v0.14.0
Classes | Public Member Functions | Public Attributes | List of all members
SurfaceSlidingConstrains Struct Reference

Shape preserving constrains, i.e. nodes sliding on body surface. More...

#include <tools/src/SurfaceSlidingConstrains.hpp>

Inheritance diagram for SurfaceSlidingConstrains:
[legend]
Collaboration diagram for SurfaceSlidingConstrains:
[legend]

Classes

struct  DriverElementOrientation
 Class implemented by user to detect face orientation. More...
 
struct  MyTriangleFE
 
struct  OpJacobian
 

Public Member Functions

MyTriangleFE & getLoopFeRhs ()
 
MyTriangleFE & getLoopFeLhs ()
 
MoFEMErrorCode getOptions ()
 
 SurfaceSlidingConstrains (MoFEM::Interface &m_field, DriverElementOrientation &orientation)
 
virtual ~SurfaceSlidingConstrains ()=default
 
MoFEMErrorCode setOperators (int tag, const std::string lagrange_multipliers_field_name, const std::string material_field_name, const double *alpha=nullptr)
 
MoFEMErrorCode setOperatorsConstrainOnly (int tag, const std::string lagrange_multipliers_field_name, const std::string material_field_name)
 
MyTriangleFE & getLoopFeRhs ()
 
MyTriangleFE & getLoopFeLhs ()
 
MoFEMErrorCode getOptions ()
 
 SurfaceSlidingConstrains (MoFEM::Interface &m_field, DriverElementOrientation &orientation)
 
virtual ~SurfaceSlidingConstrains ()=default
 
MoFEMErrorCode setOperators (int tag, const std::string lagrange_multipliers_field_name, const std::string material_field_name, const double *alpha=nullptr)
 
MoFEMErrorCode setOperatorsConstrainOnly (int tag, const std::string lagrange_multipliers_field_name, const std::string material_field_name)
 
- Public Member Functions inherited from GenericSliding
 GenericSliding ()=default
 
virtual ~GenericSliding ()=default
 
 GenericSliding ()=default
 
virtual ~GenericSliding ()=default
 

Public Attributes

MoFEM::Interface & mField
 
boost::shared_ptr< MyTriangleFE > feRhsPtr
 
boost::shared_ptr< MyTriangleFE > feLhsPtr
 
MyTriangleFE & feRhs
 
MyTriangleFE & feLhs
 
DriverElementOrientation & crackFrontOrientation
 
double aLpha
 

Detailed Description

Shape preserving constrains, i.e. nodes sliding on body surface.

Derivation and implementation of constrains preserving body surface, i.e. body shape and volume.

The idea starts form observation that body shape can be globally characterized by constant calculated as volume over its area

\[ \frac{V}{A} = C \]

Above equation expressed in integral form is

\[ \int_\Omega \textrm{d}V = C \int_\Gamma \textrm{d}S \]

where notting that,

\[ \frac{1}{3} \int_\Omega \textrm{div}[\mathbf{X}] \textrm{d}\Omega = C \int_\Gamma \textrm{d}S \]

and applying Gauss theorem we get

\[ \int_\Gamma \mathbf{X}\cdot \frac{\mathbf{N}}{\|\mathbf{N}\|} \textrm{d}\Gamma = 3C \int_\Gamma \textrm{d}S. \]

Drooping integrals on both sides, and linearizing equation, we get

\[ \frac{\mathbf{N}}{\|\mathbf{N}\|} \cdot \delta \mathbf{X} = 3C - \frac{\mathbf{N}}{\|\mathbf{N}\|}\cdot \mathbf{X} \]

where \(\delta \mathbf{X}\) is displacement sub-inctrement. Above equation is a constrain if satisfied in body shape and volume is conserved. Final form of constrain equation is

\[ \mathcal{r} = \frac{\mathbf{N}}{\|\mathbf{N}\|}\cdot \mathbf{X} - \frac{\mathbf{N_0}}{\|\mathbf{N_0}\|}\cdot \mathbf{X}_0 = \frac{\mathbf{N}}{\|\mathbf{N}\|}\cdot (\mathbf{X}-\mathbf{X}_0) \]

In the spirit of finite element method the constrain equation is multiplied by shape functions and enforce using Lagrange multiplier method

\[ \int_\Gamma \mathbf{N}^\mathsf{T}_\lambda \left( \frac{\mathbf{N}}{\|\mathbf{N}\|}\mathbf{N}_\mathbf{X}\cdot (\overline{\mathbf{X}}-\overline{\mathbf{X}}_0) \right) \|\mathbf{N}\| \textrm{d}\Gamma = \mathbf{0}. \]

Above equation is nonlinear, applying to it Taylor expansion, we can get form which can be used with Newton interactive method

\[ \begin{split} &\int_\Gamma \mathbf{N}^\mathsf{T}_\lambda \left\{ \mathbf{N}\mathbf{N}_\mathbf{X} + \left(\mathbf{X}-\mathbf{X}_0\right) \cdot \left( \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\xi}\right]\cdot\mathbf{B}_\eta - \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\eta}\right]\cdot\mathbf{B}_\xi \right) \right\} \textrm{d}\Gamma \cdot \delta \overline{\mathbf{X}}\\ = &\int_\Gamma \mathbf{N}^\mathsf{T}_\lambda \mathbf{N}\cdot(\mathbf{X}-\mathbf{X}_0) \textrm{d}\Gamma \end{split}. \]

Equation expressing forces on shape as result of constrains, as result Lagrange multiplier method have following form

\[ \begin{split} &\int_\Gamma \mathbf{N}^\mathsf{T}_\mathbf{X} \cdot \mathbf{N} \mathbf{N}_\lambda \textrm{d}\Gamma \cdot \delta\overline{\lambda}\\ + &\int_\Gamma \lambda \mathbf{N}^\mathsf{T}_\mathbf{X} \left( \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\xi}\right]\cdot\mathbf{B}_\eta - \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\eta}\right]\cdot\mathbf{B}_\xi \right) \textrm{d}\Gamma \delta\overline{\mathbf{X}}\\ = &\int_\Gamma \lambda \mathbf{N}^\mathsf{T}_\mathbf{X} \cdot \mathbf{N} \textrm{d}\Gamma \end{split} \]

Above equations are assembled into global system of equations as following

\[ \left[ \begin{array}{cc} \mathbf{K} + \mathbf{B} & \mathbf{C}^\mathsf{T} \\ \mathbf{C} + \mathbf{A} & 0 \end{array} \right] \left\{ \begin{array}{c} \delta \overline{\mathbf{X}} \\ \delta \overline{\lambda} \end{array} \right\}= \left[ \begin{array}{c} \mathbf{f} - \mathbf{C}^\mathsf{T}\overline{\lambda} \\ \overline{\mathbf{r}} \end{array} \right] \]

where

\[ \mathbf{C}= \int_\Gamma \mathbf{N}_\lambda^\mathsf{T} \mathbf{N} \cdot \mathbf{N}_\mathbf{X} \textrm{d}\Gamma, \]

\[ \mathbf{B}= \int_\Gamma \lambda (\mathbf{X}-\mathbf{X}_0)\cdot \left( \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\xi}\right]\cdot\mathbf{B}_\eta - \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\eta}\right]\cdot\mathbf{B}_\xi \right) \textrm{d}\Gamma \]

and

\[ \mathbf{A}= \int_\Gamma \mathbf{N}^\mathsf{T}_\lambda \left(\mathbf{X}-\mathbf{X}_0\right) \cdot \left( \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\xi}\right]\cdot\mathbf{B}_\eta - \textrm{Spin}\left[\frac{\partial\mathbf{X}}{\partial\eta}\right]\cdot\mathbf{B}_\xi \right). \]

Examples
mesh_smoothing.cpp.

Definition at line 323 of file SurfaceSlidingConstrains.hpp.

Constructor & Destructor Documentation

◆ SurfaceSlidingConstrains() [1/2]

SurfaceSlidingConstrains::SurfaceSlidingConstrains ( MoFEM::Interface &  m_field,
DriverElementOrientation &  orientation 
)
inline

Definition at line 405 of file SurfaceSlidingConstrains.hpp.

407  : mField(m_field), feRhsPtr(new MyTriangleFE(m_field)),
408  feLhsPtr(new MyTriangleFE(m_field)), feRhs(*feRhsPtr), feLhs(*feLhsPtr),
409  crackFrontOrientation(orientation), aLpha(1) {
410 
411  ierr = getOptions();
412  CHKERRABORT(PETSC_COMM_WORLD, ierr);
413  }

◆ ~SurfaceSlidingConstrains() [1/2]

virtual SurfaceSlidingConstrains::~SurfaceSlidingConstrains ( )
virtualdefault

◆ SurfaceSlidingConstrains() [2/2]

SurfaceSlidingConstrains::SurfaceSlidingConstrains ( MoFEM::Interface &  m_field,
DriverElementOrientation &  orientation 
)
inline

Definition at line 405 of file SurfaceSlidingConstrains.hpp.

407  : mField(m_field), feRhsPtr(new MyTriangleFE(m_field)),
408  feLhsPtr(new MyTriangleFE(m_field)), feRhs(*feRhsPtr), feLhs(*feLhsPtr),
409  crackFrontOrientation(orientation), aLpha(1) {
410 
411  ierr = getOptions();
412  CHKERRABORT(PETSC_COMM_WORLD, ierr);
413  }

◆ ~SurfaceSlidingConstrains() [2/2]

virtual SurfaceSlidingConstrains::~SurfaceSlidingConstrains ( )
virtualdefault

Member Function Documentation

◆ getLoopFeLhs() [1/2]

MyTriangleFE& SurfaceSlidingConstrains::getLoopFeLhs ( )
inline

Definition at line 387 of file SurfaceSlidingConstrains.hpp.

387 { return feLhs; }

◆ getLoopFeLhs() [2/2]

MyTriangleFE& SurfaceSlidingConstrains::getLoopFeLhs ( )
inline

Definition at line 387 of file SurfaceSlidingConstrains.hpp.

387 { return feLhs; }

◆ getLoopFeRhs() [1/2]

MyTriangleFE& SurfaceSlidingConstrains::getLoopFeRhs ( )
inline

Definition at line 385 of file SurfaceSlidingConstrains.hpp.

385 { return feRhs; }

◆ getLoopFeRhs() [2/2]

MyTriangleFE& SurfaceSlidingConstrains::getLoopFeRhs ( )
inline

Definition at line 385 of file SurfaceSlidingConstrains.hpp.

385 { return feRhs; }

◆ getOptions() [1/2]

MoFEMErrorCode SurfaceSlidingConstrains::getOptions ( )
inline

Definition at line 392 of file SurfaceSlidingConstrains.hpp.

392  {
393  MoFEMFunctionBegin;
394  ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "",
395  "Get surface sliding constrains element scaling",
396  "none");
397  CHKERRQ(ierr);
398  CHKERR PetscOptionsScalar("-surface_sliding_alpha", "scaling parameter", "",
399  aLpha, &aLpha, PETSC_NULL);
400  ierr = PetscOptionsEnd();
401  CHKERRQ(ierr);
402  MoFEMFunctionReturn(0);
403  }

◆ getOptions() [2/2]

MoFEMErrorCode SurfaceSlidingConstrains::getOptions ( )
inline

Definition at line 392 of file SurfaceSlidingConstrains.hpp.

392  {
393  MoFEMFunctionBegin;
394  ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "",
395  "Get surface sliding constrains element scaling",
396  "none");
397  CHKERRQ(ierr);
398  CHKERR PetscOptionsScalar("-surface_sliding_alpha", "scaling parameter", "",
399  aLpha, &aLpha, PETSC_NULL);
400  ierr = PetscOptionsEnd();
401  CHKERRQ(ierr);
402  MoFEMFunctionReturn(0);
403  }

◆ setOperators() [1/2]

MoFEMErrorCode SurfaceSlidingConstrains::setOperators ( int  tag,
const std::string  lagrange_multipliers_field_name,
const std::string  material_field_name,
const double *  alpha = nullptr 
)
inline

Definition at line 563 of file SurfaceSlidingConstrains.hpp.

566  {
567  MoFEMFunctionBegin;
568 
569  if (alpha != nullptr) {
570  aLpha = *alpha;
571  }
572 
573  boost::shared_ptr<VectorDouble> active_variables_ptr(
574  new VectorDouble(3 + 9));
575  boost::shared_ptr<VectorDouble> results_ptr(new VectorDouble(3 + 9));
576  boost::shared_ptr<MatrixDouble> jacobian_ptr(
577  new MatrixDouble(3 + 9, 3 + 9));
578 
579  feRhs.getOpPtrVector().clear();
580  feRhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
581  lagrange_multipliers_field_name, active_variables_ptr));
582  feRhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
583  material_field_name, active_variables_ptr));
584  feRhs.getOpPtrVector().push_back(new OpJacobian(
585  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
586  jacobian_ptr, crackFrontOrientation, false, aLpha));
587  feRhs.getOpPtrVector().push_back(
588  new OpAssembleRhs<3, 9>(lagrange_multipliers_field_name, results_ptr));
589  feRhs.getOpPtrVector().push_back(
590  new OpAssembleRhs<3, 9>(material_field_name, results_ptr));
591 
592  // Adding operators to calculate the left hand side
593  feLhs.getOpPtrVector().clear();
594  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
595  lagrange_multipliers_field_name, active_variables_ptr));
596  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
597  material_field_name, active_variables_ptr));
598  feLhs.getOpPtrVector().push_back(new OpJacobian(
599  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
600  jacobian_ptr, crackFrontOrientation, true, aLpha));
601  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
602  lagrange_multipliers_field_name, material_field_name, jacobian_ptr));
603  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
604  material_field_name, lagrange_multipliers_field_name, jacobian_ptr));
605  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
606  material_field_name, material_field_name, jacobian_ptr));
607 
608  MoFEMFunctionReturn(0);
609  }

◆ setOperators() [2/2]

MoFEMErrorCode SurfaceSlidingConstrains::setOperators ( int  tag,
const std::string  lagrange_multipliers_field_name,
const std::string  material_field_name,
const double *  alpha = nullptr 
)
inline

Definition at line 563 of file SurfaceSlidingConstrains.hpp.

566  {
567  MoFEMFunctionBegin;
568 
569  if (alpha != nullptr) {
570  aLpha = *alpha;
571  }
572 
573  boost::shared_ptr<VectorDouble> active_variables_ptr(
574  new VectorDouble(3 + 9));
575  boost::shared_ptr<VectorDouble> results_ptr(new VectorDouble(3 + 9));
576  boost::shared_ptr<MatrixDouble> jacobian_ptr(
577  new MatrixDouble(3 + 9, 3 + 9));
578 
579  feRhs.getOpPtrVector().clear();
580  feRhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
581  lagrange_multipliers_field_name, active_variables_ptr));
582  feRhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
583  material_field_name, active_variables_ptr));
584  feRhs.getOpPtrVector().push_back(new OpJacobian(
585  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
586  jacobian_ptr, crackFrontOrientation, false, aLpha));
587  feRhs.getOpPtrVector().push_back(
588  new OpAssembleRhs<3, 9>(lagrange_multipliers_field_name, results_ptr));
589  feRhs.getOpPtrVector().push_back(
590  new OpAssembleRhs<3, 9>(material_field_name, results_ptr));
591 
592  // Adding operators to calculate the left hand side
593  feLhs.getOpPtrVector().clear();
594  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
595  lagrange_multipliers_field_name, active_variables_ptr));
596  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
597  material_field_name, active_variables_ptr));
598  feLhs.getOpPtrVector().push_back(new OpJacobian(
599  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
600  jacobian_ptr, crackFrontOrientation, true, aLpha));
601  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
602  lagrange_multipliers_field_name, material_field_name, jacobian_ptr));
603  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
604  material_field_name, lagrange_multipliers_field_name, jacobian_ptr));
605  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
606  material_field_name, material_field_name, jacobian_ptr));
607 
608  MoFEMFunctionReturn(0);
609  }

◆ setOperatorsConstrainOnly() [1/2]

MoFEMErrorCode SurfaceSlidingConstrains::setOperatorsConstrainOnly ( int  tag,
const std::string  lagrange_multipliers_field_name,
const std::string  material_field_name 
)
inline

Definition at line 612 of file SurfaceSlidingConstrains.hpp.

614  {
615  MoFEMFunctionBegin;
616 
617  boost::shared_ptr<VectorDouble> active_variables_ptr(
618  new VectorDouble(3 + 9));
619  boost::shared_ptr<VectorDouble> results_ptr(new VectorDouble(3 + 9));
620  boost::shared_ptr<MatrixDouble> jacobian_ptr(
621  new MatrixDouble(3 + 9, 3 + 9));
622 
623  // Adding operators to calculate the left hand side
624  feLhs.getOpPtrVector().clear();
625  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
626  lagrange_multipliers_field_name, active_variables_ptr));
627  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
628  material_field_name, active_variables_ptr));
629  feLhs.getOpPtrVector().push_back(new OpJacobian(
630  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
631  jacobian_ptr, crackFrontOrientation, true, aLpha));
632  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
633  lagrange_multipliers_field_name, material_field_name, jacobian_ptr));
634 
635  MoFEMFunctionReturn(0);
636  }

◆ setOperatorsConstrainOnly() [2/2]

MoFEMErrorCode SurfaceSlidingConstrains::setOperatorsConstrainOnly ( int  tag,
const std::string  lagrange_multipliers_field_name,
const std::string  material_field_name 
)
inline

Definition at line 612 of file SurfaceSlidingConstrains.hpp.

614  {
615  MoFEMFunctionBegin;
616 
617  boost::shared_ptr<VectorDouble> active_variables_ptr(
618  new VectorDouble(3 + 9));
619  boost::shared_ptr<VectorDouble> results_ptr(new VectorDouble(3 + 9));
620  boost::shared_ptr<MatrixDouble> jacobian_ptr(
621  new MatrixDouble(3 + 9, 3 + 9));
622 
623  // Adding operators to calculate the left hand side
624  feLhs.getOpPtrVector().clear();
625  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsLambda(
626  lagrange_multipliers_field_name, active_variables_ptr));
627  feLhs.getOpPtrVector().push_back(new OpGetActiveDofsPositions<3>(
628  material_field_name, active_variables_ptr));
629  feLhs.getOpPtrVector().push_back(new OpJacobian(
630  tag, lagrange_multipliers_field_name, active_variables_ptr, results_ptr,
631  jacobian_ptr, crackFrontOrientation, true, aLpha));
632  feLhs.getOpPtrVector().push_back(new OpAssembleLhs<3, 9>(
633  lagrange_multipliers_field_name, material_field_name, jacobian_ptr));
634 
635  MoFEMFunctionReturn(0);
636  }

Member Data Documentation

◆ aLpha

double SurfaceSlidingConstrains::aLpha

Definition at line 391 of file SurfaceSlidingConstrains.hpp.

◆ crackFrontOrientation

DriverElementOrientation & SurfaceSlidingConstrains::crackFrontOrientation

Definition at line 389 of file SurfaceSlidingConstrains.hpp.

◆ feLhs

MyTriangleFE & SurfaceSlidingConstrains::feLhs

Definition at line 386 of file SurfaceSlidingConstrains.hpp.

◆ feLhsPtr

boost::shared_ptr< MyTriangleFE > SurfaceSlidingConstrains::feLhsPtr

Definition at line 382 of file SurfaceSlidingConstrains.hpp.

◆ feRhs

MyTriangleFE & SurfaceSlidingConstrains::feRhs

Definition at line 384 of file SurfaceSlidingConstrains.hpp.

◆ feRhsPtr

boost::shared_ptr< MyTriangleFE > SurfaceSlidingConstrains::feRhsPtr

Definition at line 382 of file SurfaceSlidingConstrains.hpp.

◆ mField

MoFEM::Interface & SurfaceSlidingConstrains::mField

Definition at line 353 of file SurfaceSlidingConstrains.hpp.

The documentation for this struct was generated from the following file:
SurfaceSlidingConstrains::feRhsPtr
boost::shared_ptr< MyTriangleFE > feRhsPtr
Definition: SurfaceSlidingConstrains.hpp:382
MoFEM::Types::MatrixDouble
UBlasMatrix< double > MatrixDouble
Definition: Types.hpp:77
SurfaceSlidingConstrains::feRhs
MyTriangleFE & feRhs
Definition: SurfaceSlidingConstrains.hpp:384
SurfaceSlidingConstrains::mField
MoFEM::Interface & mField
Definition: SurfaceSlidingConstrains.hpp:353
SurfaceSlidingConstrains::aLpha
double aLpha
Definition: SurfaceSlidingConstrains.hpp:391
SurfaceSlidingConstrains::getOptions
MoFEMErrorCode getOptions()
Definition: SurfaceSlidingConstrains.hpp:392
CHKERR
#define CHKERR
Inline error check.
Definition: definitions.h:548
SurfaceSlidingConstrains::feLhs
MyTriangleFE & feLhs
Definition: SurfaceSlidingConstrains.hpp:386
SurfaceSlidingConstrains::feLhsPtr
boost::shared_ptr< MyTriangleFE > feLhsPtr
Definition: SurfaceSlidingConstrains.hpp:382
SurfaceSlidingConstrains::crackFrontOrientation
DriverElementOrientation & crackFrontOrientation
Definition: SurfaceSlidingConstrains.hpp:389
MoFEM::Exceptions::ierr
static MoFEMErrorCodeGeneric< PetscErrorCode > ierr
Definition: Exceptions.hpp:76
MoFEM::ForcesAndSourcesCore::getOpPtrVector
boost::ptr_deque< UserDataOperator > & getOpPtrVector()
Use to push back operator for row operator.
Definition: ForcesAndSourcesCore.hpp:83
MoFEM::Types::VectorDouble
UBlasVector< double > VectorDouble
Definition: Types.hpp:68
MoFEMFunctionReturn
#define MoFEMFunctionReturn(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:429
MoFEMFunctionBegin
#define MoFEMFunctionBegin
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:359
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