Description

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

void SetArea (double ma)
 Set the A area of the beam.
 
double GetArea () const
 
void SetIzz (double ma)
 Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega \rho z^2 dA f$. Note: some textbook calls this Iyy as Iy Ex SI units: [m^4] void SetIyy(double ma) { this->Iyy = ma; } double GetIyy() const { return this->Iyy; } Set the Izz second moment of area of the beam (for bending about z in xy plane). defined as \) I_z = \int_\Omega \rho y^2 dA f$. 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 SetGshearModulus (double mG)
 Set G, the shear modulus.
 
double GetGshearModulus () const
 
void SetGwithPoissonRatio (double mpoisson)
 Set G, the shear modulus, given current E and the specified Poisson ratio.
 
virtual void ComputeStress (ChVector<> &stress_n, ChVector<> &stress_m, const ChVector<> &strain_e, const ChVector<> &strain_k) override
 Set the Rayleigh damping ratio r (as in: R = r * K ), to do: also mass-proportional term void SetBeamRaleyghDamping(double mr) { this->rdamping = mr; } OBSOLETE use ChDampingCosseratRayleigh object instead. More...
 
virtual void ComputeStiffnessMatrix (ChMatrixNM< double, 6, 6 > &K, const ChVector<> &strain_e, const ChVector<> &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 rdamping
 
double Ks_y
 
double Ks_z
 
- Public Attributes inherited from chrono::fea::ChElasticityCosserat
ChBeamSectionCosseratsection
 

Member Function Documentation

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElasticityCosseratSimple::ComputeStiffnessMatrix ( ChMatrixNM< double, 6, 6 > &  K,
const ChVector<> &  strain_e,
const ChVector<> &  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 ( ChVector<> &  stress_n,
ChVector<> &  stress_m,
const ChVector<> &  strain_e,
const ChVector<> &  strain_k 
)
overridevirtual

Set the Rayleigh damping ratio r (as in: R = r * K ), to do: also mass-proportional term void SetBeamRaleyghDamping(double mr) { this->rdamping = mr; } OBSOLETE use ChDampingCosseratRayleigh object instead.

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.

◆ SetIzz()

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

Set the Iyy second moment of area of the beam (for bending about y in xz plane), defined as \( I_y = \int_\Omega \rho z^2 dA f$. Note: some textbook calls this Iyy as Iy Ex SI units: [m^4] void SetIyy(double ma) { this->Iyy = ma; } double GetIyy() const { return this->Iyy; } Set the Izz second moment of area of the beam (for bending about z in xy plane). defined as \) I_z = \int_\Omega \rho y^2 dA f$.

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