private bool IsCutElement(XContinuumElement2D element)
{
var polygon = ConvexPolygon2D.CreateUnsafe(element.Nodes);
// Look at each segment
foreach (var crackSegment in Segments)
{
var segment = new LineSegment2D(crackSegment.Start, crackSegment.End);
CartesianPoint intersectionPoint;
foreach (var edge in polygon.Edges)
{
LineSegment2D.SegmentSegmentPosition position = segment.IntersectionWith(edge, out intersectionPoint);
if (position == LineSegment2D.SegmentSegmentPosition.Intersecting)
{
// TODO: Perhaps the element should not be flagged as a Heaviside element, if the segment passes
// through 1 node only. To detect this, check if the intersection point coincides with an element
// node. If it does store it and go to the next edge. If a second intersection point (that does
// not coincide with the stored one) is found then it is a Heaviside element.
return(true);
}
else if (position == LineSegment2D.SegmentSegmentPosition.Overlapping)
{
return(true);
}
}
}
// Look at the vertices
// (if a segment is entirely inside an element, it will not be caught by checking the segment itself)
bool previousVertexOnEdge = false;
LinkedListNode <CartesianPoint> currentNode = Vertices.First.Next;
LinkedListNode <CartesianPoint> lastNode = Vertices.Last;
while (currentNode != lastNode)
{
PolygonPointPosition position = polygon.FindRelativePositionOfPoint(currentNode.Value);
if (position == PolygonPointPosition.Inside)
{
return(true);
}
else if (position == PolygonPointPosition.OnEdge || position == PolygonPointPosition.OnVertex)
{
if (previousVertexOnEdge)
{
return(true);
}
else
{
previousVertexOnEdge = true;
}
}
else
{
previousVertexOnEdge = false;
}
currentNode = currentNode.Next;
}
return(false);
}
/// <summary>
/// If a fixed enrichment area is applied, all nodes inside a circle around the tip are enriched with tip
/// functions. They can still be enriched with Heaviside functions, if they do not belong to the tip
/// element(s).
/// </summary>
/// <param name="tipNodes"></param>
/// <param name="tipElement"></param>
private void ApplyFixedEnrichmentArea(CartesianPoint crackTip, XContinuumElement2D tipElement,
HashSet <XNode> tipNodes, IEnrichmentItem2D tipEnrichments)
{
if (enrichmentRadiusOverElementSize > 0)
{
var outline = ConvexPolygon2D.CreateUnsafe(tipElement.Nodes);
double elementArea = outline.ComputeArea();
double radius = enrichmentRadiusOverElementSize * Math.Sqrt(elementArea);
var enrichmentArea = new Circle2D(crackTip, radius);
foreach (var element in Mesh.FindElementsInsideCircle(enrichmentArea, tipElement))
{
bool completelyInside = true;
foreach (var node in element.Nodes)
{
CirclePointPosition position = enrichmentArea.FindRelativePositionOfPoint(node);
if ((position == CirclePointPosition.Inside) || (position == CirclePointPosition.On))
{
tipNodes.Add(node);
}
else
{
completelyInside = false;
}
}
if (completelyInside)
{
element.EnrichmentItems.Add(tipEnrichments);
}
}
}
}
public IReadOnlyList <GaussPoint> GenerateIntegrationPoints(XContinuumElement2D element)
{
SortedSet <CartesianPoint> cartesianDelaunyPoints = crack.FindTriangleVertices(element);
IReadOnlyList <NaturalPoint> naturalDelaunyPoints =
FindNaturalPointsForTriangulation(element, cartesianDelaunyPoints);
IReadOnlyList <Triangle2D <NaturalPoint> > subtriangles;
if (double.IsPositiveInfinity(triangleOverElementArea))
{
subtriangles = triangulator.CreateMesh(naturalDelaunyPoints);
}
else
{
double elementArea = (ConvexPolygon2D.CreateUnsafe(element.Nodes)).ComputeArea();
subtriangles = triangulator.CreateMesh(naturalDelaunyPoints, triangleOverElementArea * elementArea);
}
var integrationPoints = new List <GaussPoint>();
foreach (Triangle2D <NaturalPoint> triangle in subtriangles)
{
integrationPoints.AddRange(GenerateIntegrationPointsOfTriangle(triangle));
}
return(integrationPoints);
}
public SortedSet <CartesianPoint> FindTriangleVertices(XContinuumElement2D element)
{
var polygon = ConvexPolygon2D.CreateUnsafe(element.Nodes);
var triangleVertices = new SortedSet <CartesianPoint>(element.Nodes, pointComparer);
int nodesCount = element.Nodes.Count;
foreach (var vertex in Vertices)
{
PolygonPointPosition position = polygon.FindRelativePositionOfPoint(vertex);
if (position == PolygonPointPosition.Inside || position == PolygonPointPosition.OnEdge ||
position == PolygonPointPosition.OnVertex)
{
triangleVertices.Add(vertex);
}
}
foreach (var crackSegment in Segments)
{
var segment = new LineSegment2D(crackSegment.Start, crackSegment.End);
IReadOnlyList <CartesianPoint> intersections = segment.IntersectionWith(polygon);
foreach (var point in intersections)
{
triangleVertices.Add(point);
}
}
return(triangleVertices);
}
public List <XContinuumElement2D> FindElementsThatContains(IEnumerable <XContinuumElement2D> elements,
CartesianPoint point)
{
var result = new List <XContinuumElement2D>();
foreach (var element in elements)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes);
PolygonPointPosition position = outline.FindRelativePositionOfPoint(point);
if (position == PolygonPointPosition.Inside)
{
result.Add(element);
break;
}
else if ((position == PolygonPointPosition.OnEdge) || (position == PolygonPointPosition.OnVertex))
{
result.Add(element);
}
}
if (result.Count == 0)
{
throw new KeyNotFoundException("No element containing the point " + point + "was found");
}
return(result);
}
public CrackElementPosition FindRelativePositionOf(XContinuumElement2D element)
{
CartesianPoint crackTip = lsm.GetCrackTip(CrackTipPosition.Single);
double minBodyLevelSet = double.MaxValue;
double maxBodyLevelSet = double.MinValue;
double minTipLevelSet = double.MaxValue;
double maxTipLevelSet = double.MinValue;
foreach (XNode node in element.Nodes)
{
double bodyLevelSet = lsm.LevelSetsBody[node];
double tipLevelSet = lsm.LevelSetsTip[node];
if (bodyLevelSet < minBodyLevelSet)
{
minBodyLevelSet = bodyLevelSet;
}
if (bodyLevelSet > maxBodyLevelSet)
{
maxBodyLevelSet = bodyLevelSet;
}
if (tipLevelSet < minTipLevelSet)
{
minTipLevelSet = tipLevelSet;
}
if (tipLevelSet > maxTipLevelSet)
{
maxTipLevelSet = tipLevelSet;
}
}
//Warning: this might actually be worse than Stolarska's criterion. At least that one enriched the dubious
//intersected elements with tip enrichments. This one just ignores them.
if (minBodyLevelSet * maxBodyLevelSet <= 0.0)
{
if (minTipLevelSet * maxTipLevelSet <= 0)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes);
if (outline.IsPointInsidePolygon(crackTip))
{
return(CrackElementPosition.ContainsTip);
}
}
else if (maxTipLevelSet < 0)
{
return(CrackElementPosition.Intersected);
}
}
return(CrackElementPosition.Irrelevant);
}
public IReadOnlyList <TElement> FindElementsIntersectedByCircle(Circle2D circle, TElement startingElement = null)
{
var intersectedElements = new List <TElement>();
foreach (TElement element in Elements)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes.ToCartesianPoints());
CirclePolygonPosition relativePosition = outline.FindRelativePositionOfCircle(circle);
if (relativePosition == CirclePolygonPosition.Intersecting)
{
intersectedElements.Add(element);
}
}
return(intersectedElements);
}
// TODO: handle cases where more the point lies on an element edge or node.
public IReadOnlyList <TElement> FindElementsContainingPoint(CartesianPoint point, TElement startingElement = null)
{
var containingElements = new List <TElement>();
foreach (TElement element in Elements) // O(elementsCount)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes.ToCartesianPoints());
PolygonPointPosition pos = outline.FindRelativePositionOfPoint(point);
if ((pos == PolygonPointPosition.Inside) || (pos == PolygonPointPosition.OnEdge) ||
(pos == PolygonPointPosition.OnVertex))
{
containingElements.Add(element);
}
}
return(containingElements);
}
// TODO: This method should directly return the elements and take care of cases near the domain boundaries (see Ahmed)
// TODO: The J-integral radius should not exceed the last crack segment's length
public double ComputeRadiusOfJintegralOuterContour(TipCoordinateSystem tipSystem,
IReadOnlyList <XContinuumElement2D> tipElements)
{
double maxTipElementArea = -1.0;
foreach (var element in tipElements)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes.Select(node => (CartesianPoint)node).ToArray());
double elementArea = outline.ComputeArea();
if (elementArea > maxTipElementArea)
{
maxTipElementArea = elementArea;
}
}
return(magnificationOfJintegralRadius * Math.Sqrt(maxTipElementArea));
}
//TODO: replace this with the Faster~() version
public CrackElementPosition FindRelativePositionOf(XContinuumElement2D element)
{
CartesianPoint crackTip = lsm.GetCrackTip(CrackTipPosition.Single);
double minBodyLevelSet = double.MaxValue;
double maxBodyLevelSet = double.MinValue;
double minTipLevelSet = double.MaxValue;
double maxTipLevelSet = double.MinValue;
foreach (XNode node in element.Nodes)
{
double bodyLevelSet = lsm.LevelSetsBody[node];
double tipLevelSet = lsm.LevelSetsTip[node];
if (bodyLevelSet < minBodyLevelSet)
{
minBodyLevelSet = bodyLevelSet;
}
if (bodyLevelSet > maxBodyLevelSet)
{
maxBodyLevelSet = bodyLevelSet;
}
if (tipLevelSet < minTipLevelSet)
{
minTipLevelSet = tipLevelSet;
}
if (tipLevelSet > maxTipLevelSet)
{
maxTipLevelSet = tipLevelSet;
}
}
// Warning: This criterion might give false positives for tip elements (see Serafeim's thesis for details)
if (minBodyLevelSet * maxBodyLevelSet <= 0.0)
{
var outline = ConvexPolygon2D.CreateUnsafe(element.Nodes);
if (outline.IsPointInsidePolygon(crackTip))
{
return(CrackElementPosition.ContainsTip);
}
else if (maxTipLevelSet < 0)
{
return(CrackElementPosition.Intersected);
}
}
return(CrackElementPosition.Irrelevant);
}
private bool IsTipElement(XContinuumElement2D element, CrackTipPosition tipPosition)
{
CartesianPoint crackTip, adjacentVertex;
if (tipPosition == CrackTipPosition.Start)
{
crackTip = Vertices.First.Value;
adjacentVertex = Vertices.First.Next.Value;
}
else if (tipPosition == CrackTipPosition.End)
{
crackTip = Vertices.Last.Value;
adjacentVertex = Vertices.Last.Previous.Value;
}
else
{
throw new ArgumentException("Tip position can be either start or end");
}
var polygon = ConvexPolygon2D.CreateUnsafe(element.Nodes);
PolygonPointPosition relativeTipPos = polygon.FindRelativePositionOfPoint(crackTip);
if (relativeTipPos == PolygonPointPosition.Inside || relativeTipPos == PolygonPointPosition.OnEdge ||
relativeTipPos == PolygonPointPosition.OnVertex)
{
PolygonPointPosition previousVertexPos = polygon.FindRelativePositionOfPoint(adjacentVertex);
if (previousVertexPos == PolygonPointPosition.Inside)
{
throw new NotImplementedException("Problem with blending elements, if the tip element is also " +
"enriched with Heaviside. What happens after the crack tip? Based on the LSM, the signed " +
"distance of the blending element after the crack tip should have a positive and negative " +
"region, however that element is not split by the crack and thus should not have " +
"discontinuity in the displacement field");
//return ElementEnrichmentType.Both;
}
return(true);
}
return(false);
}
/// <summary>
///
/// </summary>
/// <param name="allVertices"></param>
/// <param name="boundaryVertices">If the all vertices are boundary, then this list needs to start and end with the same
/// vertex.</param>
public PolygonalRegion(IReadOnlyList <CartesianPoint> allVertices, HashSet <LineSegment2D> boundaries)
{
this.polygon = ConvexPolygon2D.CreateUnsafe(allVertices);
this.boundaries = boundaries;
}
public Polygonal2DBoundary(IReadOnlyList <CartesianPoint> vertices)
{
polygon = ConvexPolygon2D.CreateUnsafe(vertices);
}
private ElementEnrichmentType CharacterizeElementEnrichment(XContinuumElement2D element)
{
var polygon = ConvexPolygon2D.CreateUnsafe(element.Nodes);
int tipIndex = Vertices.Count - 1;
// Check tip element
PolygonPointPosition tipPosition = polygon.FindRelativePositionOfPoint(Vertices[tipIndex]);
if (tipPosition == PolygonPointPosition.Inside || tipPosition == PolygonPointPosition.OnEdge ||
tipPosition == PolygonPointPosition.OnVertex)
{
PolygonPointPosition previousVertexPos = polygon.FindRelativePositionOfPoint(Vertices[tipIndex - 1]);
if (previousVertexPos == PolygonPointPosition.Inside)
{
// Problem with blending elements, if the tip element is also enriched with Heaviside. What happens
// after the crack tip? Based on the LSM, the signed distance of the blending element after the
// crack tip should have a positive and negative region, however that element is not split by the
// crack and thus should not have discontinuity in the displacement field.
var builder = new StringBuilder();
builder.Append("Crack tip ");
builder.Append(Vertices[Vertices.Count - 1].ToString());
builder.Append(" and kink point ");
builder.Append(Vertices[Vertices.Count - 2].ToString());
builder.Append(" inside the same element with nodes: ");
foreach (var node in element.Nodes)
{
builder.Append(node.ToString());
builder.Append(' ');
}
throw new ArgumentException(builder.ToString());
//return ElementEnrichmentType.Both;
}
else
{
return(ElementEnrichmentType.Tip);
}
}
// Look at the other vertices
// (if a segment is inside an element, it will not be caught by checking the segment itself)
bool previousVertexOnEdge = false;
for (int v = 0; v < tipIndex; ++v)
{
PolygonPointPosition position = polygon.FindRelativePositionOfPoint(Vertices[v]);
if (position == PolygonPointPosition.Inside)
{
return(ElementEnrichmentType.Heaviside);
}
else if (position == PolygonPointPosition.OnEdge || position == PolygonPointPosition.OnVertex)
{
if (previousVertexOnEdge)
{
return(ElementEnrichmentType.Heaviside);
}
else
{
previousVertexOnEdge = true;
}
}
else
{
previousVertexOnEdge = false;
}
}
// Look at each segment
foreach (var crackSegment in Segments)
{
var segment = new LineSegment2D(crackSegment.Start, crackSegment.End);
CartesianPoint intersectionPoint;
foreach (var edge in polygon.Edges)
{
LineSegment2D.SegmentSegmentPosition position = segment.IntersectionWith(edge, out intersectionPoint);
if (position == LineSegment2D.SegmentSegmentPosition.Intersecting)
{
// TODO: Perhaps the element should not be flagged as a Heaviside element, if the segment passes
// through 1 node only. To detect this, check if the intersection point coincides with an element
// node. If it does store it and go to the next edge. If a second intersection point (that does
// not coincide with the stored one) is found then it is a Heaviside element.
return(ElementEnrichmentType.Heaviside);
}
else if (position == LineSegment2D.SegmentSegmentPosition.Overlapping)
{
return(ElementEnrichmentType.Heaviside);
}
}
}
// Then it must be a standard element
return(ElementEnrichmentType.Standard);
}