private double GetDotProduct(Vector2d Vector)
{
Vector2d A = this;
Vector2d B = Vector;
return A.X*B.X+A.Y*B.Y;
}
/// <summary>
/// Gets an angle between 0 and 90 degrees when second vector is specified
/// </summary>
/// <param name="Vector">Second Vector</param>
/// <returns></returns>
public double GetAngle0to90(Vector2d Vector)
{
double A = GetMagnitude(this);
double B = GetMagnitude(Vector);
double ABdotProduct = GetDotProduct(Vector);
double angleRad = Math.Acos(Math.Abs(ABdotProduct/(A*B))) ;
double angleDeg = angleRad*180.0/Math.PI;
return angleDeg;
}
public double FindDistance(Vector2d A)
{
//Find Cross Product of PositionVector X Force Unit Vector
//which is the moment vector for a unit force
Vector2d B = GetUnit();
double Ax = A.X;
double Ay = A.Y;
double Az = 0;
double Bx = B.X;
double By = B.Y;
double Bz = 0;
double i =Ay*Bz -Az*By;
double j = -(Ax*Bz -Az*Bx);
double k = Ax*By -Ay*Bx;
double Mag = Math.Sqrt(i * i + j * j + k * k);
return Mag;
}
public Vector2d GetUnit()
{
double M = GetMagnitude();
Vector2d Unit = new Vector2d(X/M, Y/M);
return Unit;
}
private double GetMagnitude(Vector2d v)
{
double m = Math.Sqrt(Math.Pow(v.X,2)+Math.Pow(v.Y,2));
return m;
}
/// <summary>
/// Finds bolt or weld group ultimate strength (force)
/// using instantaneous center of rotation method
/// </summary>
/// <param name="e_x">Horizontal component of eccentricity</param>
/// <param name="AngleOfLoad">Angle of load from vertical</param>
/// <returns></returns>
protected double FindUltimateEccentricForce(double e_x , double AngleOfLoad)
{
bool iterationYieldedResult = false;
int MaxNumberOfIterations = 1999;
//iteration variables
double P=0.0;
M=0.0;
J_ic = 0.0;
Ry=0.0;
Rx=0.0;
double Pprev = 0;
double Mapfunc =0.0;
ILocationArrayElement controllingElement=null ;
double Rot = AngleOfLoad.ToRadians();
double Ec = e_x;
int N = Elements.Count();
//Initial assumption of bolt center
Center = new Point2D(0, 0);
int iterationCount = 0;
while (iterationYieldedResult == false)
{
controllingElement = FindUltimateDeformationElement(Center);
//Iterate through all bolts/welds and using force-displacement
//relationship find the force in each element
//then find the contribution of this element to overall
//Force and Moment of the group.
//Calculate M and J for all elements
IterateThroughElements(controllingElement, AngleOfLoad);
//Define a force vector due to unit force
Vector2d UnitForce = new Vector2d(Math.Sin(Rot), Math.Cos(Rot));
//note: it is assumed that the force goes through the coordinate origin
//therefore for standard weld geometries the coordinates are by adding Ec to the
//IC location
Vector2d PositionVector;
PositionVector = new Vector2d(Ec - Center.X, -Center.Y);
//Distance between IC and and Force vector
double e = UnitForce.FindDistance(PositionVector); //Internal moment arm
P = M / e; //resolving the internal forces into a resultant at the given moment arm
double Py = P * Math.Cos(Rot);
double Px = P * Math.Sin(Rot);
double Fyy;
double Fxx = Px - Rx; //Horizontal Unbalanced Force
if (Ec>=0)
{
Fyy = Py - Ry; //Vertical Unbalanced Force
}
else
{
Fyy = Py + Ry;
}
double Pp = Math.Sqrt(Fyy*Fyy+ Fxx*Fxx); //Unbalanced force resultant
bool CovergedCriteria1 = Math.Abs(Fyy) <= 0.0001 && Math.Abs(Fxx) <= 0.0001 ? true : false; //reached convergence tolerance
bool CovergedCriteria2 = (iterationCount > MaxNumberOfIterations)? true :false;
bool CovergedCriteria3 = iterationCount > 200 && Pp > Pprev ? true : false;
if (CovergedCriteria1 == true)
{
break;
}
else
{
if (CovergedCriteria2==true)
{
throw new Exception("Failed to find solution for bolt group coefficient. Maximum number of iterations in bolt group has been exceeded.");
}
else
{
if (CovergedCriteria3 == true)
{
break;
}
//throw new Exception(String.Format("Failed to find solution for bolt group coefficient.The resultant force increment increased after iteration {0}.", iterationCount ));
}
}
//if the solution hasn't converged update values for next iteration
Pprev = Pp ;
Mapfunc = J_ic / (N * M); //Mapping function
//I.C. location on x-axis from bolt group C.G.
if (e_x >= 0)
{
Center.X = Center.X - Fyy * Mapfunc;
Center.Y = Center.Y + Fxx * Mapfunc;
}
else
{
Center.X = Center.X + Fyy * Mapfunc;
Center.Y = Center.Y - Fxx * Mapfunc;
}
iterationCount++;
}
#region Final run through elelents (for debug only)
IterateThroughElements(controllingElement, AngleOfLoad);
#endregion
return P;
}
/// <summary>
/// Returns a unit vector of the resultant force in the element. Which is perpendicular to
/// the ray from center of rotation to the element.
/// </summary>
/// <param name="e">Element</param>
/// <param name="c">Center of rotation</param>
/// <returns></returns>
protected Vector2d GetElementForceUnitVector(ILocationArrayElement e, Point2D c)
{
double BX = e.Location.X - c.X;
double BY = e.Location.Y - c.Y;
//Normal vector:
// cross product definition
//AXB=(AyBz -AzBy)i -(AxBz -AzBx)j +(AxBy -AyBx)k
//assuming AZ = 1, AX =AY =0;
if (BX==0 && BY == 0)
{
return new Vector2d(0, 0);
}
else
{
Vector2d perpVector = new Vector2d(-BY, BX);
return perpVector.GetUnit();
}
}
public double GetAngleTheta(Point2D Center)
{
double Dx = Center.X - this.Location.X;
double Dy = Center.Y - this.Location.Y;
//Define vector from the IC to weld element centroid
Vector2d PositionVector = new Vector2d(Dx, Dy);
Vector2d ForceVector = new Vector2d(Dy, -Dx);
Vector2d ElementLineVector = new Vector2d(this.NodeJ.X - this.NodeI.X, this.NodeJ.Y - this.NodeI.Y);
double theta = ForceVector.GetAngle0to90(ElementLineVector);
return theta;
}