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Inherits Element.
Inherited by Q4Element, and Q9Element.
Public Member Functions | |
virtual MatrixXd | getShapefunction (double zeta1, double zeta2, double zeta3)=0 |
Calculates the Matrix containing shape functions . More... | |
virtual MatrixXd | getNMatrix (double zeta1, double zeta2)=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... | |
double | xOfZeta (double xsi, double eta) |
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 xsi, double eta) |
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 () |
Calculates the area of the element. More... | |
void | calculateAreaCentre () |
Calculates the area centre of the element. More... | |
double | getBendingStiffnessX (double Ay) |
Calculates the second moment of area about the x-axis for the element. More... | |
double | getBendingStiffnessY (double Ax) |
Calculates the second moment of area about the y-axis for the element. More... | |
double | getBendingStiffnessProduct (double Ax, double Ay) |
Calculating the product of moment of inertia. More... | |
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Element () | |
Constructor. | |
virtual MatrixXd | getNMatrix (double zeta1, double zeta2, double zeta3)=0 |
Returns a matrix of matrices with shape functions. | |
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 | |
double | xsiCoord [2][2] = { { -sqrt(1 / 3.0), sqrt(1 / 3.0) } ,{ -sqrt(1 / 3.0), sqrt(1 / 3.0) } } |
double | etaCoord [2][2] = { { sqrt(1 / 3.0), sqrt(1 / 3.0) } ,{ -sqrt(1 / 3.0), -sqrt(1 / 3.0) } } |
double | weights [2][2] = { { 1, 1 } ,{ 1, 1 } } |
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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. | |
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virtual |
Calculates the area of the element.
\( A = \frac{1}{2} \sum_{i=0}^{n-1} (x_i y_{i+1} - x_{i+1}y_i) \)
Implements Element.
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virtual |
Calculates the area centre of the element.
\( C_x = \frac{1}{6A} \sum_{i=0}^{n-1} (x_i + x_{i+1})(x_i y_{i+1} - x_{i+1}y_i) \)
\( C_y = \frac{1}{6A} \sum_{i=0}^{n-1} (y_i + y_{i+1})(x_i y_{i+1} - x_{i+1}y_i) \)
Implements Element.
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pure virtual |
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virtual |
Calculating the product of moment of inertia.
\( dx_e = Ac_x - Ac_{ex} \)
\( dy_e = Ac_y - Ac_{ey} \)
\( I_{xy} = \sum{E(I_{xy_e} + dx_e*dy_e*A_e)} \)
Implements Element.
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virtual |
Calculates the second moment of area about the x-axis for the element.
\( dy_e = A_y - Ac_{ey} \)
\( I_x = \sum{( E(I_{x_e} + dy_e^2*A_e)) } \)
Ay | Area centre of the mesh |
Implements Element.
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virtual |
Calculates the second moment of area about the y-axis for the element.
\( dx_e = A_x - Ac_{ex} \)
\( I_y = \sum{(E(I_{y_e} + dx_e^2*A_e))} \)
Ax | Area centre of the mesh |
Implements Element.
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pure virtual |
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virtual |
Calculates and returns the the distance in the x-direction between the integration point in the element and the element area centre.
\( x = | \boldsymbol{N} \boldsymbol{x}^T - ecx |\)
xsi | area coordinate with value between -1 and 1 |
eta | area coordinate with value between -1 and 1 |
Implements Element.
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virtual |
Calculates and returns the the distance in the y-direction between the integration point in the element and the element area centre.
\( y = | \boldsymbol{N} \boldsymbol{y}^T - ecy |\)
xsi | area coordinate with value between -1 and 1 |
eta | area coordinate with value between -1 and 1 |
Implements Element.