/PROP/TYPE13 (SPR

Block Format Keyword

/PROP/TYPE13 - Beam Type Spring Property Set

Description

This beam type spring property works as a beam element with six independent modes of deformation. This spring accounts for non-linear stiffness, damping and different unloading. Deformation, force and energy-based failure criteria are available.

prop_type13

Format

(1)	(3)	(5)	(6)	(7)	(8)	(9)	(10)
/PROP/TYPE13/prop_ID/unit_ID or /PROP/SPR_BEAM/prop_ID/unit_ID
prop_title
Mass	Inertia	skew_ID	sens_ID	Isflag	Ifail	Ileng	Ifail2

Tension/Compression

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K1		C1		A1	B1	D1
fct_ID11	H1	fct_ID21	fct_ID31	fct_ID41
F1		E1		Ascale1	Hscale1

Shear XY

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K2		C2		A2	B2	D2
fct_ID12	H2	fct_ID22	fct_ID32	fct_ID42
F2		E2		Ascale2	Hscale2

Shear XZ

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K3		C3		A3	B3	D3
fct_ID13	H3	fct_ID23	fct_ID33	fct_ID43
F3		E3		Ascale3	Hscale3

Torsion

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K4		C4		A4	B4	D4
fct_ID14	H4	fct_ID24	fct_ID34	fct_ID44
F4		E4		Ascale4	Hscale4

Bending Y

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K5		C5		A5	B5	D5
fct_ID15	H5	fct_ID25	fct_ID35	fct_ID45
F5		E5		Ascale5	Hscale5

Bending Z

(1)	(2)	(3)	(4)	(5)	(7)	(9)
K6		C6		A6	B6	D6
fct_ID16	H6	fct_ID26	fct_ID36	fct_ID46
F6		E6		Ascale6	Hscale6

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)

c1		n1
c2		n2
c3		n3
c4		n4
c5		n5
c6		n6

Field	Contents	SI Unit Example
prop_ID	Property identifier (Integer, maximum 10 digits)
unit_ID	Optional unit identifier (Integer, maximum 10 digits)
prop_title	Property title (Character, maximum 100 characters)
Mass	Spring mass (Real)
Inertia	Spring inertia (Real)
skew_ID	Skew system identifier (Integer)
sens_ID	Sensor identifier (Integer)
Isflag	Sensor flag (Comment 10) (Integer) =0: spring element activated =1: spring element deactivated =2: spring element activated or deactivated
Ifail	Failure criteria (Comment 8) (Integer) = 0: uni-directional criteria = 1: multi-directional criteria
Ileng	Input per unit length flag (Integer) = 0: the force in the spring is computed as previously detailed formula (Comment 2) = 1: all input are per unit length (Comment 3)
Ifail2	Failure model flag Default = 0 (Integer) = 0: old displacement criteria = 1: new displacement criteria = 2: force criteria = 3: internal energy criteria
K1	Stiffness for tension (Real)
C1	Damping for tension/compression (Real)
A1	Coefficient for strain rate effect in tension/compression Default = 1.0 (Real)
B1	Coefficient for strain rate effect in tension/compression (Real)
D1	Strain coefficients for elongation velocity for tension/compression Default = 1.0 (Real)
E1	Coefficient for strain rate effect in tension/compression (Real)
Ascale1	Abscissa scale factor for in tension/compression (fct_ID11 and fct_ID31) (Real)
Hscale1	Coefficient for fct_ID41 in tension/compression Default = 1 (Real)
fct_ID11	Function identifier defining in tension/compression If H1=4: Function identifier defining upper yield curve (Integer) = 0: for linear spring
H1	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID21	Function identifier defining in tension/compression (Integer)
fct_ID31	Function used only for unloading in tension/compression If H1=4: Function identifier defining lower yield curve If H1=5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID41	Function identifier defining in tension/compression (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F1	Scale factor for in tension/compression (Real)
K2	Stiffness for shear XY (Real)
C2	Damping for shear XY (Real)
A2	Coefficient for strain rate effect in shear XY Default = 1.0 (Real)
B2	Logarithmic coefficient for strain rate effect in shear XY Default = 1.0 (Real)
D2	Scale coefficients for shear velocity Default = 1.0 (Real)
Ascale2	Abscissa scale factor for in shear XY (fct_ID12 and fct_ID32) (Real)
Hscale2	Coefficient for fct_ID42 in shear XY Default = 1 (Real)
fct_ID12	Function identifier defining in shear XY If H2=4: Function identifier defining upper yield curve (Integer) = 0: linear spring
H2	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID22	Function identifier defining in shear XY (Integer)
fct_ID32	Function used only for unloading in shear XY If H2 =4: Function identifier defining lower yield curve If H2 =5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID42	Function identifier defining in shear XY (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F2	Scale factor for in shear XY (Real)
E2	Coefficient for strain rate effect in shear XY (Real)
K3	Stiffness for shear XZ (Real)
C3	Damping for shear XZ (Real)
A3	Coefficient for strain rate effect in shear XZ Default = 1.0 (Real)
B3	Logarithmic coefficient for strain rate effect in shear XZ Default = 1.0 (Real)
D3	Scale coefficients for shear velocity Default = 1.0 (Real)
Ascale3	Abscissa scale factor for in shear XZ (fct_ID13 and fct_ID33) (Real)
Hscale3	Coefficient for fct_ID43 in shear XZ Default = 1 (Real)
fct_ID13	Function identifier defining in shear XZ If H3=4: Function identifier defining upper yield curve (Integer) = 0: linear spring
H3	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID23	Function identifier defining in shear XZ (Integer)
fct_ID33	Function used only for unloading in shear XZ If H3=4: Function identifier defining lower yield curve If H3=5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID43	Function identifier defining in shear XZ (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F3	Scale factor for in shear XZ (Real)
E3	Coefficient for strain rate effect in shear XZ (Real)
K4	Stiffness for torsion (Real)
C4	Damping for torsion (Real)
A4	Coefficient for strain rate effect in torsion (homogeneous to a moment) Default = 1.0 (Real)
B4	Logarithmic coefficient for strain rate effect in torsion (Real)
D4	Scale coefficients for torsion velocity Default = 1.0 (Real)
Ascale4	Abscissa scale factor for in torsion (fct_ID14 and fct_ID34) (Real)
Hscale4	Coefficient for fct_ID44 in torsion Default = 1 (Real)
fct_ID14	Function identifier defining in torsion If H4=4: Function identifier defining upper yield curve (Integer) = 0: linear spring
H4	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID24	Function identifier defining in torsion (Integer)
fct_ID34	Function used only for unloading in torsion If H4=4: Function identifier defining lower yield curve If H4=5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID44	Function identifier defining in torsion (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F4	Scale factor for in torsion (Real)
E4	Coefficient for strain rate effect in torsion (Real)
K5	Stiffness for bending Y (Real)
C5	Damping for bending Y (Real)
A5	Coefficient for strain rate effect in bending Y Default = 1.0 (Real)
B5	Logarithmic coefficient for strain rate effect in bending Y Default = 1.0 (Real)
D5	Scale coefficients for bending velocity Default = 1.0 (Real)
Ascale5	Abscissa scale factor for in bending Y (fct_ID15 and fct_ID35) (Real)
Hscale5	Coefficient for fct_ID45 in bending Y Default = 1 (Real)
fct_ID15	Function identifier defining in bending Y If H5=4: Function identifier defining upper yield curve (Integer) = 0: linear spring
H5	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID25	Function identifier defining in bending Y (Integer)
fct_ID35	Function used only for unloading in bending Y If H5=4: Function identifier defining lower yield curve If H5=5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID45	Function identifier defining in bending Y (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F5	Scale factor for in bending Y (Real)
E5	Coefficient for strain rate effect in bending Y (Real)
K6	Stiffness for bending Z (Real)
C6	Damping for bending Z (Real)
A6	Coefficient for strain rate effect in bending Z Default = 1.0 (Real)
B6	Logarithmic coefficient for strain rate effect in bending Z Default = 1.0 (Real)
D6	Scale coefficients for bending velocity Default = 1.0 (Real)
Ascale6	Abscissa scale factor for (fct_ID16 and fct_ID36) (Real)
Hscale6	Coefficient for fct_ID46 in bending Z Default = 1 (Real)
fct_ID16	Function identifier defining in bending Z If H6=4: Function identifier defining upper yield curve (Integer) = 0: linear spring
H6	Hardening flag (Integer) = 0: Nonlinear elastic spring = 1: Nonlinear elasto-plastic spring = 2: Nonlinear elasto-plastic spring with decoupled hardening in tension and compression = 4: Nonlinear elastic plastic spring “kinematic” hardening = 5: Nonlinear elasto-plastic spring with nonlinear unloading = 6: Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading = 7: Nonlinear spring with elastic hysteresis
fct_ID26	Function identifier defining in bending Z (Integer)
fct_ID36	Function used only for unloading in bending Z If H6=4: Function identifier defining lower yield curve If H6=5: Function identifier defining residual displacement vs maximum displacement (Integer)
fct_ID46	Function identifier defining in bending Z (Integer)
	Negative failure limit Default = -1030 (Real)
	Positive failure limit Default = 1030 (Real)
F6	Scale factor for in bending Z (Real)
E6	Coefficient for strain rate effect in bending Z (Real)
	Reference translational velocity Default = 1.0 (Real)
	Reference rotational velocity in translation X Default = 1.0 (Real)
c1	Relative velocity coefficient in translation X Default = 0.0 (Real)
n1	Relative velocity exponent in translation X Default = 0.0 (Real)
	“Mult” factor in translation X Default = 1.0 (Real)
	Exponent in translation X Default = 2.0 (Real)
c2	Relative velocity coefficient in shear XY Default = 0.0 (Real)
n2	Relative velocity exponent in shear XY Default = 0.0 (Real)
	“Mult” factor in shear XY Default = 1.0 (Real)
	Exponent in shear XY Default = 2.0 (Real)
c3	Relative velocity coefficient in shear XZ Default = 0.0 (Real)
n3	Relative velocity exponent in shear XZ Default = 0.0 (Real)
3	“Mult” factor in shear XZ Default = 1.0 (Real)
3	Exponent in shear XZ Default = 2.0 (Real)
c4	Relative velocity coefficient in torsion Default = 0.0 (Real)
n4	Relative velocity exponent in torsion Default = 0.0 (Real)
	“Mult” factor in torsion Default = 1.0 (Real)
	Exponent in torsion Default = 2.0 (Real)
c5	Relative velocity coefficient in bending Y Default = 0.0 (Real)
n5	Relative velocity exponent in bending Y Default = 0.0 (Real)
	“Mult” factor in bending Y Default = 1.0 (Real)
	Exponent in bending Y Default = 2.0 (Real)
c6	Relative velocity coefficient in bending Z Default = 0.0 (Real)
n6	Relative velocity exponent in bending Z Default = 0.0 (Real)
	“Mult” factor in bending Z Default = 1.0 (Real)
	Exponent in bending Z Default = 2.0 (Real)

(Spring Beam)

In this example beside mass and inertia just simple set stiffness for 6 DOF for this beam type of spring property.

/UNIT/2

unit for prop

Mg mm s

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/PROP/TYPE13/1/2

spr_beam example

# Mass Inertia skew_ID sens_ID Isflag Ifail Ileng Ifail2

2.7e-5 2e-4 0 0 0 0 0 0

# K1 C1 A1 B1 D1

7e+4 0 0 0 0

# fct_ID11 H1 fct_ID21 fct_ID31 fct_ID41 delta_min1 delta_max1

0 0 0 0 0 0 0

# F1 E1 Ascale1 Hscale1

0 0 0 0

# K2 C2 A2 B2 D2

7e+4 0 0 0 0

# fct_ID12 H2 fct_ID22 fct_ID32 fct_ID42 delta_min2 delta_max2

0 0 0 0 0 0 0

# F2 E2 Ascale2 Hscale2

0 0 0 0

# K3 C3 A3 B3 D3

7e+4 0 0 0 0

# fct_ID13 H3 fct_ID23 fct_ID33 fct_ID43 delta_min3 delta_max3

0 0 0 0 0 0 0

# F3 E3 Ascale3 Hscale3

0 0 0 0

# K4 C4 A4 B4 D4

1e+5 0 0 0 0

# fct_ID14 H4 fct_ID24 fct_ID34 fct_ID44 delta_min4 delta_max4

0 0 0 0 0 0 0

# F4 E4 Ascale4 Hscale4

0 0 0 0

# K5 C5 A5 B5 D5

1e+5 0 0 0 0

# fct_ID15 H5 fct_ID25 fct_ID35 fct_ID45 delta_min5 delta_max5

0 0 0 0 0 0 0

# F5 E5 Ascale5 Hscale5

0 0 0 0

# K6 C6 A6 B6 D6

1e+5 0 0 0 0

# fct_ID16 H6 fct_ID26 fct_ID36 fct_ID46 delta_min6 delta_max6

0 0 0 0 0 0 0

# F6 E6 Ascale6 Hscale6

0 0 0 0

# V0 Omega0

0 0

# C n alpha beta

0 0 0 0

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

#ENDDATA

1.	The spring’s X direction is defined using nodes N1 and N2 of the spring.

If the third node of the spring N3 is defined, the spring’s Y’ direction is defined using nodes N1 and N3 of the spring. N3, N2, and N1 should not be in a line.

•	The Z direction is:

•	If node N3 is not defined in the element input, and skew system is defined in the property input, the Z direction is:

•	If neither node N3 nor skew system are defined in input, the Z direction is:

prop_spr_beam14

Finally, Y direction is found as:

2.	If Ileng =0, translational DOFs i=1,2,3 - use elongation to determine spring forces and use rotational angle in radians for rotational DOFs i=4,5,6 to determine spring moments.

The value of forces and moments in the spring are computed as:

Linear spring:

with i=1,2,3

with i=4,5,6

Nonlinear spring:

with i=1,2,3

with i=4,5,6

Note:

•	Here (with ) is the difference between the current length l and the initial length l0 of the of the spring element for corresponding translational DOF.

•	is the relative angle for corresponding rotational DOF in radians.

•	For linear springs, , and , , and are null functions and Ai, Bi, Ei, Hscalei are not taken into account.

•	If stiffness function or is requested, then K is used as a slope for unloading only.

•	If K is lower than the maximum slope of the function or (K is not consistent with the maximum slope of the curve), K is set to the maximum slope of the curve.

3.	If Ileng = 1, translational DOFs i=1,2,3 - use elongation per unit length to determine spring forces and use rotational angle in radians for rotational DOFs i=4,5,6 to determine spring moments. Spring parameters are related to initial spring length.

•	Spring mass = Spring stiffness =

•	Spring damping = Spring inertia =

Where, l0 is the initial spring length.

The forces and moments in the spring are computed as:

- Linear spring:

with i=1,23

with i=4,5,6

- Nonlinear spring:

with i=1, 2, 3

with i=4, 5, 6

Where, is the engineering strain and defined as:

- Force functions are given versus engineering strain and engineering strain rate.

- Failure criteria are defined with respect to strain. Input negative/positive failure limit should be related to initial length

4.	Unloading behavior of spring is determined by unloading parameter Hi (with i=1, 2, 3, 4, 5, 6) for corresponding DOFs. The figures below show typical unloading behaviors for translational DOF. It is similar behavior for rotational DOF.

linear_spring

Linear spring

nonlinear_spring_0

Nonlinear elastic spring, Hi=0

nonlinear_spring_1

Nonlinear elastic plastic spring, Hi=1

nonlinear_spring_2

Nonlinear elasto-plastic spring with decoupled hardening in tension and compression Hi=2

nonlinear_spring_4

Nonlinear elastic plastic spring “kinematic” hardening Hi=4

nonlinear_spring_5

Nonlinear elasto-plastic spring with nonlinear unloading Hi=5

nonlinear_spring_6

Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading Hi=6

nonlinear_spring_7

Nonlinear spring with elastic Hysteresis Hi=7

If hardening flag Hi = 4, the loading curve should be positive for all values of abscissa. The unloading curve in this case should be negative for all values of abscissa. For flag Hi = 4, these curves represents upper and lower limits of yield force as function of current spring length variation or strain. The force jumps between the curves each time when the direction of deformation changes.

6.	If hardening flag Hi = 5, residual deformation is a function of maximum displacement:

with i=1, 2, 3

with i=4, 5, 6

7.	Time step calculation

•	Time step for translational DOF is computed as:

with i=1, 2, 3, 4

•	Time step for rotational DOF is computed as:

with i=4, 5, 6

where, , , with t=1, 2, 3 and i=4, 5, 6

is used as spring time step.

8.	Failure criteria:

•	For uni-directional failure criteria Ifail=0, the spring fails as soon as one of the criteria is met in one direction:

or with and being the failure limits in direction i =1, 2, 3

or with and being the failure limits in direction i=4, 5, 6

For each direction (or ) should be negative and (or ) should be positive. If the values are zero, then no failure will be taken into account.

•	For multi-directional failure criteria Ifail=1, the spring fails when the following relation is fulfilled:

For “old” displacement formulation (Ifail2 = 0), the coefficients and are equal to 1.0 and 2.0, respectively.

The new formulation (Ifail2 =1) allows to model velocity dependent failure limit for translational DOF:

Where, or is the static failure limit in translational directions (Lines 5, 8 and 11), and v0 is the reference velocity.

Force and energy criteria are active with Ifail2 = 2 or 3:

In this case, the displacement values are replaced by positive failure force or failure energy values.

The new formulation (Ifail2 =1) allows to model velocity dependent failure limit for rotational DOF:

Where, or is the static failure limit in rotational direction (Lines 14, 17 and 20), and is the reference velocity.

Moment and energy criteria are activated with Ifail2= 2 or 3:

In this case, the rotation values are replaced by positive failure moment or failure energy values.

9.	If Ileng = 1, then displacement failure limits are replaced with failure strain .

10.	Spring activated and/or deactivated by sensor:

•	If sens_ID ≠ 0 and Isflag = 0, the spring element is activated by the sens_ID.

•	If sens_ID ≠ 0 and Isflag = 1, the spring element is deactivated by the sens_ID.

o	If a sensor is used for activating or deactivating a spring, the reference length of the spring at sensor activation (or deactivation) is equal to the nodal distance at time =0.

•	If sens_ID ≠ 0 and Isflag = 2, then:

o	The spring is activated and/or deactivated by sens_ID (if sensor is ON, spring is ON; if sensor is OFF, spring is OFF).

o	The spring reference length () is the distance between node N1 and N2 at the time of sensor’s activation.

11.	Spring elements with sensor activation or deactivation are mainly used in the pretension models.

/PROP/TYPE13 (SPR_BEAM)

/PROP/TYPE13 (SPR_BEAM)

/PROP/TYPE13 (SPR_BEAM)