finite element procedures for multiphysics analyses...

MSC Software Confidential

Finite element procedures for

multiphysics analyses and nonlinear

responsesPaolo Gaudenzi and Luca lampani

Presented By: Prof. Paolo Gaudenzi, Università di Roma La Sapienza

June 15, 2012


- Strong form equations for

the 3 physical fields

- The piezoelectric problem

joins structural and electric

domain at the level of

constitutive relationships

- The fluid-structural

interaction is at the level of

the domains interface

kkijklijklij

jijklikli

EeC

EeD

Governing equations for a fluid-active structure

interaction: a typical multiphysics problem


Structural equations: weak form Electric equations : weak form

Divergence theorem application Divergence theorem application

Constitutive relations Constitutive relations

Shape functions Shape functions

Discrete space Discrete space

dSufdVufdVdVuu i

St

Sii

t

Vijij

t

ViiV tttt

SV

iiSiV

ijij dVuudVufSS

)()( ,

VpPji dVD 0,

dSqdVED S

Sii

t

V tt

uzyxHzyxu uˆ),,(),,( ˆ),,(),,( zyxHzyx

S

u

B

uupuupuu FFkukum ˆˆ̂ S

pu Fkuk ˆˆ

0)( dSfufdVudVeECdVuu ST

S

T

V

T

V

T

V tttt 0)( dVEeEdSq T

V

ST

S tt

The weak form/virtual work approach for finite

elements


Electricsolver

Structuralsolver

TMC interaction

ttE tt

Subroutine tocalculate

stresses withincremental

approach

Subroutine tocalculate

electrical fluxeswith incremental

approach

2nd HYPOTHESYS: constant materials

properties

- Non linear problem due to two domains

coupling

- No hypothesis about non linear kinematic

conditions:

total Lagrangian approach

Vt

K

ij

ttK

ij

tt

Vt

tt

ij

K

klijkl dVRdVC )1()1()(

Vt

Ktttt

Vt

ijkl

K

ij EdVDQdVEE )1()(

)(

)()(

Ktt V

K

ij

ttK

ij

tttt dVRError

)(

)()(

Ktt V

K

i

ttK

i

tttt dVEDQError

Incremental solution for nonlinear response

problems


Weak form

- The use of a finite element model needs the definitions of a MIXED model with the following unknowns:

INCREMENTAL APPROACH

velocity

pressure

- For incompressible flows problems the velocity field is governed by continuity equation that is divergence velocity.

- The pressure field depends directly to velocity field, it is a Lagrange multiplying of continuity equation. [Saddle-point problem]

-Discretization element: fulfillment of inf-sup condition, the velocity approximation order has to be higher than pressure approximation order

BXA )()(

xfBx

xfA

0ˆ)( ,, dVvgvvv iVf

ijijjjii

Vfji dVpv 0~ˆ

,

FVVKVM )(

P

VV

ˆ

ˆ

FEM approach for incompressible fluid


Smart Materials Systems and Structures

Multiphysics

StructuralMechanics

ElectricalField

HeatTransfer

FluidDynamics

Composite materials

and delaminations

Projects for industry

FEM solutions for scientific and industrial

problems


Backward facing step with active flapHeat

Transfer StructuralMechanics

FluidDynamics

ElectricalField

Multiphysics

Active fluid-structure

interaction

Application:

Active flow control with a piezo actuator

L.Lampani, R.Grillo, P.Gaudenzi. Finite element models of

piezoelectric actuation for active flow control. Acta Astronautica

71 (2012), pp.129–138, doi:10.1016/j.actaastro.2011.07.026


•The near-wall region stretch out faster

then the outer region

•Non equilibrium situation between two

regions, the wall stress is not suitable

for adimensionalization

•The reattachment point is at 6.8 x/ht,

according with the universal

characteristic for which the

reattachment is at about 7 x/ht (step

W/ht ~ 1)

•Maximum velocity in the recirculation

zone until the 20% of the freestream

velocity

Fluid field solution validation on a backward facing step

Application:



Complete solution approach

Application:



Composite materials

and delaminations

Structural verification of VEGA Zefiro 9 solid booster

Composite multilayered structure model. Hydroproof test. Compression and

bending tests. Correlation with experimental results

► High stress state :

Non-linear analysis

Stiffness matrix update

► Composite macromechanical

failure test

First ply failure

Last ply failure

Max stress theory

Tsai-Hill theory

Tsai-Wu theory


Propagation of the delaminations in a composite

structure with the cohesive zone model (CZM)

technique.

Luca Lampani. Finite element analysis of delamination of a composite component

with the cohesive zone model technique. Engineering Computations (2011) Vol. 28

Iss: 1-2, pp.30 – 46, doi: 10.1108/02644401111097000

Composite materials

and delaminations


Propagation of the delaminations in a skirt of VEGA

motors under compressive loads

1.5m radius

Composite materials

and delaminations


The flexible bearing joint is a non-rigid connection between the motor case and the movable nozzle,

which then allows the deflection of the nozzle itself in any direction by a system of forces applied by two

actuators. The configuration of the flexible bearing joint aims to reproduce a spherical kinematism by

means of a flexible structure. For this reason it is composed in a laminated way and consists of a series

of layers of rubber and steel or composite with spherical section.

Flexible bearing joint of VEGA solid motors


Flexible bearing joint of VEGA solid motors


Risø (Danish National Laboratory) sensor/actuator prototype

Centro Piaggio (UniPisa) buckling sensor/actuator prototype

FE constitutive models of the Dielectric Elastomer Actuators (DEA)

Technological demonstrator of application for space:

CFRP boom with vibration control system DEA based

HeatTransfer Structural

Mechanics

FluidDynamics

ElectricalField

MultiphysicsElectro-mechanical

materials

Application:

Electroactive polymers

Luca Lampani and Paolo Gaudenzi. 3D finite element analyses of multilayer dielectric

elastomer actuators with metallic compliant electrodes for space application for structural

vibration control. Journal of Intelligent Material Systems and Structures, Vol. 21, Issue 6,

April 2010, pp.621-632, doi: 10.1177/1045389X10363507

http://images.google.it/imgres?imgurl=http://misilmeriblog.files.wordpress.com/2008/06/euro.jpg&imgrefurl=http://misilmeriblog.wordpress.com/2008/06/27/a-proposito-di-risparmio-per-i-consumatori/&usg=__edm-PmEd8AxbpRGNBlpS6cdt_t4=&h=354&w=354&sz=58&hl=it&start=1&um=1&itbs=1&tbnid=qALTiq2zXVGKaM:&tbnh=121&tbnw=121&prev=/images?q=euro&um=1&hl=it&sa=N&tbs=isch:1


Risø (Danish National Laboratory) sensor/actuator ESA-C-4/II prototype

Centro Piaggio (UniPisa) buckling sensor/actuator prototype

Application:



Breadbording activity:

Inflated rigidized CFRP boom

FE flexible model

(Nastran)

Multibody model

(ESA DCAP)

Control algorithm

(Simulink)

Application:



Comparison of implicit vs. explicit direct integration

methods. “Shear locking” problem in thin shell

elements for implicit schemes. “Hourglassing”

problem in thin shell elements for explicit

schemes.

Benchmark cases of pressurization,

deployment, wrinkling of folded and unfolded

structures made in thin membranes

L.Lampani, P.Gaudenzi. Numerical

simulation of the behaviour of inflatable

structures for space. Acta Astronautica 67

(2010) pp.362–368,

doi:10.1016/j.actaastro.2010.02.006


Structural analyses (FEM) for a satcom antenna system

mounted on high-speed trains (TGV) for broadband

communication.

Quasi-static (SOL101),

Modal with mass factor (SOL103),

Random load (SOL111)

Half-sine shock load (SOL112)

ANTENNA LHTA S0 Modal Shape n. 5

Projects for industry

AlphaSat Ka-Band Filter and Diplexer

Dimensional stability

finite element procedures for multiphysics analyses...

Documents