/// <summary>
/// Calculates the geometric properties for the current finite element.
/// </summary>
/// <param name="coords"></param>
/// <returns>Tuple containing the geometric properties and the elastic
/// and shear moduli of the element: *(area, qx, qy, ixx, iyy, ixy, e, g)</returns>
public (double area, double qx, double qy, double ixx, double iyy, double ixy) geometric_properties(double[,] coords)
{
// initialise geometric properties
var area = 0.0;
var qx = 0.0;
var qy = 0.0;
var ixx = 0.0;
var iyy = 0.0;
var ixy = 0.0;
//Gauss points for 6 point Gaussian integration
var gps = ShapeFunctionHelper.gauss_points(6);
double[,] B;
double[] N;
double j;
for (int i = 0; i < gps.RowCount(); i++)
{
var gp = gps.Row(i);
ShapeFunctionHelper.shape_function(coords, gp, out N, out B, out j);
area += gp[0] * j;
var x = N.Dot(coords.Row(1));
var y = N.Dot(coords.Row(0));
qx += gp[0] * x * j;
qy += gp[0] * y * j;
ixx += gp[0] * x * x * j;
iyy += gp[0] * y * y * j;
ixy += gp[0] * x * y * j;
}
return(area, qx, qy, ixx, iyy, ixy);
}
/// <summary>
/// Calculates total force resisted by the element when subjected to a
/// stress equal to the yield strength. Also returns the modulus weighted
/// area and first moments of area, and determines whether or not the
/// element is above or below the line defined by the unit vector *u* and
/// point* p*.
/// </summary>
/// <param name="mat"></param>
/// <param name="coords"></param>
/// <param name="u">Unit vector in the direction of the line</param>
/// <param name="p">Point on the line</param>
/// <returns></returns>
public (double f_el, double ea_el, double qx_el, double qy_el, bool is_above) plastic_properties(SectionMaterial mat,
double[,] coords, double[] u, double[] p)
{
//# initialise geometric properties
var e = mat.elastic_modulus;
var area = 0.0;
var qx = 0.0;
var qy = 0.0;
var force = 0.0;
var gps = ShapeFunctionHelper.gauss_points(3);
double[] N;
double j;
double[,] B;
for (int i = 0; i < gps.RowCount(); i++)
{
var gp = gps.Row(i);
ShapeFunctionHelper.shape_function(coords, gp, out N, out B, out j);
area += gp[0] * j;
var x = N.Dot(coords.Row(1));
var y = N.Dot(coords.Row(0));
qx += gp[0] * x * j;
qy += gp[0] * y * j;
force += gp[0] * j * mat.yield_strength;
}
//# calculate element centroid
var cx = qy / area;
var cy = qx / area;
//# determine if the element is above the line p + u
bool is_above = point_above_line(u, p[0], p[1], cx, cy);
return(force, area *e, qx *e, qy *e, is_above);
}