Description

Simple linear elasticity model for a Cosserat beam, using basic material properties (zz and yy moments of inertia, area, Young modulus, etc.).

Uniform stiffness properties E,G are hence assumed through the section. The classical Timoshenko beam theory is encompassed in this model, that can be interpreted as a 3D extension of the Timoshenko beam theory. This can be shared between multiple beams.

#include <ChBeamSectionCosserat.h>

Inheritance diagram for chrono::fea::ChElasticityCosseratSimple:
Collaboration diagram for chrono::fea::ChElasticityCosseratSimple:

Public Member Functions

 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.
 
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 Attributes

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

◆ ChElasticityCosseratSimple()

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 
)
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

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratSimple::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::ChElasticityCosserat.

Reimplemented in chrono::fea::ChElasticityCosseratAdvanced.

◆ ComputeStress()

void chrono::fea::ChElasticityCosseratSimple::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

Implements chrono::fea::ChElasticityCosserat.

Reimplemented in chrono::fea::ChElasticityCosseratAdvanced.

◆ SetAsCircularSection()

void chrono::fea::ChElasticityCosseratSimple::SetAsCircularSection ( double  diameter)
virtual

Shortcut: set Area, Ixx, Iyy, Ksy, Ksz and J torsion constant at once, given the diameter of the beam assumed with circular shape.

You must set E and G anyway.

◆ SetAsRectangularSection()

void chrono::fea::ChElasticityCosseratSimple::SetAsRectangularSection ( double  width_y,
double  width_z 
)
virtual

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.

You must set E and G anyway.

◆ SetIyy()

void chrono::fea::ChElasticityCosseratSimple::SetIyy ( double  ma)
inline

Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega z^2 dA \).

Note: some textbook calls this Iyy as Iy Ex SI units: [m^4]

◆ SetIzz()

void chrono::fea::ChElasticityCosseratSimple::SetIzz ( double  ma)
inline

Set the Izz second moment of area of the beam (for bending about z in xy plane).

defined as \( I_z = \int_\Omega y^2 dA \). Note: some textbook calls this Izz as Iz Ex SI units: [m^4]

◆ SetKsy()

void chrono::fea::ChElasticityCosseratSimple::SetKsy ( double  ma)
inline

Set the Timoshenko shear coefficient Ks for y shear, usually about 0.8, (for elements that use this, ex.

the Timoshenko beams, or Reddy's beams)

◆ SetKsz()

void chrono::fea::ChElasticityCosseratSimple::SetKsz ( double  ma)
inline

Set the Timoshenko shear coefficient Ks for z shear, usually about 0.8, (for elements that use this, ex.

the Timoshenko beams, or Reddy's beams)


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