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>
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. More... | |
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 (ChVector<> &stress_n, ChVector<> &stress_m, const ChVector<> &strain_e, const ChVector<> &strain_k) override |
Compute the generalized cut force and cut torque. 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 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 | 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. | |
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 | |
ChBeamSectionCosserat * | section |
Constructor & Destructor Documentation
◆ ChElasticityCosseratAdvanced()
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inline |
- Parameters
-
mIyy Iyy second moment of area of the beam \( I_y = \int_\Omega z^2 dA \) mIzz Izz second moment of area of the beam \( I_z = \int_\Omega y^2 dA \) mJ torsion constant (torsion rigidity will be G*J, torsional stiffness = G*J*length) mG G shear modulus mE E young modulus mA A area mKs_y Timoshenko shear coefficient Ks for y shear mKs_z Timoshenko shear coefficient Ks for z shear malpha section rotation for which Iyy Izz are computed mCy Cy offset of elastic center about which Iyy Izz are computed mCz Cz offset of elastic center about which Iyy Izz are computed mbeta section rotation for which Ks_y Ks_z are computed mSy Sy offset of shear center mSz Sz offset of shear center
Member Function Documentation
◆ ComputeStiffnessMatrix()
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overridevirtual |
Compute the 6x6 tangent material stiffness matrix [Km] = dσ/dε.
- Parameters
-
K 6x6 stiffness matrix strain_e local strain (deformation part): x= elongation, y and z are shear strain_k local strain (curvature part), x= torsion, y and z are line curvatures
Reimplemented from chrono::fea::ChElasticityCosseratSimple.
◆ ComputeStress()
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overridevirtual |
Compute the generalized cut force and cut torque.
- Parameters
-
stress_n local stress (generalized force), x component = traction along beam stress_m local stress (generalized torque), x component = torsion torque along beam strain_e local strain (deformation part): x= elongation, y and z are shear strain_k local strain (curvature part), x= torsion, y and z are line curvatures
Reimplemented from chrono::fea::ChElasticityCosseratSimple.
◆ SetShearCenter()
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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.
◆ SetShearRotation()
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inline |
"Shear reference": set beta, the rotation of the section for shear decoupling, respect to the reference section coordinate system placed at centerline.
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