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MBDynモデル集

## 10. 転がり落ちる円柱

### 入力ファイル

```# rolling_cylinder.mbd

#-----------------------------------------------------------------------------
# [Data Block]

begin: data;
problem: initial value;
end: data;

#-----------------------------------------------------------------------------
# [<Problem> Block]

begin: initial value;
initial time:   0.;
final time:     2.;
time step:      1.e-3;
max iterations: 10;
tolerance:      1.e-7;
end: initial value;

#-----------------------------------------------------------------------------
# [Control Data Block]

begin: control data;
output frequency: 5;
structural nodes: 3;
abstract nodes:   1;
rigid bodies:     1;
joints:           3;
forces:           3;
genels:           1;
gravity;
end: control data;

#-----------------------------------------------------------------------------
# Design Variables
set: real Cylinder_Mass           = 5.;    #[kg]
set: real Cylinder_Radius         = 0.2;   #[m]
set: real Surface_Angle           = pi/6.; #[rad]
set: real Offset_Cylinder_Surface = 0.4;   #[m] Initial Offset of Cylinder Center
#       from Surface (>=Cylinder_Radius)

set: real Kc = 100000.; #[N/m]  Contact Stiffness
set: real Ec = 1.2;     #[-]    Contact Stiffness Exponent
set: real Cc = 10.;     #[Ns/m] Contact Damping
set: real Dc = 0.0001;  #[m]    Contact Damping Activation Depth

set: real Mu = 0.1;   #[-]   Friction Coefficient
set: real Vt = 0.001; #[m/s] Friction Threshold Velocity

#-----------------------------------------------------------------------------
# Intermediate Variables
set: real Cylinder_Inertia = 1./2.*Cylinder_Mass*Cylinder_Radius^2.; #[kg-m^2]

#-----------------------------------------------------------------------------
# Reference Labels
set: integer Ref_Surface = 1;

# Node Labels
set: integer NoSta_Surface      = 1;
set: integer NoDyn_Cylinder     = 2;
set: integer NoDum_Cylinder     = 3;
set: integer NoAbs_Force_Normal = 4;

# Body Labels
set: integer Body_Cylinder = 1;

# Joint Labels
set: integer JoClamp_Surface           = 1;
set: integer JoInp_Surface_Cylinder    = 2;
set: integer JoRevrot_Surface_Cylinder = 3;

# Force Labels
set: integer FoStrin_Normal_Cylinder_Surface   = 1;
set: integer FoStrin_Friction_Cylinder_Surface = 2;
set: integer CoStrin_Friction_Cylinder_Surface = 3;

# Genel Labels
set: integer GeClamp_NoAbs_Force_Normal = 1;

#-----------------------------------------------------------------------------
# Scalar Functions
scalar function: "cubstep",
cubicspline, do not extrapolate,
-0.03, 0.00,
-0.02, 0.00,
-0.01, 0.00,
0.00, 0.00,
1.00, 1.00,
1.01, 1.00,
1.02, 1.00,
1.03, 1.00;

scalar function: "cubsign",
cubicspline, do not extrapolate,
-1.03, -1.00,
-1.02, -1.00,
-1.01, -1.00,
-1.00, -1.00,
1.00,  1.00,
1.01,  1.00,
1.02,  1.00,
1.03,  1.00;

#-----------------------------------------------------------------------------
# References
reference: Ref_Surface,
reference, global, null,                         # absolute position
reference, global, euler, Surface_Angle, 0., 0., # absolute orientation
reference, global, null,                         # absolute velocity
reference, global, null;                         # absolute angular velocity

#-----------------------------------------------------------------------------
# [Nodes Block]

begin: nodes;

#-----------------------------------------------------------------------------
# Nodes
structural: NoSta_Surface, static,
reference, Ref_Surface, null, # absolute position
reference, Ref_Surface, eye,  # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity

structural: NoDyn_Cylinder, dynamic,
0., 0., Offset_Cylinder_Surface/cos(Surface_Angle), # absolute position
euler, 0., pi/2., 0.,                               # absolute orientation
null,                                               # absolute velocity
null,                                               # absolute angular velocity
accelerations;

structural: NoDum_Cylinder, dummy, NoDyn_Cylinder,
relative frame, NoSta_Surface;

abstract: NoAbs_Force_Normal, algebraic;

end: nodes;

#-----------------------------------------------------------------------------
# Plugin Variables
set: [node, W, NoDyn_Cylinder, structural, string="omega[3]"];
set: [node, DZ_Dum, NoDum_Cylinder, structural, string="X[3]"];
set: [node, VY_Dum, NoDum_Cylinder, structural, string="XP[2]"];
set: [node, VZ_Dum, NoDum_Cylinder, structural, string="XP[3]"];

#-----------------------------------------------------------------------------
# [Elements Block]

begin: elements;

#-----------------------------------------------------------------------------
# Bodies
body: Body_Cylinder, NoDyn_Cylinder,
Cylinder_Mass,                  # mass
null,                           # relative center of mass
diag, 1., 1., Cylinder_Inertia; # inertia matrix

#-----------------------------------------------------------------------------
# Joints
joint: JoClamp_Surface,
clamp,
NoSta_Surface,
position, node,
orientation, node;

joint: JoInp_Surface_Cylinder,
in plane,
NoSta_Surface,
null,       # relative plane position
1., 0., 0., # relative normal direction
NoDyn_Cylinder;

joint: JoRevrot_Surface_Cylinder,
revolute rotation,
NoSta_Surface,
hinge,
euler, 0., pi/2., 0., # relative orientation matrix
NoDyn_Cylinder;

#-----------------------------------------------------------------------------
# Genels
genel: GeClamp_NoAbs_Force_Normal,
clamp,
NoAbs_Force_Normal, abstract,

#-----------------------------------------------------------------------------
# Plugin Variables
set: [dof, FN, NoAbs_Force_Normal, abstract, algebraic];

#-----------------------------------------------------------------------------
# Forces
force: FoStrin_Normal_Cylinder_Surface,
absolute internal,
NoDyn_Cylinder,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 0., 1., string, "FN"; # force value

force: FoStrin_Friction_Cylinder_Surface,
absolute internal,
NoDyn_Cylinder,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 1., 0.,
string, "-model::sf::cubsign((VY_Dum+Cylinder_Radius*W)/Vt)*Mu*FN"; # force value

couple: CoStrin_Friction_Cylinder_Surface,
absolute internal,
NoDyn_Cylinder,
NoSta_Surface,
single, reference, Ref_Surface, 1., 0., 0.,