Simple Multi-body System Models of Bolted Connections to

Transcription

TRB AFB(20)2 Meeting on Road Side Safety Design
Multibody dynamics for analyzing
limit-states in structural engineering
B-1000 Brussels, Wednesday 5 November 2014
Simple Multi-body System Models of
Bolted Connections to
Consider all Relevant Nonlinearities of
Failure mechanisms
Detlef H.-J. F. Neuenhaus
post
spacer
guardrail
AFB20 2014
cover
plate
TRB AFB(20)2 Meeting on
Road Side Safety Design
Simple multi-body system
models of bolted connections to
Detlef Neuenhaus
consider all relevant nonlinearities of failure mechanisms
Detlef Neuenhaus
Contents
Introduction to Multi-Body Systems (MBS)
Used Strategy in MEPHISTO
Typecast Body Groups
Depiction of the demonstration example
MBS model of single fastener connection
Determining spring parameter
Outlook
Contents
2
Detlef Neuenhaus
Multi-body System Formalisms
Synthetic Method, based on
Analytic Method, based on
NEWTON / EULER’s equations
LAGRANGE’s equations (2nd kind) or
Euler-Langrange equations
• Principle of linear momentum
·
•
Principle of angular momentum
where
·
·
where
1,2, ⋯ , represents the th degree of freedom
: mass of the body
: acceleration of the center of mass
1,2, ⋯ ,
#
1
!
2
"
: total force acting on body
: moment of inertia
represents the th degree of freedom
" "
·
"
: total kinetic energy of the system
: total potential energy of the system
$" : generalized coordinates
: angular acceleration of the body
: angular velocity of the body
$" : generalized velocities
: total torque acting on body
Calculation of the equation of motion by synthesizing the
single parts of forces and moments.
+ : Very efficiently in case of large systems.
- : Kinematical constraints have to be described by
additional constraint equations
Calculation of the equation of motion by analyzing of the total
energy to generalized forces and displacements.
+ : It’s clear and transparent procedure.
- : Expensive differential process, in particular to many
degree of freedoms
Introduction to MBS
(base Formalisms)
3
Detlef Neuenhaus
Used Formalism in MEPHISTO
axis of a
virtual rotation
The JOURDAIN‘s principle of virtual power
(based on NEWTON-EULER‘s equations, but with dependency on velocities)
#
body
! % &' ' · d -. ()
d
&+
0
center
of mass
The differential equation of virtual power is:
#
!&
&
-.
/
&+
inertial
reference base
0
'
y
Notation in matrix-form:
&
0
&
0
&+
0
z
<
;
;
x
With the generalized coordinates $ of the system and the relationships
&
1 &$,
&+
5 0 &$
&$ 0
1 0 1
&
we get
3 &$,
1 $
2,
&$ 0 56
57
3 $
3 0 3 $
8
4,
10
total virtual power of all generalized
forces and moments
2
30
4
5
9
Introduction to MBS
(used Formalism)
0
⟹ 8$
9
4
Detlef Neuenhaus
Typecast Body-Group
body 4
Hinge-Beam –
Element 3D
YZ[ \]^
_X
`
;
Yef \g^
Yeh \g^
Yef \n^
Yeh \n^
Ya[ \]^
body 3
bcd
`
>? @
6jkg
1 2m ?
l
6jkn
1 2m ?
l
2? @
body 2
y
where
l : total length of the beam element
.
.
m ? 1
: divisional coefficient
A
body 1
x
z
=. 4
=A 4
=A '
=. '
Tyre –
Element 3D
longitudinal: O
lateral:
#
vertical:
P
longitudinal: Q
RS
lateral:
T
vertical:
1 0
0 1
0 0
0
0
T⁄cos O
0
T · tan O 0
0
tan O
1⁄cos O
T · tan O
0
0
0 0 0
W
0 0 0
W#
0 0 0
· Q WX
1
0
0
W
QW#
0 1⁄cos O
0
QWX
0
tan O
1
Coordinate system, unit vectors and
velocity vectors of the wheel
Typecast Body-Groups
5
Detlef Neuenhaus
Analysis of Road Restraint System
MBS model for the restraint system GS2
5
7
8
3
7
9
7
5
Rz, Lz
8
3
4
4
2
7
Ry, Lz
Rx, Ry
6
7
8
5
7
Ri : free rotation
Li : free translation
9
Rx, Ly 3
7
5
8
3
1
Rx, Rz 2
y
4
Lx,Ly,Lz
7 Rx,Ry,Rz,
Lx,Ly,Lz
5
3
4
Ry 1
4
2
x
z
1
2x4[m] segments of the MBS model for the GS2 restraint system with a post distance of 2.0[m]
MBS modelling of bolted connection
(demonstration example)
MBS-model of the
restrained systems
6
Detlef Neuenhaus
Demonstration example of MBS modelling of
bolted connection: post-spacer; rail-spacer
Guardrail System: GS2
(steel guardrail of the Round Robin
benchmark test example)
7
Detlef Neuenhaus
Post distance: 2.0[m]
8
Detlef Neuenhaus
Posts: C100x50x5
Guardrail-beam: A-profile
Spacer
9
Detlef Neuenhaus
Posts: C100x50x5
Guardrail-beam: A-profile
Spacer
One single bolt M16,5.8
(at rail with nut and cover plate
instead of a washer)
10
Detlef Neuenhaus
Springs for the bolt M16
Ultimate limit state analysis to define nonlinear springs
Bolt M16x40, 5.8 and slotted hole at the post and guardrail
The kinematic movements are separated,
so that for each kinetic property an internal force
element can act separately
Nonlinear spring with hysteretical characteristic for
the shear between the post and spacer and the spacer
and guardrail.
post
spacer
guardrail
Syz-shear
cover
plate
Syz-shear
(ultimate limit state analysis)
11
Detlef Neuenhaus
post
Nonlinear spring with hysteretical characteristic for
the tensile bolt load between the post and spacer and
the spacer and guardrail.
Sx-tensile
spacer
guardrail
Syz-shear
cover
plate
Syz-shear
Sx-tensile
12
Detlef Neuenhaus
post
Linear spring for the vertical slip of the slotted hole
(max 50[mm]) between the post and spacer
and the horizontal slip of the slotted hole (max.64[mm])
between the guardrail and the spacer.
Sx-tensile
spacer
guardrail
Syz-shear
cover
plate
Sy-slot
Syz-shear
Sx-tensile
Sx-slot
13
Detlef Neuenhaus
Determining the spring parameters
To capture the failure state close to reality, the characteristic
values have to be adjust:
The relevant material data can be taken from steel standards such as EN 10025,
or if available, from the steel producer‘s factory production control;
Resistance calculations are carried out according to Eurocode design rules;
Neglecting partial safety factors (accidental loads);
The resistances and the elastic limits could be increased by the factor 1.1
(constructions are able to resist higher loads as defined by ultimate limit state,
if it is excited by a suddenly applied nonperiodic excitation);
(resistances)
14
Detlef Neuenhaus
Spring characteristics
Spring characteristics for bolt M16, 5.8
Lyz7_1M16_5-8.hys
(7) post: hole slot of 50 [mm]
Ly7_1M16_l50.lin
(4) rail: hole slot of 64 [mm]
90
Lx7_1M16_5-8_sp.hys
Lyz4_1M16_5-8.hys
80
Lz4_1M16_l64.lin
Lx4_1M16_5-8_sp.hys
spring force F [kN]
70
60
50
40
30
20
10
0
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
spring-strain s [m]
Shearing:
Hole bearing:
Tension:
Punching shear:
Typ:
nS =
(TH M16x40) fub =
γM2 =
A=
AS =
d=
dm =
αv =
(post/spacer | rail/spacer) d0,ǁ =
(post/spacer | rail/spacer) d0,⊥=
e1 / e2 =
(spacer) e1 / e2 =
p1 / p2 =
min{2.8∙e2/d0,⊥;2.5} = k1 =
min{e1/(3∙d0,ǁ ); fub/ fu;1} = αb =
k2 =
(spacer | cover plate) tp =
(post | guardrail) fu =
(spacer) fu =
(post | guardrail) t =
Post
1M16
1
728
1.25
201
157
16
25
0.6
50 / 20.7
17 / 20.7
110 / 50
100 / 50
0/0
2.5
1.0
0.9
2.98
432
478
4.98
Guardrail
1M16
1
728
1.25
201
157
16
25
0.6
64 / 17
19.5 / 17
158 / 235
60 / 50
0/0
2.5
1.0
0.9
5.00
387
478
3.03
Fv,Rd = nS αv 1.1∙fub A / γM2 =
77284.99
77284.99 [N]
Fb,Rd = nS k1 αb 1.1∙fu d t / γM2 =
50140.29
50140.29 [N]
Ft,Rd = nS k2 1.1∙fub AS / γM2 =
90522.43
90522.43 [N]
Bp,Rd = nS 0.6 π dm tp 1.1∙fu / γM2 =
59956.19
81446.20 [N]
(characteristics)
5.8
[-]
[N/mm^2]
[-]
[mm^2]
[mm^2]
[mm]
[mm]
[-]
[mm]
[mm]
[mm]
[mm]
[mm]
[-]
[-]
[-]
[mm]
[N/mm^2]
[N/mm^2]
[mm]
15
Detlef
Post
9 Neuenhaus
Post 10
Simple MBS model of
bolted connection in use
Post 11
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Detlef
Post
9 Neuenhaus
Post 11
Post 10
Post 12
Copyright © Neuenhaus Engineering 2014
Detlef Neuenhaus
-
MultiBody dynamics for analysing LImit states in Structural Engineering
GS2
Test TB11 – Level N2
(900 [kg] – 100 [km/h] – 20 [°])
lateral front
lateral back
Test item took place on
the 28th June 2007
0,140 [sec]
GS2
Test TB11 – Level N2
(900 [kg] – 100 [km/h] – 20 [°])
top view
Test item took place on
the 28th June 2007
0,280 [sec]
Detlef Neuenhaus
Comparison between test and simulation results
Wp
(m)
Diff
0,34
0,44
0,64
0,86
±0.16
1.04
±0.21
1,02
±0.24
0,87
±0.20
0,71
±0.15
0,62
0,45
0,36
0,34
ASI
THIV
0,63
18
(0.6 … 0.8)
(20 … 26)
(km/h)
38
Detlef Neuenhaus
Outlook
Only the application of simulation techniques allows the important issue
of changing parameters.
The use of MBS where the viscoelastic and elastic-plastic characteristics are
defined directly by internal force elements, is the easiest and quickest way to
analyze modifications of road restraint systems.
Replacing full-scale impact tests by means of computational simulations,
reduce the costs for classifying and certifying a VRS
An easy manageable and still flexible classification of VRS can only be achieved
by tolerance ranges, which are well defined in the EN 1317. Drawback is,
sometimes a VRS got by coincidence no certification and unfortunately also vice
versa.
It is for this reason that numerical simulations shall be also prescribed to
analyze the effects of the tolerance ranges and to isolate better the risks.
Statistical methods, e.g. DOE, could help to localize the reason of possible
unexpected results. In combination with multi-body CAE approaches this
lead to efficiently robustness design of VRS.
Outlook
39
Detlef Neuenhaus
Thank you very much
for your attention
Simple Multi-body System Models of
Bolted Connections to
Consider all Relevant Nonlinearities of
Failure mechanisms
40

Simple Multi-body System Models of Bolted Connections to

Transcription

Similar documents

News Clipping February 1961

Rochester Flyer - Tyler Relph Basketball

76-020 USAF 76-0020 F-15A c/n 199/A172 Built 1976 by McDonnell

Airman Second Class Elton L. Blanchard

Welcome to Los Angeles AFB South Bay Association of Chambers

Eavesdropping Protection systems

Connecticut State Teachers` Retirement Board

Ramon E. Nugent, P.E. Acentech Inc.

Connecticut State Teachers` Retirement Board

Spring 2014 - Safeside Association