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Class for implementation of T6 elements. More...
#include <T6Element.h>
Inherits TriangularElement.
Public Member Functions | |
T6Element () | |
Constructor. | |
void | calculateElementLoadTorsion () |
Calculates the initial load vector for torsion. | |
void | calculateElementLoadShearX () |
Calculates the initial load vector for shear along X. | |
void | calculateElementLoadShearY () |
Calculates the initial load vector for shear along Y. | |
void | calculateConstants () |
Calculates the constant vectors and matrices for the element; i.e. G, xCoordinates, and yCoordinates. | |
MatrixXd | getShapefunction (double zeta1, double zeta2, double zeta3) |
Calculates shapefunctions. More... | |
MatrixXd | getNMatrix (double zeta1, double zeta2, double zeta3) |
Returns a matrix of matrices with shape functions. | |
void | calculateStiffnessMatrix () |
Calculates element stiffness matrix K. More... | |
void | calculateBMatrix (double zeta1, double zeta2, double zeta3) |
Calculates the B matrix for T3 elements. More... | |
void | checkBMatrix () |
A method used for verification of the B matrix calculations. | |
void | computeTau () |
Calculates shear stresses at nodes using initialStrain and elementsDisplacement. More... | |
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double | xOfZeta (double zeta1, double zeta2) |
Calculates and returns the the distance in the x-direction between the integration point in the element and the element area centre. More... | |
double | yOfZeta (double zeta1, double zeta2) |
Calculates and returns the the distance in the y-direction between the integration point in the element and the element area centre. More... | |
void | calculateArea () |
void | calculateAreaCentre () |
Calculates the area centre of the element. More... | |
double | getBendingStiffnessX (double) |
Calculates the second moment of area about the x-axis for the element. More... | |
double | getBendingStiffnessY (double) |
Calculates the second moment of area about the y-axis for the element. More... | |
double | getBendingStiffnessProduct (double, double) |
Calculating the product of moment of inertia. More... | |
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Element () | |
Constructor. | |
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. | |
Additional Inherited Members | |
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const double | zeta [3][3] = { { 0.5, 0.5, 0.0 },{ 0.0, 0.5, 0.5 },{ 0.5, 0.0, 0.5 } } |
Zeta values for integration ponts. | |
const double | weight [3] = { 1.0 / 3, 1.0 / 3, 1.0 / 3 } |
Weighting of each integration point. | |
double | xl1 |
Distance in x-direction from node to element area center. | |
double | xl2 |
Distance in x-direction from node to element area center. | |
double | xl3 |
Distance in x-direction from node to element area center. | |
double | yl1 |
Distance in y-direction from node to element area center. | |
double | yl2 |
Distance in y-direction from node to element area center. | |
double | yl3 |
Distance in y-direction from node to element area center. | |
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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. | |
Class for implementation of T6 elements.
void T6Element::calculateBMatrix | ( | double | zeta1, |
double | zeta2, | ||
double | zeta3 | ||
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Calculates the B matrix for T3 elements.
\( \begin{equation} \textbf{B} = = \frac{1}{2A} \begin{bmatrix} y_{23}&y_{31}& y_{12}\\ x_{32}& x_{13} & x_{21} \\ \end{bmatrix} \begin{bmatrix} (2\zeta_1 -1) & 0 & 0 & 4 \zeta_2 & 0 & 4 \zeta_3 \\ 0 & (2\zeta_2 -1)& 0 & 4 \zeta_1 & 4\zeta_3 & 0 \\ 0 & 0 & (2\zeta_3-1) & 0 & 4\zeta_2 & 4\zeta_1 \\ \end{bmatrix} \end{equation} \)
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Calculates element stiffness matrix K.
\( \begin{equation} K = \int_{area} B^T G B dA \end{equation} \)
Implements TriangularElement.
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Calculates shear stresses at nodes using initialStrain and elementsDisplacement.
\( \tau = Bv + \epsilon_0 \)
Implements Element.
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Calculates shapefunctions.
\(\begin{equation} \textbf{N} = \begin{bmatrix} \zeta_1 (2\zeta_1 -1) & \zeta_2(2\zeta_2-1) & \zeta_3(2\zeta_3-1) & 4\zeta_1 \zeta_2 & 4\zeta_2\zeta_3 & 4 \zeta_1 \zeta_3 \end{bmatrix} \end{equation} \)
Implements TriangularElement.