/PROP/TYPE33 (KJOINT)
Block Format Keyword Describes the joint type spring.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/PROP/TYPE33/prop_ID/unit_ID or /PROP/KJOINT/prop_ID/unit_ID  
prop_title  
Type  Skflag  
skew_ID_{1}  skew_ID_{2}  X_{k}  Cr 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{rx}  K_{ry}  K_{rz}  
fct_ID_{XR}  fct_ID_{YR}  fct_ID_{ZR}  
C_{rx}  C_{ry}  C_{rz}  
fct_ID_{XRC}  fct_ID_{YRC}  fct_ID_{ZRC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{rx}  fct_ID_{XR}  
C_{rx}  fct_ID_{XRC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{tx}  K_{rx}  fct_ID_{XT}  fct_ID_{XR}  
C_{tx}  C_{rx}  fct_ID_{XTC}  fct_ID_{XRC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{ty}  K_{tz}  fct_ID_{YT}  fct_ID_{ZT}  
K_{rx}  fct_ID_{XR}  
C_{ty}  C_{tz}  C_{rx}  
fct_ID_{YTC}  fct_ID_{ZTC}  fct_ID_{XRC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{ry}  K_{rz}  fct_ID_{YR}  fct_ID_{ZR}  
C_{ry}  C_{rz}  fct_ID_{YRC}  fct_ID_{ZRC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{tx}  fct_ID_{XT}  
C_{tx}  fct_ID_{XTC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n}  K_{ty}  K_{tz}  fct_ID_{YT}  fct_ID_{ZT}  
C_{ty}  C_{tz}  fct_ID_{YTC}  fct_ID_{ZTC} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{n} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

K_{tx}  K_{ty}  K_{tz}  
K_{rx}  K_{ry}  K_{rz}  
fct_ID_{XT}  fct_ID_{YT}  fct_ID_{ZT}  
fct_ID_{XR}  fct_ID_{YR}  fct_ID_{ZR}  
C_{tx}  C_{ty}  C_{tz}  
C_{rx}  C_{ry}  C_{rz}  
fct_ID_{XTC}  fct_ID_{YTC}  fct_ID_{ZTC}  
fct_ID_{XRC}  fct_ID_{YRC}  fct_ID_{ZRC} 
Definition
Field  Contents  SI Unit Example 

prop_ID  Property
identifier (Integer, maximum 10 digits) 

unit_ID  Unit Identifier (Integer, maximum 10 digits) 

prop_title  Property
title (Character, maximum 100 characters) 

Type  Joint type.
(Integer) 

Skflag  Skew frame selection.
10
(Integer) 

skew_ID_{1}  First skew system
identifier. (Integer) 

skew_ID_{2}  Second skew system
identifier. (Integer) 

X_{k}  Stiffness for
interface. (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
C_{r}  Critical damping
factor. Default = 0.0 (Real) 

K_{n}  Stiffness for blocked
DOF. (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
K_{rx}  X rotational stiffness
coefficient. 12 Default = 1.0 (Real) 
$\left[\frac{\text{Nm}}{\text{rad}}\right]$ 
K_{ry}  Y rotational stiffness
coefficient. 12 Default = 1.0 (Real) 
$\left[\frac{\text{Nm}}{\text{rad}}\right]$ 
K_{rz}  Z rotational stiffness
coefficient . 12
Default = 1.0 (Real) 
$\left[\frac{\text{Nm}}{\text{rad}}\right]$ 
fct_ID_{XR}  X rotational stiffness
function (Integer) 

fct_ID_{YR}  Y rotational stiffness
function. (Integer) 

fct_ID_{ZR}  Z rotational stiffness
function. (Integer) 

C_{rx}  X rotational viscosity
coefficient. 13 Default = 1.0 (Real) 
$\left[\frac{\text{Nms}}{\text{rad}}\right]$ 
C_{ry}  Y rotational viscosity
coefficient. 13 Default = 1.0 (Real) 
$\left[\frac{\text{Nms}}{\text{rad}}\right]$ 
C_{rz}  Z rotational viscosity
coefficient. 13
Default = 1.0 (Real) 
$\left[\frac{\text{Nms}}{\text{rad}}\right]$ 
fct_ID_{XRC}  X rotational viscosity
function. (Integer) 

fct_ID_{YRC}  Y rotational viscosity
function. (Integer) 

fct_ID_{ZRC}  Z rotational viscosity
function. (Integer) 

fct_ID_{XT}  X translational stiffness
function. (Integer) 

fct_ID_{YT}  Y translational stiffness
function. (Integer) 

fct_ID_{ZT}  Z translational stiffness
function. (Integer) 

K_{tx}  X translational stiffness
coefficient. 12 Default = 1.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
K_{ty}  Y translational stiffness
coefficient. 12 Default = 1.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
K_{tz}  Z translational stiffness
coefficient. 12
Default = 1.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
C_{tx}  X translational viscosity
coefficient. 13
Default = 1.0 (Real) 
$\left[\frac{\text{Ns}}{\text{m}}\right]$ 
C_{ty}  Y translational viscosity
coefficient. 13
Default = 1.0 (Real) 
$\left[\frac{\text{Ns}}{\text{m}}\right]$ 
C_{tz}  Z translational viscosity
coefficient. 13 Default = 1.0 (Real) 
$\left[\frac{\text{Ns}}{\text{m}}\right]$ 
fct_IDX_{TC}  X translational viscosity
function (Integer) 

fct_IDY_{TC}  Y translational viscosity
function (Integer) 

fct_IDZ_{TC}  Z translational viscosity
function (Integer) 
Comments
 Joints are defined by a spring and two local coordinate axes, which belong to connected bodies. Assume that the connected bodies are rigid to ensure the orthogonality of their local axes. Yet, deformable bodies may be connected with a joint, but a warning will be displayed by Radioss in this case; moreover if the axis becomes nonorthogonal during deformation, the stability of the joint cannot be insured.
 Joint properties are defined in a local frame computed with respect to two connected coordinate systems. They do not need to be initially coincident. If the initial position of the local coordinate axis coincides at any time, the joint local frames are defined at a mean position. If the local axes' are not initially coincident, they are first transformed into a mean position between the initial state. Then the joint local frame will be computed with respect to these rotated axes.
 Total number of joint DOF's
computed in the local skew frame is six:${\delta}_{{X}^{\prime}},{\delta}_{{Y}^{\prime}},{\delta}_{{Z}^{\prime}},{\theta}_{{X}^{\prime}},{\theta}_{{Y}^{\prime}},{\theta}_{{Z}^{\prime}}$
 Blocked and free DOFs are distinguished for each joint type.
 The blocked DOFs are characterized by a constant stiffness.
 Selecting a high value with respect to the free DOF stiffness is recommended. The free DOF have userdefined characteristics, which can be linear or nonlinear elastic, combined with a subcritical viscous damping.
 The translational and
rotational DOF are defined as:
(1) Where $d{x}_{1}$ and $d{x}_{2}$ are total displacements of two joint nodes in the local coordinate system.$$\delta =d{x}_{2}d{x}_{1}$$(2) $$\theta ={\theta}_{2}{\theta}_{1}$$Where ${\theta}_{1}$ and ${\theta}_{2}$ are total relative rotations of two connected body axes, with respect to the local joint coordinate frame.
 Forces and moments
calculation:
 The force in direction
$\delta $
is computed as:Linear spring:
(3) $$F={K}_{t}\delta +{C}_{t}\dot{\delta}$$${{\rm K}}_{t}$ : translational stiffness $\left({K}_{tx},{K}_{ty},{K}_{tz}\right)$
${C}_{t}$ : translational viscosity $\left({C}_{tx},{C}_{ty},{C}_{tz}\right)$
Nonlinear spring:(4) $$F={K}_{t}\mathrm{f}\left(\delta \right)+{C}_{t}\mathrm{g}\left(\dot{\delta}\right)$$  The moment in
$\theta $
direction is computed as:Linear spring:
(5) $$M={K}_{r}\theta +{C}_{r}\dot{\theta}$$${{\rm K}}_{r}$ : rotational stiffness (K_{rx}, K_{ry}, and K_{rz})
${C}_{r}$ : rotational viscosity (C_{rx}, C_{ry}, and C_{rz})
Nonlinear spring:(6) $$M={K}_{r}\mathrm{f}\left(\theta \right)+{C}_{r}\mathrm{g}\left(\dot{\theta}\right)$$  The joint length may be, but is not necessarily equal to 0. It is recommended; however, to use a 0 length spring to define a spherical joint or an universal joint.
 To satisfy the global balance of moments in a general case, correction terms
in the rotational DOF are calculated as:
(7) $${M}_{\theta x}={M}_{\theta x}+{L}_{y}\times {F}_{z}{L}_{z}\times {F}_{y}$$(8) $${M}_{\theta y}={M}_{\theta y}+{L}_{z}\times {F}_{x}{L}_{x}\times {F}_{z}$$(9) $${M}_{\theta z}={M}_{\theta z}+{L}_{x}\times {F}_{y}{L}_{y}\times {F}_{x}$$
 The force in direction
$\delta $
is computed as:
 Available
joint types:
Table 1. Available Joints Type No. Joint Type dx dy dz ${\theta}_{X}$ ${\theta}_{Y}$ ${\theta}_{Z}$ 1 Spherical x x x 0 0 0 2 Revolute x x x 0 x x 3 Cylindrical 0 x x 0 x x 4 Planar x 0 0 0 x x 5 Universal (development source only) x x x x 0 0 6 Translational 0 x x x x x 7 Oldham x 0 0 x x x 8 Rigid x x x x x x 9 Free 0 0 0 0 0 0 Where:
x: denotes a blocked DOF
0: denotes a free (userdefined) DOF: Joints do not have userdefined mass or inertia, so the nodal time step is always used.
 There are two ways to introduce viscous damping:
 Defining a critical damping (for blocked DOF only):
Viscous damping is defined in terms of the critical damping factor. The critical damping coefficient is calculated using the blocking stiffness value of the element. The mass and inertia are equal to half of the values of each rigid body connected to the joint. The approximation is then satisfactory, if only one joint is connected to each rigid body. Otherwise, the critical damping is overestimated, in which case the damping factor in the Radioss input should be decreased. The same damping is applied to all blocked DOF.
 Userdefined constant or nonlinear damping:
It is possible to define independent damping parameters for each free DOF.
 If Skflag = 1, the joint local frame is chosen as the local coordinate system of the first connected body. In this case, a mean skew position is not calculated. However, the second local coordinate system must still be defined.
 For a universal joint, this option is not active, and both skew axes are always used to calculate the local joint frame.
 Coefficients K_{rx}, K_{ry}, K_{rz}, K_{tx}, K_{ty}, and K_{tz} are used for linear joint if there are no userdefined functions. If a function number in any DOF is not 0, the corresponding stiffness coefficient becomes a scale factor for the function. This rule is applied to any DOF of all joint types.
 Coefficients C_{rx}, C_{ry}, C_{rz}, C_{tx}, C_{ty}, and C_{tz} are used as linear viscosity coefficients if there are no userdefined functions. If a function number in any DOF is not 0, the corresponding coefficient becomes a scale factor for the function.
 The universal joint length
must be equal to 0, in the initial state. The universal joint local skew system is
defined as:
Y local axis = Xaxis of the first body local skew system
Z local axis = Xaxis of the second body local skew system
X local axis = YΛ Z
 This local frame must be initially orthogonal. The Xaxis of two defining body skew axes must; therefore, be orthogonal in the initial position. The joint local frame can further become nonorthogonal due to deformation. The forces and moments are then computed in this nonorthogonal frame.
 Each /PROP/KJOINT uses a unique definition of local coordinate system; therefore, one property can refer to only one spring element.