Description
Advanced linear elasticity for a Cosserat section, not assuming homogeneous elasticity.
This is the case where one uses a FEA preprocessor to compute the rigidity of a complex beam made with multilayered reinforcements with different elasticity  in such a case you could not use ChElasticityCosseratAdvanced because you do not have a single E or G, but you rather have collective values of bending/shear/axial rigidities. This class allows using these values directly, bypassing any knowledge of area, Izz Iyy, E young modulus, etc. 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  
ChElasticityCosseratAdvancedGeneric (const double mAx, const double mTxx, const double mByy, const double mBzz, const double mHyy, const double mHzz, const double malpha, const double mCy, const double mCz, const double mbeta, const double mSy, const double mSz)  
virtual void  SetAxialRigidity (const double mv) 
Sets the axial rigidity, usually A*E for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
virtual void  SetTorsionRigidityX (const double mv) 
Sets the torsion rigidity, for torsion about X axis, at elastic center, usually J*G for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
virtual void  SetBendingRigidityY (const double mv) 
Sets the bending rigidity, for bending about Y axis, at elastic center, usually Iyy*E for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
virtual void  SetBendingRigidityZ (const double mv) 
Sets the bending rigidity, for bending about Z axis, at elastic center, usually Izz*E for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
virtual void  SetShearRigidityY (const double mv) 
Sets the shear rigidity, for shear about Y axis, at shear center, usually A*G*(Timoshenko correction factor) for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
virtual void  SetShearRigidityZ (const double mv) 
Sets the shear rigidity, for shear about Z axis, at shear center, usually A*G*(Timoshenko correction factor) for uniform elasticity, but for nonuniform elasticity here you can put a value adhoc from a preprocessor.  
void  SetSectionRotation (double ma) 
Set the rotation in [rad] of the Y Z axes for which the YbendingRigidity and ZbendingRigidity values are defined.  
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) 
Set the rotation in [rad] of the Y Z axes for which the YshearRigidity and ZshearRigidity values are defined.  
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...  
Additional Inherited Members  
Public Attributes inherited from chrono::fea::ChElasticityCosserat  
ChBeamSectionCosserat *  section 
Constructor & Destructor Documentation
◆ ChElasticityCosseratAdvancedGeneric()

inline 
 Parameters

mAx axial rigidity mTxx torsion rigidity mByy bending regidity on Y of reference at elastic center mBzz bending rigidity on Z of reference at elastic center mHyy shear rigidity on Y of reference at shear center mHzz shear rigidity on Y of reference at shear center malpha rotation of reference at elastic center, for bending effects [rad] mCy elastic center y displacement respect to centerline mCz elastic center z displacement respect to centerline mbeta rotation of reference at shear center, for shear effects [rad] mSy shear center y displacement respect to centerline mSz shear center z displacement respect to centerline
Member Function Documentation
◆ ComputeStiffnessMatrix()

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::ChElasticityCosserat.
◆ ComputeStress()

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
Implements chrono::fea::ChElasticityCosserat.
◆ SetShearCenter()

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