2-D Shell Elements Dynamic Validation 29 Rotating plate: isotropic Accelerated from rest to constant angular velocity Correlation with open literature (authors seldom mention mesh details) [1] Yoo, Chung, 2001, J. of Sound and Vibration [2] Jinyang, Jiazhen, 2005, Mech. Research Comm. [3] Singh, Chopra, 2008, AIAA Journal.

25 Flexibility: 2-D Shell Elements Dynamic Validation 30 Rotating plate: Convergence of proposed implementation Coarser meshes better correlate with [1] Finer meshes better correlate with [2, 3] [1] Yoo, Chung, 2001, J. of Sound and Vibration [2] Jinyang, Jiazhen, 2005, Mech. Research Comm. [3] Singh, Chopra, 2008, AIAA Journal.

26 Flexibility: 2-D Shell Elements Dynamic Validation Flapping plate: case 4 in [1] isotropic material pinched close to a corner prescribed large amplitude (±40 deg) harmonic flapping 5 Hz 31 First normal mode, 25.5 Hz good agreement [1] Chimakurthi, Stanford, Cesnik, Shyy, Flapping wing CFD/CSD aeroelastic formulation based on a corotational shell finite element. In 50th SDM Conference. AIAA

27 Flexibility: 2-D Shell Elements Dynamic Validation Flapping plate: case 4 in [1] isotropic material pinched close to a corner prescribed large amplitude (±40 deg) harmonic flapping 30 Hz 32 First normal mode, 25.5 Hz results strongly mesh-dependent [1] Chimakurthi, Stanford, Cesnik, Shyy, Flapping wing CFD/CSD aeroelastic formulation based on a corotational shell finite element. In 50th SDM Conference. AIAA

28 Flexibility: 2-D Shell Elements Dynamic Validation Flapping plate: case 4 in [1] isotropic material pinched close to a corner prescribed harmonic flapping 30 Hz 33 First normal mode, 25.5 Hz 3/4 T 13/4 T 11/4 T 7/4 T 1/4 T 5/4 T Strong mesh dependence close to 1st mode 9/4 T [1] Chimakurthi, Stanford, Cesnik, Shyy, Flapping wing CFD/CSD aeroelastic formulation based on a corotational shell finite element. In 50th SDM Conference. AIAA

29 Flexibility: 2-D Membrane element 34 2-D: Membrane element Mainly developed for Fluid-Structure Interaction of flapping wing MAV Direct dynamics analysis (ARL MAST-CTA) Inverse dynamics analysis (USAF/EOARD) Shape and loads reconstruction from DIC measured membrane strains

30 Component Mode Synthesis 35 Helicopter-Pilot Interaction: Flexible rotor (beams) Flexible airframe (CMS) Pilot biomechanics (rods)

31 36 Interaction with C::E

32 Interaction with C::E 37 Asteroid interactional dynamics Granular asteroid aggregation simulated using C::E (in progress) Orbital interaction with frozen asteroid in MBDyn (in progress) Close interaction/impact with asteroid in C::E (or co-simulation? Todo) Activity at SPLab, Politecnico di Milano (F. Ferrari, M. Lavagna) in cooperation with FRAMELab, Politecnico di Milano (P. Masarati) and University of Parma (A. Tasora)

33 Interaction with C::E Motivation 38 Accurate mass distribution model of the asteroid Effective trajectory design around an asteroid

34 Interaction with C::E Motivation 39 Evidence from recent studies/observations: asteroids between 100 m and 100 km in size are likely to be gravitational aggregates (low tensile strength) Research goal: Obtain a high accuracy model of asteroids mass distribution by studying them as gravitational aggregates Study of asteroid gravitational aggregation dynamics Study of properties of the final aggregate depending on initial conditions

35 Interaction with C::E Approach CHRONO::ENGINE N-body integrator Handling of complex (non spherical) shape of bodies Collision handling C++ implementation Optimized for multi-body problems 40 40

36 Interaction with C::E Approach Aggregation phase N rigid bodies: rotation and translation of each body 41 Final aggregate Single body: rotation and translation of the cluster of bodies

37 Interaction with C::E Approach Gravitational forces 42 Contact forces If contact between two bodies occurs Collisions Friction friction collision

38 Interaction with C::E Approach 43 Aggregation dynamics Final aggregate Physical parameters Dynamical state Inertia tensor Mass Volume Bulk density / void fraction Velocity of center of mass Angular velocity

39 Interaction with C::E Example Aggregation Sequence Simulation time: ~ tens of hours Computational time: ~ minutes

40 Interaction with C::E Example Final Aggregate Identification Vertices of each body 45 Final aggregate geometry (alpha shape)

41 46 Conclusions

42 Conclusions 47 MBDyn supports several models for flexible components It is a versatile tool for several general-purpose dynamics simulations It is dedicated to smooth dynamics very limited non-smooth capabs. Co-simulation (with SICONOS) has been investigated for NS dyn. Co-simulation with C::E is an option (e.g. CUDA user-defined modules to parallelize assembly of configuration-dependent loads have already been tested) We are willing to cooperate; e.g.: to implementation of flexible components multi-step DVI capable numerical schemes

43 Acknowledgements 48 Partial support from: Hutchinson Centre de Recherche for constitutive law development University of Maryland/Army Research Laboratory under the MAST/CTA program for shell implementation School of Energy Resources, UWyo for fluid-structure interaction EC 7th FP project ARISTOTEL for biomechanics development USAF-EOARD for membrane direct and inverse dynamics is gratefully acknowledged

44 49 Thank you for your attention Questions?