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Methodology and Tools for Virtual Prototyping:

Finite Element Analysis (Structural, Thermal,

Mechanical, Coupled)

Nastran/Marc

Daniele Catelani

Senior Project Manager MSC Software

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FEM Structure representation

• Real behavior of structures is

extremely complex

• Mathematical Representation has

to take into account:

– Geometry

– Structure charachteristic

– Material

– Constraints

– Load

– Analysis to perform

– Output to get

– ...

• Some representation is needed to

allow study

?

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FINITE ELEMENTS

● A finite element model of a component or system is a

mathematical representation of it using small, but finite

sized, simply shaped, connected entities ( i.e. line, surface,

solid) called finite elements.

Component (Geometric Model) Tetrahedral Mesh of Geometry

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FINITE ELEMENTS

● Finite elements come in different shapes and forms

● Linear and parabolic elements

Bar Tri

Tet HexWedge

Quad

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• Displacement method

• Every subdomain is represented by stiffness matrix, depending on

element type and characteristic

• For each element the following equation is evaluated

{ P }e = [ k ]e { u }e

{ P }e = applied external forces

[ k ]e = element stiffness matrix, in which the term kij represents force on the j dof when i dof disp = 1.0 ( kij= kji )

{ u }e = disp vector of element nodes

• STRUCURE Σ{ P }e = Σ[ k ]e Σ{ u }e { P } = [ k ] { u }

FEM introduction

ASSEMBLY

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FEM introductionHow to choose the structural element

• Depending on geometry

– Geometrical dimension ratio

– 1D Lateral Dimensions are negligible wrt Longitudinal

– 2D two dimensions are greater

– 3D No dimension is greatest

Undeformed configuration

}

Modello realizzato con elementi tridimensionali

Solu

tio

n 1

Solu

tio

n 2

Analysis goal influences element choice

• 1D element; properties have to simulate right behavior

• Lumped mass for wheels

• Lumped mass for representing inertia distribution

Simplified model

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FEM introduction

element library MSC Nastran

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FEM introductionMaterial

• Elastic or non elastic

– Plastic deformation = residual deformation

– Temperature effects

– Deformation ratio effect

– Hardening effect

– …

e

s T2

T1

e2

e3

Superficie di

snervamento

iniziale

Superficie di snervamento

dopo la deformazione plastica

O

L’incremento di carico

aumenta le dimensioni

della superficie di

snervamento

e1

e2

e3

O

e1

O’

Superficie di

snervamento

iniziale

Superficie di snervamento

dopo la deformazione plastica

L’incremento di carico sposta la

superficie di snervamento senza

aumentarne le dimensioni

INCRUDIMENTO ISOTROPOINCRUDIMENTO CINEMATICO

e

s

e

t (time)

e0

t1

Creep Recovery

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• Elasto-Plastic : (MATEP)

• Temperature dependence : (MATORT), (MATTEMP)

• Failure : (MATF)

– ( Hill, Tsai-Hu, Hoffmann, Puck, Hashin, Hashin Tape and Fabric,...)

– Progressive failure analysis

• Gasket : Nonlinear elastic and elasto-plastic (MATG)

• Cohesive : (MCOHE)

• Orthotropic Nonlinear Elasticity

(MATORT/MATSORT)

• Anisotropic Plasticity (MATEP with ‘aniso’ option –

Hill and Barlat’s models)

FEM introductionMaterial library MSC Nastran

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• Pressure dependent plasticity (MATEP - Mohr-Coulomb and Drucker-Prager)

• Shape memory (MATSMA)

• Other: (MATEP ,MATVE,MATVP)

• Creep (MATVP - Maxwell and Kevin models)

• Elastomers (MATHE - Mooney, Ogden, Arruda-Boyce

and Gent models)

SOL 400 Nonlinear Material Implementation Marc material models in the standard Nastran elements (Cont.)

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Tipi di carichi Schede di input MD NASTRAN Forze applicate direttamente ai nodi Momenti applicati direttamente ai nodi

FORCE, FORCE1, FORCE2 MOMENT, MOMENT1, MOMENT2

Carichi sugli elementi 1D Carichi di pressione e trazione su elementi 2D e 3D

PLOAD1 PLOAD, PLOAD2, PLOAD4, PLOADX

Carichi di accelerazione traslazionale (Gravità,..) Carichi derivanti da diversi campi di accelerazione Carichi dovuti a force centripete e/o accelerazioni angolari

GRAV ACCEL, ACCEL1 RFORCE

Carichi termici TEMP, TEMPD, TEMPP1, TEMPRB (+ Coefficiente di espansione termica)

Deformazioni assiali su elementi 1D DEFORM

Spostamenti imposti ai nodi (cedimenti vincolari..) SPC, SPCD

Combinazione lineare dei carichi LOAD

FEM introductionLoads /Constraints/Contacts

Touching Contact Permanent- Glue Contact

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FEM introductionThermal Case with ‘Permanent Glued’

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• Linear Static

• Modal

• Buckling

• Frequency response

• Transient response

FEM analysis

MODAL ANALYSIS

Detailed FEM

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FEM analysis

• Damped modes

• Random

• Response Shock Spectrum

• Aeroelasticity (Static, Flutter, Transient)

• Nonlinear Static

• Nonlinear transient

• Strucural optimization (Properties, Material, Shape, Topology, Topometry, Topography)

• Superelements

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WORKFLOW IN Patran

● The Main Menu

2 - Import Geometry

1 - Select Analysis Code

2 - or Build

Geometry3 – Create

Analysis Model

5 - Evaluate and Publish

Analysis Results

4 - Perform the

Analysis

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