chrono::fea::ChElasticityCosseratAdvanced Class Reference

Description

Advanced linear elasticity for a Cosserat beam.

Uniform stiffness properties E,G are assumed through the section as in ChElasticityCosseratSimple, but here it also supports the advanced case of Iyy and Izz axes rotated respect reference, elastic center with offset from reference, and shear center with offset from reference. This material can be shared between multiple beams. The linear elasticity is uncoupled between shear terms S and axial terms A as to have this stiffness matrix pattern:

 n_x   [A       A A ]   e_x
 n_y   [  S S S     ]   e_y
 n_z = [  S S S     ] * e_z
 m_x   [  S S S     ]   k_x
 m_y   [A       A A ]   k_y
 m_z   [A       A A ]   k_z
 

#include <ChBeamSectionCosserat.h>

Inheritance diagram for chrono::fea::ChElasticityCosseratAdvanced:
Collaboration diagram for chrono::fea::ChElasticityCosseratAdvanced:

Public Member Functions

 ChElasticityCosseratAdvanced (const double mIyy, const double mIzz, const double mJ, const double mG, const double mE, const double mA, const double mKs_y, const double mKs_z, const double malpha, const double mCy, const double mCz, const double mbeta, const double mSy, const double mSz)
 
void SetSectionRotation (double ma)
 "Elastic reference": set alpha, the rotation of the section for which the Iyy Izz are defined, respect to the reference section coordinate system placed at centerline.
 
double GetSectionRotation ()
 
void SetCentroid (double my, double mz)
 "Elastic reference": set the displacement of the elastic center (or tension center) respect to the reference section coordinate system placed at centerline.
 
double GetCentroidY ()
 
double GetCentroidZ ()
 
void SetShearRotation (double mb)
 "Shear reference": set beta, the rotation of the section for shear decoupling, respect to the reference section coordinate system placed at centerline.
 
double GetShearRotation ()
 
void SetShearCenter (double my, double mz)
 "Shear reference": set the displacement of the shear center S respect to the reference beam line placed at centerline. More...
 
double GetShearCenterY ()
 
double GetShearCenterZ ()
 
virtual void ComputeStress (ChVector3d &stress_n, ChVector3d &stress_m, const ChVector3d &strain_e, const ChVector3d &strain_k) override
 Compute the generalized cut force and cut torque. More...
 
virtual void ComputeStiffnessMatrix (ChMatrix66d &K, const ChVector3d &strain_e, const ChVector3d &strain_k) override
 Compute the 6x6 tangent material stiffness matrix [Km] = dσ/dε. More...
 
- Public Member Functions inherited from chrono::fea::ChElasticityCosseratSimple
 ChElasticityCosseratSimple (const double mIyy, const double mIzz, const double mJ, const double mG, const double mE, const double mA, const double mKs_y, const double mKs_z)
 
void SetArea (double ma)
 Set the A area of the beam.
 
double GetArea () const
 
void SetIyy (double ma)
 Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega z^2 dA \). More...
 
double GetIyy () const
 
void SetIzz (double ma)
 Set the Izz second moment of area of the beam (for bending about z in xy plane). More...
 
double GetIzz () const
 
void SetJ (double ma)
 Set the J torsion constant of the beam (for torsion about x axis)
 
double GetJ () const
 
void SetKsy (double ma)
 Set the Timoshenko shear coefficient Ks for y shear, usually about 0.8, (for elements that use this, ex. More...
 
double GetKsy () const
 
void SetKsz (double ma)
 Set the Timoshenko shear coefficient Ks for z shear, usually about 0.8, (for elements that use this, ex. More...
 
double GetKsz () const
 
virtual void SetAsRectangularSection (double width_y, double width_z)
 Shortcut: set Area, Ixx, Iyy, Ksy, Ksz and J torsion constant at once, given the y and z widths of the beam assumed with rectangular shape. More...
 
virtual void SetAsCircularSection (double diameter)
 Shortcut: set Area, Ixx, Iyy, Ksy, Ksz and J torsion constant at once, given the diameter of the beam assumed with circular shape. More...
 
void SetYoungModulus (double mE)
 Set E, the Young elastic modulus (N/m^2)
 
double GetYoungModulus () const
 
void SetShearModulus (double mG)
 Set G, the shear modulus.
 
double GetShearModulus () const
 
void SetShearModulusFromPoisson (double mpoisson)
 Set G, the shear modulus, given current E and the specified Poisson ratio.
 

Public Attributes

double alpha
 Rotation of Izz Iyy respect to reference section, centered on line x.
 
double Cy
 Elastic center, respect to reference section (elastic center, tension center)
 
double Cz
 
double beta
 Rotation of shear reference section, centered on line x.
 
double Sy
 Shear center, respect to reference section.
 
double Sz
 
- Public Attributes inherited from chrono::fea::ChElasticityCosseratSimple
double Iyy
 
double Izz
 
double J
 
double G
 
double E
 
double A
 
double Ks_y
 
double Ks_z
 
- Public Attributes inherited from chrono::fea::ChElasticityCosserat
ChBeamSectionCosseratsection
 

Constructor & Destructor Documentation

◆ ChElasticityCosseratAdvanced()

chrono::fea::ChElasticityCosseratAdvanced::ChElasticityCosseratAdvanced ( const double  mIyy,
const double  mIzz,
const double  mJ,
const double  mG,
const double  mE,
const double  mA,
const double  mKs_y,
const double  mKs_z,
const double  malpha,
const double  mCy,
const double  mCz,
const double  mbeta,
const double  mSy,
const double  mSz 
)
inline
Parameters
mIyyIyy second moment of area of the beam \( I_y = \int_\Omega z^2 dA \)
mIzzIzz second moment of area of the beam \( I_z = \int_\Omega y^2 dA \)
mJtorsion constant (torsion rigidity will be G*J, torsional stiffness = G*J*length)
mGG shear modulus
mEE young modulus
mAA area
mKs_yTimoshenko shear coefficient Ks for y shear
mKs_zTimoshenko shear coefficient Ks for z shear
malphasection rotation for which Iyy Izz are computed
mCyCy offset of elastic center about which Iyy Izz are computed
mCzCz offset of elastic center about which Iyy Izz are computed
mbetasection rotation for which Ks_y Ks_z are computed
mSySy offset of shear center
mSzSz offset of shear center

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratAdvanced::ComputeStiffnessMatrix ( ChMatrix66d K,
const ChVector3d strain_e,
const ChVector3d strain_k 
)
overridevirtual

Compute the 6x6 tangent material stiffness matrix [Km] = dσ/dε.

Parameters
K6x6 stiffness matrix
strain_elocal strain (deformation part): x= elongation, y and z are shear
strain_klocal strain (curvature part), x= torsion, y and z are line curvatures

Reimplemented from chrono::fea::ChElasticityCosseratSimple.

◆ ComputeStress()

void chrono::fea::ChElasticityCosseratAdvanced::ComputeStress ( ChVector3d stress_n,
ChVector3d stress_m,
const ChVector3d strain_e,
const ChVector3d strain_k 
)
overridevirtual

Compute the generalized cut force and cut torque.

Parameters
stress_nlocal stress (generalized force), x component = traction along beam
stress_mlocal stress (generalized torque), x component = torsion torque along beam
strain_elocal strain (deformation part): x= elongation, y and z are shear
strain_klocal strain (curvature part), x= torsion, y and z are line curvatures

Reimplemented from chrono::fea::ChElasticityCosseratSimple.

◆ SetShearCenter()

void chrono::fea::ChElasticityCosseratAdvanced::SetShearCenter ( double  my,
double  mz 
)
inline

"Shear reference": set the displacement of the shear center S respect to the reference beam line placed at centerline.

For shapes like rectangles, rotated rectangles, etc., it corresponds to the elastic center C, but for "L" shaped or "U" shaped beams this is not always true, and the shear center accounts for torsion effects when a shear force is applied.


The documentation for this class was generated from the following files:
  • /builds/uwsbel/chrono/src/chrono/fea/ChBeamSectionCosserat.h
  • /builds/uwsbel/chrono/src/chrono/fea/ChBeamSectionCosserat.cpp