BEAM 161(Explicit 3-D Beam)

BEAM161

Explicit 3-D Beam

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BEAM161 Element Description

BEAM161 has several characteristics:

• It is incrementally objective (rigid body rotations do not generate strains), allowing for the treatmentof finite strains that occur in many practical applications.

• It is simple for computational efficiency and robustness.

• It is compatible with the brick elements.

• It includes finite transverse shear strains. However, the added computations needed to retain this straincomponent, compared to those for the assumption of no transverse shear strain, are significant.

The Belytschko beam element formulation (KEYOPT(1) = 2, 4, 5) is part of a family of structural finite elementsthat use a "co-rotational technique" for treating large rotation.

This element is used in explicit dynamic analyses only. Refer to the LS-DYNA Theoretical Manual for moreinformation.

Figure 1: BEAM161 Geometry

3

J

K

I

s

r

t

2

1

973Release 12.0 - © 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

BEAM161 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1: BEAM161

Geometry (p. 973). Node K determines the initial orientation of the cross section.

The element is defined by nodes I and J in the global coordinate system. Node K defines a plane (with I andJ) containing the element s-axis. The element r-axis runs parallel to the centroidal line of the element andthrough nodes I and J. Node K is always required to define the element axis system and it must not be co-linear with nodes I and J. The location of node K is used only to initially orient the element. (For informationabout orientation nodes and beam meshing, see Meshing Your Solid Model in the Modeling and Meshing

Guide.)

Use the EDLOAD command to apply nodal loads and other load types described below. For detailed inform-ation on how to apply loads in an explicit dynamic analysis, see the ANSYS LS-DYNA User's Guide.

Pressures can be input as surface loads on the element faces as shown by the circled numbers in Fig-

ure 1: BEAM161 Geometry (p. 973). Note, however, that pressure is actually a traction load applied to the center

line of the element. Use the EDLOAD command to apply the pressure load, and input the pressure as a forceper unit length value. Positive normal pressures act into the element.

Base accelerations and angular velocities in the x, y, and z directions can be applied at the nodes using theEDLOAD command. To apply these loads, you need to first select the nodes and create a component. Theload is then applied to that component.

You can also use the EDLOAD command to apply loads (displacements, forces, etc.) on rigid bodies.

You can choose from the following materials when working with BEAM161, with the restrictions as noted:

• Isotropic Elastic

• Bilinear Kinematic (Except KEYOPT(1) = 2)

• Plastic Kinematic (Except KEYOPT(1) = 2)

• Viscoelastic (KEYOPT(1) = 1 only)

• Power Law Plasticity (KEYOPT(1) = 1 only)

• Piecewise Linear Plasticity (KEYOPT(1) = 1 only)

KEYOPT(1) allows you to specify one of four element formulations for BEAM161 (see "BEAM161 Input Sum-

mary" (p. 977)). For details of real constants to be specified for each element formulation, see Table 1: BEAM161

Real Constants (p. 978).

KEYOPT(2) is valid only with rectangular element formulations (KEYOPT(1) = 0, 1, 4).

The following illustrations show the valid standard beam cross sections when KEYOPT(4)>0, and KEYOPT(5)= 2 (standard beam cross section).

Release 12.0 - © 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.974

BEAM161

Figure 2: Standard Beam Cross Sections

tw

s

t

tw

w

stw

3 4 5

1

2

2 3 4

9

6

7

8

1 5

w = flange widthtf = flange thicknessd = depthtw = web thicknesssref = location of reference surface normal to s, Hughes-Liu beam onlytref = location of reference surface normal to t, Hughes-Liu beam only

Type 1: W-section Type 2: C-section

1 2 3

4

5

6

7 8 9

s

123

4

5

6

7 8 9

Type 4: T-sectionType 3: Angle section

t

tf

d d

w

tf

t

tf

s

twd

w

d

t

w

tf



BEAM161

Figure 3: Standard Beam Cross Sections (continued)

t

Type 5: Rectangular tubing

1 2 3

4 5

6 7 8

Type 6: Z-section

Type 7: Trapezoidal section

1 2 3

4 5 6

7 8 9

tw

tf

s

w

d

t

d

w

tf

tw

1 2 3

4

5

6

7 8 9

d

w

tw

KEYOPT(5) is not valid when KEYOPT(1) = 2.

A summary of the element input is given in "BEAM161 Input Summary" (p. 977). Additional information aboutreal constants for this element is provided in Table 1: BEAM161 Real Constants (p. 978). For more informationabout this element, see the ANSYS LS-DYNA User's Guide.


BEAM161

BEAM161 Input Summary

NodesI, J, K (K is the orientation node)

Degrees of FreedomUX, UY, UZ, VX, VY, VZ, AX, AY, AZ, ROTX, ROTY, ROTZ

Note

For explicit dynamics analyses, V(X, Y, Z) refers to nodal velocity, and A(X, Y, Z) refers tonodal acceleration. Although V(X, Y, Z) and A(X, Y, Z) appear as DOFs, they are not actuallyphysical DOFs. However, these quantities are computed as DOF solutions and stored for post-processing.

Real ConstantsSee Table 1: BEAM161 Real Constants (p. 978) for a description of the real constants.

Material Properties

EX, NUXY, DENS, DAMP (MP command)RIGID (KEYOPT(1) = 1,2) (EDMP command)BKIN, EVISC, PLAW (TB command; see Material Models in the ANSYS LS-DYNA User's Guide)

Surface Loads

Pressure -- face 1 (I-J) (+r tangential direction), face 2 (I-J) (-s normal direction), face 3 (I) (-t normal direction)

Body LoadsNone

Special FeaturesThis element supports all nonlinear features allowed for an explicit dynamic analysis.

KEYOPT(1)Element formulation:

0, 1 -- Hughes-Liu with cross section integration (default)

2 -- Belytschko-Schwer resultant beam (resultant)

4 -- Belytschko-Schwer full cross section integration

5 -- Belytschko-Schwer circular beam with cross section integration

KEYOPT(2)Quadrature rule:

1 -- One integration point

0, 2 -- 2 x 2 Gauss quadrature (default)



BEAM161

3 -- 3 x 3 Gauss quadrature

4 -- 3 x 3 Lobatto quadrature

5 -- 4 x 4 Gauss quadrature

Note

KEYOPT(2) is valid only with rectangular element formulations (KEYOPT(1) = 0, 1, 4).

KEYOPT(4)Integration rule for section:

0 -- Standard integration option

n -- User-defined integration rule ID (valid range: 1 to 9999)

KEYOPT(5)Cross section type:

0 -- Rectangular cross section

1 -- Circular cross section

2 -- Arbitrary cross section (user defined integration rule) or standard beam cross section, if KEYOPT (4)> 0.

Table 1 BEAM161 Real Constants

Use if...DescriptionNameNo.

KEYOPT (1) = 0,1, 4, or 5Shear factor.SHRF1

Default = 1.0

Recommended for rectangular sections= 5/6.

KEYOPT (1) = 0, 1, or 4

KEYOPT (5) = 0 or 2

Beam thickness in s direction at node1;

if KEYOPT (5) = 2, then use for arbitrarycross section only.

TS12

KEYOPT (1) = 0, 1, or 4

KEYOPT (5) = 0 or 2

Beam thickness in s direction at node2;


TS23


BEAM161


KEYOPT (1) = 0, 1, or 4Beam thickness in t direction at node 1;TT14

KEYOPT (5) = 0 or 2if KEYOPT (5) = 2, then use for arbitrarycross section only.

KEYOPT (1) = 0, 1, or 4

KEYOPT (5) = 0 or 2

Beam thickness in t direction at node 2;


TT25

KEYOPT (1) = 0, 1, or 5

KEYOPT (4) = 0

Beam outer diameter at node1[1 (p. 981)]

DS12

KEYOPT (5) = 1

KEYOPT (1) = 0, 1, or 5

KEYOPT (4) = 0

Beam outer diameter at node2[1 (p. 981)]

DS23

KEYOPT (5) = 1

KEYOPT (1) = 0, 1, or 5

KEYOPT (4) = 0

Beam inner diameter at node1[1 (p. 981)]

DT14

KEYOPT (5) = 1

KEYOPT (1) = 0, 1, or 5

KEYOPT (4) = 0

Beam inner diameter at node2[1 (p. 981)]

DT25

KEYOPT (5) = 1

KEYOPT (1) = 0, 1, 4, or 5

KEYOPT (4) = 0

Location of reference surface normal tos-axis

= 1 side at s = 1

NSLOC6

= 0 center

= -1 side at s = -1

KEYOPT (1) = 0, 1, 4, or 5

KEYOPT (4) = 0

Location of reference surface normal tot-axis

= 1 side at t = 1

NTLOC7

= 0 center

= -1 side at t = -1

KEYOPT (4) = 0

KEYOPT (1) = 2

Cross sectional area

See Figure 4: Properties of Beam Cross

Sections for Several Common Cross Sec-

tions (p. 982)

A8



BEAM161


KEYOPT (4) = 0Moment of inertia about s-axisISS9

KEYOPT (1) = 2See Figure 4: Properties of Beam Cross


tions (p. 982)

KEYOPT (4) = 0

KEYOPT (1) = 2

Moment of inertia about t-axis



tions (p. 982)

ITT10

KEYOPT (4) = 0

KEYOPT (1) = 2

Polar moment of inertia



tions (p. 982)

IRR11

KEYOPT (4) = 0

KEYOPT (1) = 2

Shear area



tions (p. 982)

SA12

KEYOPT (4) > 0 and KEYOPT(5) = 2

Number of integration points

See Figure 6: Definition of Integration

Points for User Defined Integration

Rule (p. 984)

NIP13

KEYOPT (4) > 0 and KEYOPT(5) = 2

Relative area of cross section; that is,the actual cross-sectional area divided

RA14

by the area defined by the product ofthe specified thickness in the s directionand the thickness in the t direction.

See Figure 5: Definition of Relative Area

for User Defined Integration Rule (p. 984).

KEYOPT (4) > 0[2 (p. 982)]and KEYOPT (5) = 2 (stand-ard cross section only)

Standard cross section type.

Note

If this type is nonzero, thenNIP and RA should be zero.

ICST15

Cross section types are:

1 - W-section2 - C-section3 - Angle section4 - T-section5 - Rectangular tubing6 - Z-section


BEAM161


7 - Trapezoidal section

See Figure 2: Standard Beam Cross Sec-

tions (p. 975), Figure 3: Standard Beam

Cross Sections (continued) (p. 976).

ICST > 0, and NIP = RA = 0Flange widthW16

ICST > 0, and NIP = RA = 0Flange thicknessTF17

ICST > 0, and NIP = RA = 0DepthD18

ICST > 0, and NIP = RA = 0Web thicknessTW19

ICST > 0, and NIP = RA = 0Location of reference surface normal tos

SREF20

Note

If KEYOPT (1) = 1 only

ICST > 0, and NIP = RA = 0Location of reference surface normal tot

TREF21

Note

If KEYOPT (1) = 1 only

KEYOPT (4) > 0

KEYOPT (5) = 2, arbitrarycross section only

s coordinate of integration point

i = 1, NIP (NIP = 20 max)[3 (p. 982)]

S(i)22, 25,28, ...79

NIP > 0, RA > 0, ICST = 0

KEYOPT (4) > 0


t coordinate of integration point

i = 1, NIP (NIP = 20 max)[3 (p. 982)]

T(i)23, 26,29, ...80

NIP > 0, RA > 0, ICST = 0

KEYOPT (4) > 0


Weighting factor; that is, the area asso-ciated with the integration point dividedby the actual cross-section area.

i = 1, NIP (NIP = 20 max)[3 (p. 982)]

WF(i)24, 27,30, ...81

NIP > 0, RA > 0, ICST = 0See Figure 4: Properties of Beam Cross


tions (p. 982)

1. DS1, DS2, DT1, and DT2 are used only if KEYOPT (5) = 1. If KEYOPT (5) = 0 or 2, then use TS1, TS2, TT1,and TT2.



BEAM161

2. For KEYOPT (5) = 2, standard cross-section type, the integration point ID (KEYOPT (4) > 0) is not usedsince NIP = RA = 0. However, you must provide this input in any case.

3. Specify S(i), T(i), and WF(i) for each integration point. For example, for 20 integration points, specifyS(1), T(1), WF(1), S(2), T(2), WF(2), ... S(20), T(20), WF(20).

Figure 4: Properties of Beam Cross Sections for Several Common Cross Sections

s

t

b

tw

h

tf

s

t

r

I Ir

Jr

f f

A r

tt ss

tt ss

= =

=

= =

=

π

π

π

4

4

2

2

2

10

9

s

t

r h

I I r h

J r h

f f

A rh

tt ss

tt ss

= ≅

≅= =

≅

π

π

π

3

32

2

2

Ih

ht bt

Ib

bt ht

Jb h

tt w f

ss f w

≅

+

≅

+

≅

2

2

2 2

63

63

2

( )

( )

(tt t

bt ht

fA

b t t

fA

h t t

A bt ht

w f

w f

ttw f

ssf w

f w

)

( )

[ ( ) ]

[ ( ) ]

(

+

=+

=+

= +

2

2

2 ))


BEAM161

s

th

b

Ibh

Ib h

Jb

h

b

h

tt

ss

=

=

≅ −

−

3

3

4

4

12

12

1

30 21 1

12.

= =

=

hb

f f

A bh

tt ss

3

6

5

Shear area = =A

fAµ



BEAM161

Figure 5: Definition of Relative Area for User Defined Integration Rule

t

s

St

tt

Relative area = A

St tttt = input as TT1 or TT2 on R commandSt = input as TS1 or TS2 on R command

Figure 6: Definition of Integration Points for User Defined Integration Rule

A1 A2 A3 A4A5

A6

A7

A8

A9A10A11A12

s

t

BEAM161 Output Data

To store output data for this element, you first need to specify the number of integration points for whichyou want output data. Use the EDINT,,BEAMIP command during the solution phase of your analysis to


BEAM161

specify the number of integration points. By default, output is written for 4 integration points. For the res-ultant beam formulation (KEYOPT(1) = 2), there is no stress output (regardless of the BEAMIP setting). Ifyou set BEAMIP = 0, no stress output is written for any of the beam elements. In this case, the beams willnot appear in any POST1 plots because the program assumes they are failed elements.

To display the data for BEAM161, you must use the ETABLE command. Then, you can use the PRETAB

command to print the output data. The RSYS command has no effect when postprocessing output for thiselement.

The following items are available on the results file.

Table 2 BEAM161 Element Output Definitions

DefinitionName

StressesS (r, rs, rt)

Equivalent plastic strainEPEQ

Axial strainEPTO

Member force in the element coordinate system, r directionMFORr

Out-of-plane (s, t) shearN (s, t )

Element (s, t) momentsM (s, t )

Torsional resultantTORQ

For each of these output data, one set of values, given at the centroid, is output for the entire beam.

Table 3: BEAM161 Item and Sequence Numbers (p. 985) lists output available through the ETABLE and ESOL

commands using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Ana-

lysis Guide and The Item and Sequence Number Table (p. 9) in this manual for more information. The followingnotation is used in Table 3: BEAM161 Item and Sequence Numbers (p. 985):

Nameoutput quantity as defined in the Table 2: BEAM161 Element Output Definitions (p. 985)

Itempredetermined Item label for ETABLE or ESOL command

Esequence number for single-valued or constant element data

1st IPsequence number for the first integration point

nth IPsequence number for the nth integration point as defined by the EDINT command.

Table 3 BEAM161 Item and Sequence Numbers

ETABLE and ESOL Command InputOutput Quant-

ity Name nth IP1st IPEItem

--1SMISCMFORr

--2SMISCNs

--3SMISCNt



BEAM161

ETABLE and ESOL Command InputOutput Quant-

ity Name nth IP1st IPEItem

--4SMISCMs

--5SMISCMt

--6SMISCTORQ

5 x (n-1) +11-LSSr

5 x (n-1) +22-LSSrs

5 x (n-1) +33-LSSrt

5 x (n-1) +44-LSEPEQ

5 x (n-1) +55-LSEPTO

1. In this table, n refers to the current integration point for which you want output data.

BEAM161 Assumptions and Restrictions

• The beam must not have a zero length.

• The beam can have any open or single-cell closed cross-sectional shape for which the area and momentsof inertia are nonzero.

• Warping torsion is assumed negligible and the warping moment of inertia is not used in the stiffnesscomputation.

• Warping of the cross section is unconstrained and is the same for all cross-sections; therefore, the tor-sional rotation of the cross-section is assumed to vary linearly along the length. However, warping isnot applicable to the resultant beam formulation (KEYOPT(1) = 2).

BEAM161 Product Restrictions

There are no product-specific restrictions for this element.


BEAM161

Documents

BEAM 161(Explicit 3-D Beam)