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Contains element data and relevant functions. More...
#include <Element.h>
Inherited by QuadraticElement, and TriangularElement.
Public Member Functions | |
Element () | |
Constructor. | |
virtual MatrixXd | getShapefunction (double zeta1, double zeta2, double zeta3)=0 |
Calculates the Matrix containing shape functions . More... | |
virtual MatrixXd | getNMatrix (double zeta1, double zeta2, double zeta3)=0 |
Returns a matrix of matrices with shape functions. | |
virtual void | calculateConstants ()=0 |
Calculates the constant vectors and matrices for the element; i.e. G, xCoordinates, and yCoordinates. | |
virtual void | calculateStiffnessMatrix ()=0 |
Calculates the element stiffness matrix K. | |
virtual void | calculateElementLoadTorsion ()=0 |
Calculates the initial load vector for torsion. | |
virtual void | calculateElementLoadShearX ()=0 |
Calculates the initial load vector for shear along X. | |
virtual void | calculateElementLoadShearY ()=0 |
Calculates the initial load vector for shear along Y. | |
virtual void | computeTau ()=0 |
Calculates shear stresses at nodes using initialStrain and elementsDisplacement. More... | |
virtual double | xOfZeta (double zeta1, double zeta2)=0 |
virtual double | yOfZeta (double zeta1, double zeta2)=0 |
virtual void | calculateArea ()=0 |
virtual void | calculateAreaCentre ()=0 |
virtual double | getBendingStiffnessX (double)=0 |
virtual double | getBendingStiffnessY (double)=0 |
virtual double | getBendingStiffnessProduct (double, double)=0 |
MatrixXd | getNxMatrix () |
Returns the shapefunction as a function of x and y. More... | |
MatrixXd | getNyMatrix () |
Returns the second row of the B matrix, i.e. N differentiated with respect to y. | |
std::vector< int > | getIEG () |
Creates a vector with node numbers that makes up the element. More... | |
void | setElementValue (MatrixXd &system, MatrixXd &local) |
Uses getIEG() to assign system values to corresponding local parameters. | |
Public Attributes | |
std::vector< int > | nodes |
Vector containing the nodes of the element. | |
double | area |
Elements total area. | |
Material | material |
Element material with Youngs modulus, poisson's ratio and shear modulus. | |
int | elementType |
Defines what type of element this element is (value '2' for T3 and value '9' for T6) | |
double | Iex |
Elements second area moment about x-axis. | |
double | Iey |
Elements second area moment about y-axis. | |
double | Iexy |
Elements second area moment product. | |
double | ecx |
Elements area centre in x-direction. | |
double | ecy |
Elements area centre in y-direction. | |
double | dx |
Distance in x-direction between mesh- and node area centre. | |
double | dy |
Distance in y-direction between mesh- and node area centre. | |
std::vector< double > | xNodePositions |
Elements nodepositions in x-direction. | |
std::vector< double > | yNodePositions |
Elements nodepositions in y-direction. | |
std::vector< double > | xNodePositionPrincipal |
Nodal x-coordinates in principal axes. | |
std::vector< double > | yNodePositionPrincipal |
Nodal y-coordinates in principal axes. | |
MatrixXd | B |
2x3 Matrix containing differentials of shapefunction with respect to x and y respectively | |
MatrixXd | G |
Matrix with shearmodule used to determine initial element loads in tortional analysis. | |
MatrixXd | XoverY |
6x1 matrix with x1, x2, x3, y1, y2, and y3 of the element. | |
MatrixXd | xCoordinates |
1x3 matrix with x-coordinates. | |
MatrixXd | yCoordinates |
1X3 matrix with y-coordinates. | |
MatrixXd | elementStiffness |
Matrix used to temporarily hold element stiffnes coefficients. | |
MatrixXd | elementLoad |
Matrix used to temporarily hold element load coefficients. | |
MatrixXd | elementDisplacement |
Matrix used to temporarily hold element displacement values. | |
MatrixXd | initialStrain |
Matrix used to temporarily hold element initial strain coefficients. | |
std::vector< MatrixXd > | tau |
Vector temporarily storing shear stresses during calculation. | |
Contains element data and relevant functions.
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pure virtual |
Calculates shear stresses at nodes using initialStrain and elementsDisplacement.
\( \tau = Bv + \epsilon_0 \)
Implemented in T6Element, T3Element, Q4Element, Q9Element, and QuadraticElement.
std::vector< int > Element::getIEG | ( | ) |
Creates a vector with node numbers that makes up the element.
MatrixXd Element::getNxMatrix | ( | ) |
Returns the shapefunction as a function of x and y.
\( \zeta_1 = y_{23}x + x_{32}y + (x_2y_3 - x_3y_2) \)
\( \zeta_1 = y_{31}x + x_{13}y + (x_3y_1 - x_1y_3) \)
\( \zeta_1 = y_{12}x + x_{21}y + (x_1y_2 - x_2y_1) \)
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pure virtual |
Calculates the Matrix containing shape functions
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Implemented in T3Element, T6Element, TriangularElement, QuadraticElement, Q4Element, and Q9Element.